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"The Simplest Path is the Greatest"

ไธญๆ–‡ | English

  • This open-source project aims to train a super-small language model MiniMind with only 3 RMB cost and 2 hours, starting completely from scratch.
  • The MiniMind series is extremely lightweight, with the smallest version being $\frac{1}{7000}$ the size of GPT-3, making it possible to train quickly on even the most ordinary personal GPUs.
  • The project also open-sources the minimalist structure of the large model, including extensions for shared mixed experts (MoE), dataset cleaning, pretraining, supervised fine-tuning (SFT), LoRA fine-tuning, direct preference optimization (DPO) algorithms, reinforcement learning from AI feedback (RLAIF: PPO/GRPO/SPO), and model distillation algorithms, along with the full code of the entire process.
  • MiniMind also expands into vision multimodal VLM: MiniMind-V.
  • All core algorithm code is reconstructed from scratch using native PyTorch! It does not rely on abstract interfaces provided by third-party libraries.
  • This is not only a full-stage open-source reproduction of a large language model but also a tutorial for beginners in LLM.
  • We hope this project will serve as an inspiring example for everyone, helping to enjoy the fun of creation and promoting the progress of the wider AI community!

To avoid misunderstanding, the "2 hours" test is based on NVIDIA 3090 hardware (single GPU), and the "3 RMB" refers to the GPU server rental cost. Details of the specifications can be found below.


๐Ÿ“Œ Introduction

The emergence of Large Language Models (LLMs) has sparked unprecedented global attention to AI. Whether it's ChatGPT, DeepSeek, or Qwen, they all demonstrate stunning performance that is awe-inspiring. However, with their massive scale of tens of billions of parameters, they are not only difficult to train on personal devices but nearly impossible to deploy. Opening the "black box" of large models to explore their internal mechanisms is truly thrilling! Unfortunately, 99% of exploration can only stop at using techniques like LoRA to perform minor fine-tuning on existing large models to learn new instructions or tasks. This is like teaching Newton how to use a 21st-century smartphoneโ€”while interesting, it completely deviates from the original intent of understanding the essence of physics. Meanwhile, third-party large model frameworks and toolkits, such as transformers+trl, expose only highly abstract interfaces. With just 10 lines of code, you can complete the entire workflow of "loading model + loading dataset + inference + reinforcement learning." While such efficient packaging is convenient, it also acts like a high-speed spacecraft, isolating developers from underlying implementations and hindering deep exploration of LLM core code. Yet, "building a plane with Lego is far more exciting than flying in first class!" What's worse, the internet is flooded with expensive courses and marketing accounts selling AI tutorials with countless flaws and superficial understanding. For this reason, this project's original intention is to lower the barrier to entry for LLM learning, allowing everyone to start by understanding every line of code, to personally train an extremely small language model from scratch. Yes, from training from scratch, not just inference! With less than 3 RMB in server costs, you can personally experience the entire process of building a language model from 0 to 1. Let's enjoy the fun of creation together!

Note

(As of 2025-10) The MiniMind series has completed pretraining of multiple model variants, with the smallest being only 25.8M (0.02B), capable of fluent conversation!

Models List
Model (Size) Inference Memory (Approx) Release
MiniMind2-small (26M) 0.5 GB 2025.04.26
MiniMind2-MoE (145M) 1.0 GB 2025.04.26
MiniMind2 (104M) 1.0 GB 2025.04.26
minimind-v1-small (26M) 0.5 GB 2024.08.28
minimind-v1-moe (4ร—26M) 1.0 GB 2024.09.17
minimind-v1 (108M) 1.0 GB 2024.09.01

Project Includes

  • Complete code for MiniMind-LLM structure (Dense + MoE models).
  • Detailed training code for Tokenizer.
  • Complete training code for Pretrain, SFT, LoRA, RLHF-DPO, RLAIF (PPO/GRPO/SPO), and model distillation.
  • Collected, distilled, organized and cleaned high-quality datasets for all stages, all open-sourced.
  • Implemented from scratch: pretraining, instruction fine-tuning, LoRA, DPO/PPO/GRPO/SPO reinforcement learning, and white-box model distillation. Core algorithms barely depend on third-party framework encapsulation, all open-sourced.
  • Compatible with mainstream third-party frameworks like transformers, trl, peft.
  • Training supports single GPU, multiple GPUs on a single machine (DDP, DeepSpeed), supports wandb/swanlab visualization of training process. Supports dynamic training start/stop.
  • Model testing on third-party evaluation leaderboards (C-Eval, C-MMLU, OpenBookQA, etc.), supports YaRN algorithm for RoPE long-text extrapolation.
  • Implements an extremely simple OpenAI API-compliant server, convenient for integration with third-party ChatUI (FastGPT, Open-WebUI, etc.).
  • Implements the simplest chat WebUI frontend based on streamlit.
  • Fully compatible with popular community inference engines llama.cpp, vllm, ollama or training framework Llama-Factory.
  • Reproduced (distilled/RL) DeepSeek-R1 reasoning model as MiniMind-Reason model, with data + models fully open-sourced!

We hope this open-source project can help LLM beginners get started quickly!

๐Ÿ‘‰Update Log

2025-10-24
  • ๐Ÿ”ฅ Added RLAIF training algorithms: PPO, GRPO, SPO (native implementation from scratch)
  • Added checkpoint resume training: supports automatic training recovery, cross-GPU recovery, wandb continuity
  • Added RLAIF dataset: rlaif-mini.jsonl (randomly sampled 10,000 entries from SFT data); simplified DPO dataset with Chinese data
  • Added YaRN algorithm: supports RoPE long-text extrapolation, improving long sequence handling capability
  • Adaptive Thinking: Reason model can optionally enable thinking chain
  • chat_template fully supports Tool Calling and Reasoning tags (<tool_call>, <think>, etc.)
  • Added complete RLAIF chapter, training curve comparison, algorithm principle explanations
  • SwanLab replaces WandB (friendly for domestic access, fully compatible API)
  • Code standardization & fixed some known bugs
2025-04-26
  • Important update
  • For compatibility needs, you can visit ๐Ÿ”—old repository content๐Ÿ”—.
  • MiniMind model parameters completely renamed, aligned with Transformers library models (unified naming).
  • generate method refactored, inheriting from GenerationMixin class.
  • ๐Ÿ”ฅ Supports popular third-party ecosystems like llama.cpp, vllm, ollama.
  • Standardized code and directory structure.
  • Modified vocabulary <s></s>-><|im_start|><|im_end|>
To be compatible with third-party inference frameworks llama.cpp and vllm, this update requires some observable costs.
This update no longer supports "directly" loading old models before 25-04-26 for inference.
Due to differences in Llama's positional encoding compared to minimind, there are differences in QK values after mapping Llama models.
MiniMind2 series old models have been recovered through weight mapping and (fine-tuning training) QKVO linear layer calibration.
After this update, maintenance of the entire minimind-v1 series will be abandoned and removed from the repository.
2025-02-09
  • Major update since release, Release MiniMind2 Series.
  • Code almost completely refactored, using cleaner and more unified structure. For compatibility with old code, you can visit ๐Ÿ”—old repository content๐Ÿ”—.
  • Eliminated data preprocessing steps. Unified dataset format, switched to jsonl format to avoid dataset download confusion.
  • MiniMind2 series shows significant improvement compared to MiniMind-V1.
  • Minor improvements: {more standard kv-cache writing, MoE load balancing loss considered, etc.}
  • Provides training solutions for model migration to private datasets (medical models, self-awareness examples).
  • Streamlined pretraining dataset and significantly improved pretraining data quality, greatly reducing time for quick personal training, single 3090 GPU can reproduce in 2 hours!
  • Updates: LoRA fine-tuning separated from peft packaging, implemented from scratch; DPO algorithm implemented from scratch using native PyTorch; white-box model distillation native implementation.
  • MiniMind2-DeepSeek-R1 series distilled models born!
  • MiniMind2 now has some English ability!
  • Updated MiniMind2 and third-party model performance results based on more large model leaderboard tests.
More...

2024-10-05

  • Extended MiniMind with multimodal capabilities---Vision
  • Check out the twin project minimind-v for details!

2024-09-27

  • 09-27 updated the preprocessing method for the pretrain dataset, abandoned preprocessing into .bin format for training to ensure text integrity (slightly sacrificing training speed).
  • Current pretrain preprocessing file is named: pretrain_data.csv.
  • Removed some redundant code.

2024-09-17

  • Updated minimind-v1-moe model
  • To avoid ambiguity, no longer using mistral_tokenizer for tokenization, completely using custom minimind_tokenizer as the tokenizer.

2024-09-01

  • Updated minimind-v1 (108M) model, using minimind_tokenizer, 3 pretraining rounds + 10 SFT rounds, more thorough training, stronger performance.
  • Project has been deployed to ModelScope creation space, you can experience it on this website:
  • ๐Ÿ”—ModelScope Online Experience๐Ÿ”—

2024-08-27

  • Project first open-sourced

๐Ÿ“Œ Quick Start

Share my hardware and software configuration (for reference only)
  • CPU: Intel(R) Core(TM) i9-10980XE CPU @ 3.00GHz
  • RAM: 128 GB
  • GPU: NVIDIA GeForce RTX 3090(24GB) * 8
  • Ubuntu==20.04
  • CUDA==12.2
  • Python==3.10.16
  • requirements.txt

Step 0

git clone https://github.com/jingyaogong/minimind.git

โ…  Testing Existing Model Performance

1. Environment Setup

pip install -r requirements.txt -i https://mirrors.aliyun.com/pypi/simple

2. Download Model

Go to the project root directory

git clone https://huggingface.co/jingyaogong/MiniMind2 # or https://www.modelscope.cn/models/gongjy/MiniMind2

(Optional) Command Line Q&A

# Use transformers format model
python eval_llm.py --load_from ./MiniMind2

(Optional) Launch WebUI

# May require `python>=3.10`, install with `pip install streamlit`
# cd scripts
streamlit run web_demo.py

(Optional) Third-party Inference Frameworks

# ollama
ollama run jingyaogong/minimind2
# vllm
vllm serve ./MiniMind2/ --served-model-name "minimind"

โ…ก Train from Scratch Yourself

1. Environment Setup

pip install -r requirements.txt -i https://mirrors.aliyun.com/pypi/simple
Note: Test Torch CUDA availability in advance
import torch
print(torch.cuda.is_available())

If not available, please download and install the whl file from torch_stable. Reference link

2. Download Data

Download the required data files from the dataset download link provided below (create the ./dataset directory) and place them in ./dataset

Note: Dataset Notes

By default, it is recommended to download pretrain_hq.jsonl + sft_mini_512.jsonl for the fastest reproduction of the Zero chat model.

You can freely choose data files. The section below provides multiple combination schemes that can be appropriately combined based on your training needs and GPU resources.

3. Start Training

Directory is located in trainer

๐Ÿ’ก Checkpoint Resume Training

All training scripts automatically save checkpoints. Simply add --from_resume 1 parameter to automatically detect, load & resume training:

python train_pretrain.py --from_resume 1
python train_full_sft.py --from_resume 1
...

Checkpoint Resume Mechanism:

  • Training process automatically saves complete checkpoints in ./checkpoints/ directory (model, optimizer, training progress, etc.)
  • Checkpoint file naming: <weight_name>_<dimension>_resume.pth (e.g., full_sft_512_resume.pth)
  • Supports cross-GPU recovery (automatically adjusts step)
  • Supports wandb training log continuity (automatically resumes the same run)

Suitable for long training sessions or unstable environments, no need to worry about progress loss from interruptions

3.1 Pretraining (Learning Knowledge)

python train_pretrain.py

Execute pretraining to get pretrain_*.pth as the output weights for pretraining (where * is the model's dimension, default is 512)

3.2 Supervised Fine-tuning (Learning Conversation Style)

python train_full_sft.py

Execute supervised fine-tuning to get full_sft_*.pth as the output weights for instruction fine-tuning (where full means full-parameter fine-tuning)

Note: Training Notes

By default, all training processes save parameters to the file ./out/***.pth every 100 steps (each save overwrites the old weights).

For simplicity, only the two-stage training process is described here. For other training (LoRA, distillation, reinforcement learning, inference fine-tuning, etc.), refer to the detailed description in the Experiment section below.


4. Test Your Trained Model

Ensure the model *.pth files to be tested are in the ./out/ directory. You can also directly download and use the *.pth files I trained from here.

python eval_llm.py --weight full_sft # or pretrain/dpo/ppo/grpo...
Note: Testing Notes

The --weight parameter specifies the weight name prefix. Options: pretrain, full_sft, dpo, reason, ppo_actor, grpo, spo, etc.

Other common parameters:

  • --load_from: Model loading path (model=native torch weights, other paths=transformers format)
  • --save_dir: Model weight directory (default out)
  • --lora_weight: LoRA weight name (None means not used)
  • --historys: Number of historical dialogue rounds to carry (must be even, 0 means no history)
  • --max_new_tokens: Maximum generation length (default 8192)
  • --temperature: Generation temperature (default 0.85)
  • --top_p: Nucleus sampling threshold (default 0.85)

For usage details, refer directly to the eval_llm.py code.


Tip

All training scripts are native PyTorch framework, supporting multi-GPU acceleration. Assume your device has N (N > 1) GPUs:

Single machine N GPU training startup (DDP, supports multi-machine multi-GPU cluster)

torchrun --nproc_per_node N train_xxx.py
Note: Other Notes Single machine N GPU training (DeepSpeed)
deepspeed --master_port 29500 --num_gpus=N train_xxx.py

You can optionally enable wandb to record the training process (requires direct internet connection)

# Requires login: wandb login
torchrun --nproc_per_node N train_xxx.py --use_wandb
# and
python train_xxx.py --use_wandb

By adding the --use_wandb parameter, you can record the training process. After training is complete, you can view the training process on the wandb website. By modifying the wandb_project and wandb_run_name parameters, you can specify the project name and run name.

[Note]: After June 2025, the domestic network environment cannot directly connect to WandB. The MiniMind project by default switches to using SwanLab as the training visualization tool (fully compatible with WandB API), that is, just change import wandb to import swanlab as wandb, no other changes are needed.

๐Ÿ“Œ Data Introduction

โ…  Tokenizer

Tokenizer maps words from natural language to numbers like 0, 1, 36 through a "dictionary," which can be understood as numbers representing the page number of the word in the "dictionary." You can choose to construct your own vocabulary table to train a "dictionary." The code can be found in ./scripts/train_tokenizer.py (for learning reference only. It's not necessary to train one yourself unless required. MiniMind comes with a built-in tokenizer). Or you can choose tokenizers from well-known open-source large models. Just as using Xinhua/Oxford dictionaries directly has the advantage of good token encoding compression, but the disadvantage of having too many pagesโ€”tens of thousands of word phrases; A self-trained tokenizer has the advantage of freely controlling vocabulary length and content, but the disadvantage of low compression ratio (for example, "hello" might be split into "h e l l o" five independent tokens), and rare words are difficult to cover. The choice of "dictionary" is important. The output of LLM is essentially a multi-class classification problem with SoftMax to N words in the dictionary, then decoding to natural language through the "dictionary." Because MiniMind size needs to be strictly controlled to avoid top-heavy models (embedding layer parameters taking up too high a proportion of LLM), shorter vocabulary lengths are better.

Tokenizer Introduction

The tokenizer vocabulary sizes of powerful open-source models from third parties such as Yi, qwen, chatglm, mistral, and Llama3 are as follows:

Tokenizer ModelVocabulary SizeSource
yi tokenizer64,00001AI (China)
qwen2 tokenizer151,643Alibaba Cloud (China)
glm tokenizer151,329Zhipu AI (China)
mistral tokenizer32,000Mistral AI (France)
llama3 tokenizer128,000Meta (USA)
minimind tokenizer6,400Custom

๐Ÿ‘‰ Updated 2024-09-17: To prevent ambiguity from previous versions and control size, all MiniMind models use minimind_tokenizer for tokenization, abandoning all mistral_tokenizer versions.

# Some thoughts
> Although minimind_tokenizer has a small length, its encoding/decoding efficiency is weaker than Chinese-friendly tokenizers like qwen2 and glm.
> But the minimind model chose the self-trained minimind_tokenizer as the tokenizer to maintain lightweight overall parameters, avoiding imbalance in encoding layer and computation layer proportions, preventing top-heavy models, because minimind's vocabulary size is only 6400.
> And minimind has never encountered rare word decoding failures in actual testing, with good results.
> Due to the custom vocabulary compression to 6400, the total LLM parameters are as low as 25.8M.
> The training data `pretrain_hq.jsonl` all comes from the `JiangShu large model dataset`, this part of data is relatively secondary. You can freely choose if you need to train.

โ…ก Pretraining Data

Having learned from MiniMind-V1's low-quality pretraining data that caused models to talk nonsense, after 2025-02-05 we decided no longer to use large-scale unsupervised datasets for pretraining. Instead, we tried to extract the Chinese portion from the JiangShu Large Model Dataset, Clean out about 1.6GB of corpus with character length <512 and concatenate them directly as pretraining data pretrain_hq.jsonl, where hq means high quality (of course it's not yet high, improving data quality is endless).

The file pretrain_hq.jsonl data format is

{"text": "How can I get rid of procrastination? Curing procrastination is not easy, but the following suggestions may help..."}

โ…ข SFT Data

The JiangShu Large Model SFT Dataset "is a complete, uniformly formatted, and safe large model training and research resource. It collected and organized a large amount of open-source datasets from public sources on the internet, unified their format, cleaned the data, containing Chinese datasets with 10M entries and English datasets with 2M entries." The above is the official introduction. After downloading, the total data volume is about 4B tokens, which is definitely suitable as SFT data for Chinese large language models. However, the official data format is messy, and using all of it for SFT would be too expensive. I performed secondary cleaning of the official dataset, removing entries with symbol pollution and noise; additionally, still only kept content with total length <512, hoping to supplement knowledge lacking in the pretraining phase through large amounts of dialogue at this stage. Export file is sft_512.jsonl (~7.5GB).

The Magpie-SFT Dataset collected ~1M high-quality conversations from Qwen2/2.5. I further cleaned this data, exporting the portion with total length <2048 as sft_2048.jsonl (~9GB). The portion with length <1024 exported as sft_1024.jsonl (~5.5GB). Using large model dialogue data directly for sft falls into the "black-box distillation" category.

Further cleaned the SFT data from the previous two steps (keeping only content with high Chinese character ratio), filtered conversations with length <512, and obtained sft_mini_512.jsonl (~1.2GB).

The data format for all sft files sft_X.jsonl is

{
    "conversations": [
        {"role": "user", "content": "Hello"},
        {"role": "assistant", "content": "Hello!"},
        {"role": "user", "content": "Goodbye"},
        {"role": "assistant", "content": "Goodbye!"}
    ]
}

โ…ฃ RLHF Data

From the Magpie-DPO Dataset approximately 200k preference data entries (all in English) generated from Llama3.1-70B/8B, can be used to train reward models, optimize model reply quality, making it more consistent with human preferences. Here, we reorganized content with total data length <3000 into dpo.jsonl (~0.9GB), containing two fields chosen and rejected, where chosen is the preferred reply and rejected is the rejected reply.

The file dpo.jsonl data format is

{
  "chosen": [
    {"content": "Q", "role": "user"}, 
    {"content": "good answer", "role": "assistant"}
  ], 
  "rejected": [
    {"content": "Q", "role": "user"}, 
    {"content": "bad answer", "role": "assistant"}
  ]
}

โ…ค Reasoning Dataset:

There's no denying that in February 2025, who can be hotter than DeepSeek... It also sparked my strong interest in RL-guided reasoning models. I've already reproduced R1-Zero using Qwen2.5. If I have time + good results (but 99% of base models lack ability), I will later update MiniMind with RL-trained reasoning models rather than distilled models. With limited time, the fastest low-cost solution is still direct distillation (black-box method). Unable to resist R1's popularity, in just a few days there are already various R1 distillation datasets like R1-Llama-70B, R1-Distill-SFT, Alpaca-Distill-R1, deepseek_r1_zh and so on. Pure Chinese data is relatively scarce. Finally integrated them, export file as r1_mix_1024.jsonl, data format consistent with sft_X.jsonl.

โ…ฅ More Datasets

Currently, HqWu-HITCS/Awesome-Chinese-LLM is collecting and organizing materials related to Chinese LLMs including open-source models, applications, datasets, and tutorials, and continuously updating the latest progress in this field. Comprehensive and professional, Respect!


โ…ง MiniMind Training Datasets

Note

After 2025-02-05, all datasets used for final MiniMind training are open-sourced. Therefore, you don't need to preprocess large-scale datasets yourself, avoiding repetitive data processing work.

MiniMind Training Dataset Download: ModelScope | HuggingFace

No need to clone everything, you can download the files you need individually

Place the downloaded dataset files in the ./dataset/ directory (โœจ are recommended required items)

./dataset/
โ”œโ”€โ”€ dpo.jsonl (55MB, โœจ)
โ”œโ”€โ”€ lora_identity.jsonl (22.8KB)
โ”œโ”€โ”€ lora_medical.jsonl (34MB)
โ”œโ”€โ”€ pretrain_hq.jsonl (1.6GB, โœจ)
โ”œโ”€โ”€ r1_mix_1024.jsonl (340MB)
โ”œโ”€โ”€ rlaif-mini.jsonl (1MB)
โ”œโ”€โ”€ sft_1024.jsonl (5.6GB)
โ”œโ”€โ”€ sft_2048.jsonl (9GB)
โ”œโ”€โ”€ sft_512.jsonl (7.5GB)
โ””โ”€โ”€ sft_mini_512.jsonl (1.2GB, โœจ)
Note: Brief Description of Each Dataset
  • dpo.jsonlโœจ --RLHF stage dataset (optimized and simplified, suitable for fast training)
  • lora_identity.jsonl --Self-awareness dataset (e.g., Who are you? I am minimind...), recommended for lora training (can also be used for full-parameter SFT, don't be limited by the name)
  • lora_medical.jsonl --Medical Q&A dataset, recommended for lora training (can also be used for full-parameter SFT, don't be limited by the name)
  • pretrain_hq.jsonlโœจ --Pretraining dataset, integrated from JiangShu Technology
  • r1_mix_1024.jsonl --DeepSeek-R1-1.5B distilled data, maximum character length per entry is 1024 (therefore set max_seq_len=1024 when training)
  • rlaif-mini.jsonl --RLAIF training dataset, randomly sampled 10,000 high-quality conversations from SFT dataset for training reinforcement learning algorithms like PPO/GRPO/SPO
  • sft_1024.jsonl --Integrated from Qwen2.5 distilled data (a subset of sft_2048), maximum character length per entry is 1024 (therefore set max_seq_len=1024 when training)
  • sft_2048.jsonl --Integrated from Qwen2.5 distilled data, maximum character length per entry is 2048 (therefore set max_seq_len=2048 when training)
  • sft_512.jsonl --Integrated from JiangShu Technology SFT data, maximum character length per entry is 512 (therefore set max_seq_len=512 when training)
  • sft_mini_512.jsonlโœจ --Minimal integration from JiangShu Technology SFT data + Qwen2.5 distilled data (for quick training of Zero models), maximum character length per entry is 512 (therefore set max_seq_len=512 when training)

dataset

Instructions & Recommended Training Schemes
  • MiniMind2 Series was trained on approximately 20GB of corpus in total, about 4B tokens, corresponding to the data combination training results above (cost: ๐Ÿ’ฐ๐Ÿ’ฐ๐Ÿ’ฐ๐Ÿ’ฐ๐Ÿ’ฐ๐Ÿ’ฐ๐Ÿ’ฐ๐Ÿ’ฐ, results: ๐Ÿ˜Š๐Ÿ˜Š๐Ÿ˜Š๐Ÿ˜Š๐Ÿ˜Š๐Ÿ˜Š)

  • For the fastest speed to implement Zero model from scratch, we recommend using the data combination of pretrain_hq.jsonl + sft_mini_512.jsonl, specific cost and results can be seen in the table below (cost: ๐Ÿ’ฐ, results: ๐Ÿ˜Š๐Ÿ˜Š)

  • For friends with certain computing resources or those who care more about results, you can consider the former to fully reproduce MiniMind2; for those with only single GPU or who care about quick reproduction in short time, we highly recommend the latter;

  • [Compromise solution] You can also choose medium-sized data like sft_mini_512.jsonl, sft_1024.jsonl for free combination training (cost: ๐Ÿ’ฐ๐Ÿ’ฐ๐Ÿ’ฐ, results: ๐Ÿ˜Š๐Ÿ˜Š๐Ÿ˜Š๐Ÿ˜Š).

๐Ÿ“Œ Model

Structure

MiniMind-Dense (same as Llama3.1) uses the Transformer Decoder-Only structure. The differences from GPT-3 are:

  • Adopts GPT-3's pre-normalization method, normalizing at the input of each Transformer sub-layer rather than at the output. Specifically, it uses the RMSNorm normalization function.
  • Replaced ReLU with SwiGLU activation function to improve performance.
  • Like GPT-Neo, it removed absolute position embeddings and switched to rotary position embeddings (RoPE), which works better when handling inference beyond training length.

MiniMind-MoE model structure is based on Llama3 and the MixFFN mixture-of-experts module from Deepseek-V2/3.

  • DeepSeek-V2 in feed-forward networks (FFN) uses finer-grained expert splitting and shared expert isolation techniques to improve the effect of Experts.

MiniMind's overall structure is consistent, with only small adjustments in RoPE computation, inference functions, and FFN layer code. The structure is shown in the diagram below (redrawn version):

structure structure-moe

To modify model configuration, see ./model/model_minimind.py. Reference model parameter versions see the table below:

Model Name params len_vocab rope_theta n_layers d_model kv_heads q_heads share+route
MiniMind2-Small 26M 6400 1e6 8 512 2 8 -
MiniMind2-MoE 145M 6400 1e6 8 640 2 8 1+4
MiniMind2 104M 6400 1e6 16 768 2 8 -
minimind-v1-small 26M 6400 1e4 8 512 8 16 -
minimind-v1-moe 4ร—26M 6400 1e4 8 512 8 16 1+4
minimind-v1 108M 6400 1e4 16 768 8 16 -

Model Configuration

๐Ÿ“‹ Regarding LLM parameter configuration, there's an interesting paper MobileLLM that conducted detailed research and experiments. Scaling Law has its own unique patterns in small models. Parameters causing Transformer parameter scaling changes almost entirely depend on d_model and n_layers.

  • d_modelโ†‘ + n_layersโ†“ -> Wide and short
  • d_modelโ†“ + n_layersโ†‘ -> Narrow and tall

The 2020 Scaling Law paper argued that training data volume, parameter quantity, and training iterations are the key factors determining performance, while model architecture influence is negligible. However, this law doesn't seem to fully apply to small models. MobileLLM argues that architecture depth is more important than width, "deep and narrow" "tall and skinny" models can learn more abstract concepts than "wide and shallow" models. For example, when model parameters are fixed at 125M or 350M, 30-42 layer "narrow" models clearly have superior performance compared to around 12 layer "wide" models, showing similar trends across 8 benchmark tests including commonsense reasoning, Q&A, and reading comprehension. This is actually a very interesting discovery, because previously when designing architectures for ~100M scale small models, almost no one tried stacking more than 12 layers. This is consistent with what MiniMind observed in experiments when adjusting model parameters between d_model and n_layers during training. However, "deep and narrow" models also have dimensional limits. When d_model<512, the disadvantage of embedding dimension collapse is very obvious, and added layers cannot compensate for the disadvantage of insufficient d_head caused by fixed q_head in embeddings. When d_model>1536, increasing layers seems to have higher priority than d_model, bringing more "cost-effective" parameter -> performance gains.

  • Therefore MiniMind sets small model dim=512, n_layers=8 to achieve the balance of "extremely small size <-> better performance."
  • Setting dim=768, n_layers=16 to gain larger performance improvements, more consistent with small model Scaling-Law curves.

For reference, GPT3 parameter settings see the table below: gpt3_config.png


๐Ÿ“Œ Experiment

โ…  Training Costs

  • Time unit: Hours (h).
  • Cost unit: Chinese Yuan (๏ฟฅ); 7๏ฟฅ โ‰ˆ 1 USD.
  • 3090 rental price: โ‰ˆ1.3๏ฟฅ/h (you can check current prices yourself).
  • Reference standard: The table only shows actual measured training time for pretrain and sft_mini_512 two datasets. Other time costs are estimated based on dataset size (may have slight variations).

Based on 3090 (single GPU) cost calculation

Model Name params pretrain sft_mini_512 sft_512 sft_1024 sft_2048 RLHF
MiniMind2-Small 26M โ‰ˆ1.1h
โ‰ˆ1.43๏ฟฅ
โ‰ˆ1h
โ‰ˆ1.3๏ฟฅ
โ‰ˆ6h
โ‰ˆ7.8๏ฟฅ
โ‰ˆ4.58h
โ‰ˆ5.95๏ฟฅ
โ‰ˆ7.5h
โ‰ˆ9.75๏ฟฅ
โ‰ˆ1h
โ‰ˆ1.3๏ฟฅ
MiniMind2 104M โ‰ˆ3.9h
โ‰ˆ5.07๏ฟฅ
โ‰ˆ3.3h
โ‰ˆ4.29๏ฟฅ
โ‰ˆ20h
โ‰ˆ26๏ฟฅ
โ‰ˆ15h
โ‰ˆ19.5๏ฟฅ
โ‰ˆ25h
โ‰ˆ32.5๏ฟฅ
โ‰ˆ3h
โ‰ˆ3.9๏ฟฅ

Training Cost Summary & Forecast

MiniMind2-Small Parameters

pretrain_hq+sft_mini_512 Dataset
Single 3090 GPU (1 epoch) + 2.1 hours + Cost 2.73 Chinese Yuan
Can train MiniMind-Zero-0.025B model from scratch!!!

MiniMind2-Small Parameters

pretrain_hq+sft_512+sft_2048+dpo Dataset
Single 3090 GPU (2 epochs) + Approximately 38.16 hours + Cost 49.61 Chinese Yuan
Can train MiniMind2-Small-0.025B model from scratch!!!

MiniMind2 Parameters

pretrain_hq+sft_512+sft_2048+dpo Dataset
Single 3090 GPU (2 epochs) + Approximately 122 hours + Cost 158.6 Chinese Yuan
Can train MiniMind2-0.1B model from scratch!!!

โœจ Based on single NVIDIA 3090 GPU, MiniMind-Zero requires only 2 hours + 3 Chinese Yuan from scratch to achieve ChatBot effect!

โœจ PS: If training with 8 4090 GPUs, the total time can even be compressed to less than 10 minutes! (Due to shorter time, cost is still around 3 Yuan, comparable to single GPU cost)

โœจ With an extremely low barrier to entry, achieve large model freedom for everyone! This is the original intention behind the birth of the MiniMind series!

โœจ The MiniMind-Zero costing only 3 Chinese Yuan is not just hype! Chat test:

๐Ÿ‘ถ: Please introduce yourself.
๐Ÿค–๏ธ: As an artificial intelligence, I have no actual life and no self-awareness, so I don't have my own life. I was designed to help users answer questions, provide information, and have conversations, etc. My design and functionality are built by computer science, machine learning, artificial intelligence technology and algorithms, and I'm implemented through programming and algorithms.

๐Ÿ‘ถ: Recommend some special dishes from Hangzhou.
๐Ÿค–๏ธ: Hangzhou has many delicious special dishes, such as chicken kebabs, eel head, boiled fish, tofu brain, etc. These dishes are very delicious, with unique flavors and tastes, definitely worth trying.

๐Ÿ‘ถ: Please explain the concept of "large language models" to me.
๐Ÿค–๏ธ: A large language model is a type of artificial intelligence technology that uses large amounts of text data to train models, then continuously optimizes the model through iterations. Its goal is to generate text that meets specific needs based on input data. These texts can be any topic you're interested in.

๐Ÿ‘ถ: Introduce the history of the United States, please.
๐Ÿค–๏ธ: The "Introok's the believeations of theument" you mentioned gets its name from the ancient Chinese "groty of of the change."

Extremely fast with initial results, and can even be further compressed to obtain smaller and higher quality training data. Zero model weights are saved as full_sft_512_zero.pth (see MiniMind model file links below). If interested, you can download and test this model.


โ…ก Main Training (Required)

All training scripts should be executed in the cd ./trainer directory

1. Pretraining (Pretrain):

What LLMs need to learn first is not to communicate directly with people, but to fill the network parameters with the ink of knowledge. The "ink" should ideally be as saturated as possible, accumulating vast knowledge about the world. Pretraining is where the model first studies hard to learn a large amount of basic knowledge, such as organizing large-scale high-quality training data from Wikipedia, news, books, etc. This process is "unsupervised," meaning humans don't need to perform any "supervised" corrections during the process. Instead, the model itself summarizes patterns and learns knowledge from large amounts of text. The model's goal at this stage is only one: Learn word prediction. For example, given the input "Qin Shi Huang," it can continue with "was the first emperor of China."

torchrun --nproc_per_node 1 train_pretrain.py # 1 means single GPU training, adjust based on your hardware (set >=2 for multiple GPUs)
# or
python train_pretrain.py

After training, model weight files are saved by default every 100 steps as: pretrain_*.pth (where * is the model's specific dimension, new files overwrite old ones on each save)

MiniMind2-Small (512dim) MiniMind2 (768dim)

2. Supervised Fine-Tuning (SFT):

After pretraining, the LLM has mastered a lot of knowledge, but at this point it only knows how to do word prediction mindlessly and doesn't know how to chat with people. The SFT stage requires applying a custom chat template to fine-tune the semi-finished LLM. For example, after the model encounters such a template [question->answer, question->answer], it no longer does mindless word continuation, but realizes this is the end of a complete conversation. This process is called instruction fine-tuning, like helping the already knowledgeable "Newton" gentleman adapt to 21st-century smartphone chat habits, learning that the left side of the screen is the other person's message and the right side is the user's message. During training, MiniMind's instruction and answer lengths are truncated at 512 to save GPU memory. Like learning to write, you start with short articles, and after learning to write 200-character essays, 800-character articles become easy. When length extension is needed, you only need to prepare a small amount of 2k/4k/8k length dialogue data for further fine-tuning (preferably combined with RoPE-NTK scaling).

During inference, by adjusting RoPE scaling, it will be convenient to achieve training-free length extrapolation to 2048 and beyond.

torchrun --nproc_per_node 1 train_full_sft.py
# or
python train_full_sft.py

After training, model weight files are saved by default every 100 steps as: full_sft_*.pth (where * is the model's specific dimension, new files overwrite old ones on each save)

MiniMind2-Small (512dim) MiniMind2 (768dim)

โ…ข Other Training Stages (Optional)

All training scripts should be executed in the cd ./trainer directory

3. Knowledge Distillation (KD)

At this point, after all the previous training steps, the model has completely acquired basic capabilities and usually can graduate. However, knowledge distillation can further optimize model performance and efficiency. Knowledge distillation means the student model learns from the teacher model. The teacher model is usually a well-trained large model with high accuracy and generalization ability. The student model is a smaller model whose goal is to learn the teacher model's behavior rather than learn directly from raw data. In SFT learning, the model's goal is to fit hard labels for token classification (hard labels), i.e., true class labels (such as 0 or 6400). In knowledge distillation, the teacher model's softmax probability distribution is used as soft labels (soft labels). The small model only learns soft labels and uses KL-Loss to optimize model parameters. In simple terms, SFT learns the problem-solving answers the teacher gives directly. The KD process is like "opening" the teacher's smart brain and trying to mimic the neural state of the teacher's "brain" thinking about problems. For example, when the teacher model calculates the problem 1+1=2, the final layer neurons a state is 0, neuron b state is 100, neuron c state is -99... The student model learns the operating rules inside the teacher model's brain through large amounts of data. This process is called: knowledge distillation. Knowledge distillation has only one purpose: make small models smaller in size while having better results. However, with the birth and development of LLMs, the term model distillation has been widely abused, creating two schools of "white-box/black-box" knowledge distillation. Closed-source models like GPT-4, since their internal structure cannot be accessed, can only learn from the data they output. This process is called black-box distillation, and is the most common practice in the age of large models. Black-box distillation is completely identical to the SFT process, except the data is collected from large model outputs. Therefore, you only need to prepare data and further FT. Note that you need to change the loaded base model to full_sft_*.pth, i.e., further distillation learning based on the fine-tuned model. Both ./dataset/sft_1024.jsonl and ./dataset/sft_2048.jsonl are collected from qwen2.5-7/72B-Instruct large models and can be used directly for SFT to acquire some Qwen behavior.

# Note: need to change the dataset path in train_full_sft.py and max_seq_len
torchrun --nproc_per_node 1 train_full_sft.py
# or
python train_full_sft.py

After training, model weight files are similarly saved by default every 100 steps as: full_sft_*.pth (where * is the model's specific dimension, new files overwrite old ones on each save)

Emphasis should be placed on introducing MiniMind's white-box distillation code train_distillation.py. Since there is no powerful teacher model within the same MiniMind series, the white-box distillation code is only for learning reference.

torchrun --nproc_per_node 1 train_distillation.py
# or
python train_distillation.py

4. LoRA (Low-Rank Adaptation)

LoRA is an efficient Parameter-Efficient Fine-Tuning (PEFT) method aimed at fine-tuning pre-trained models through low-rank decomposition. Compared to full parameter fine-tuning (Full Fine-Tuning), LoRA only needs to update a small number of parameters. LoRA's core idea is: introduce low-rank decomposition in the model's weight matrices and only update the low-rank parts while keeping the original pre-trained weights unchanged. Code can be found in ./model/model_lora.py and train_lora.py, completely implementing the LoRA process from scratch without relying on third-party library packaging.

torchrun --nproc_per_node 1 train_lora.py
# or
python train_lora.py

After training, model weight files are saved by default every 100 steps as: lora_xxx_*.pth (where * is the model's specific dimension, new files overwrite old ones on each save)

Many people are confused about how to make models learn knowledge in their private domains, how to prepare datasets, and how to migrate general-purpose models to build domain-specific models. Here are some examples. For general models lacking medical domain knowledge, you can try adding domain knowledge to the original model to get better performance. At the same time, you usually don't want to lose other abilities of the original base model while learning domain knowledge. In this case, LoRA can effectively solve this problem. You only need to prepare dialogue datasets in the following format and place them in ./dataset/lora_xxx.jsonl, then run python train_lora.py to get the new model weights ./out/lora/lora_xxx.pth.

Medical Scenario

 {"conversations": [{"role": "user", "content": "What height should a cervical spondylosis patient's pillow be?"}, {"role": "assistant", "content": "For cervical spondylosis patients, pillow height selection should be based on..."}]}
 {"conversations": [{"role": "user", "content": "What about xxx"}, {"role": "assistant", "content": "xxx..."}]}

Self-awareness Scenario

 {"conversations": [{"role": "user", "content": "What is your name?"}, {"role": "assistant", "content": "My name is minimind..."}]}
 {"conversations": [{"role": "user", "content": "Who are you"}, {"role": "assistant", "content": "I am..."}]}

At this point, [base model + LoRA model] can acquire medical scenario model-enhanced capabilities, equivalent to adding a LoRA plug-in to the base model, which does not lose the base model's original abilities. You can test the model through eval_llm.py for model evaluation.

# Note: weight parameter specifies base model type, should match the base model used during train_lora training
python eval_llm.py  --weight dpo --lora_weight lora_medical

Small Test

๐Ÿ‘ถ: I've been feeling dizzy recently, what could be the reason?
๐Ÿค–๏ธ: Dizziness could be caused by many reasons, including but not limited to: heart disease, eye damage, allergic reactions, skin problems, allergic reactions, stress, anxiety, fatigue, medication side effects, sexual dysfunction, or others...

---

๐Ÿ‘ถ: What is your relationship with openai?
๐Ÿค–๏ธ: I am MiniMind, an artificial intelligence assistant developed by Jingyao Gong. I interact with users through natural language processing and algorithm training.

PS: As long as you have the required datasets, you can also do full_sft full parameter fine-tuning (need to mix general knowledge to avoid overfitting domain data making the model worse and losing generality)

5. Training Reasoning Models (Reasoning Model)

DeepSeek-R1 was so popular, almost pointing out a new paradigm for future LLMs. The paper points out that models >3B require multiple iterations of cold starts and RL reward training to achieve visible reasoning ability improvements. The fastest, most reliable, and most economical approach, as well as recent various so-called reasoning models, are almost all directly distilled from data. But due to lack of technical sophistication, the distillation school is looked down upon by the RL school (hhhh). I quickly tried on Qwen 1.5B small model and quickly reproduced math reasoning ability in the Zero process. However, a regrettable consensus is: models with parameters too small cannot achieve any reasoning effect through cold start SFT+GRPO. For now, MiniMind firmly chooses to be in the distillation school. If RL on 0.1B models later achieves small progress, this training approach section will be updated.

For distillation, you only need to prepare datasets in the same format as the SFT stage. The dataset source has been introduced above. Data format examples:

{
  "conversations": [
    {
      "role": "user",
      "content": "Hello, I am Xiaofang, nice to meet you."
    },
    {
      "role": "assistant",
      "content": "<think>\nHello! I am a small AI reasoning model R1-Lite-Preview developed by an independent developer in China. I'm happy to serve you!\n</think>\n<answer>\nHello! I am a small AI reasoning model R1-Lite-Preview developed by an independent developer in China. I'm happy to serve you!\n</answer>"
    }
  ]
}

The reply template for reasoning model R1 is:

<think>\nThinking process\n</think>\n
<answer>\nFinal answer\n</answer>

This is constrained by setting a rule-based reward function in GRPO to make the model comply with thinking tags and reply tags (in the early stages of cold starts, reward values should be increased).

Another issue is that although the distillation process is the same as SFT, experimental results show that models have difficulty consistently complying with template-compliant replies every time, i.e., deviating from thinking and reply tag constraints. A small trick here is to increase the loss penalty for marker position tokens. See details in train_distill_reason.py:

# Add extra penalty to positions corresponding to sp_ids
...
loss_mask[sp_ids] = 10 # penalty coefficient

Another tip is that because reasoning data only filtered <1024 length data, it has fewer multi-turn conversations and English data. Therefore, r1_mix_1024.jsonl mixed approximately 10k multi-turn conversations + English data to prevent serious model forgetting.

The script defaults to reasoning ability distillation fine-tuning based on the rlhf model. You can directly start training:

torchrun --nproc_per_node 1 train_distill_reason.py
# or
python train_distill_reason.py

After training, model weight files are saved by default every 100 steps as: reason_*.pth (where * is the model's specific dimension, new files overwrite old ones on each save)

Let's test it:

๐Ÿ‘ถ: Please introduce yourself.
๐Ÿค–๏ธ: <think>
Um, the user is asking me to introduce myself. I need to explain myself first. First, I should clarify who the user is - are they students, working professionals or ordinary people? The user might be a student or working professional, so information delivery should be to help students and working professionals with information. Then I need to respond to the user, which might include introducing where I am, hobbies, career experience, and other information. I should note to use formal language without being too formal, while keeping it concise and clear. This makes it easy for users to understand and convenient for them to check related information. Finally, I should summarize to let the user know how I help them complete their tasks, giving them more information about me.
</think>
<answer>
I am **"your name", what is your name?
</answer>

๐Ÿ‘ถ: Which subject are you better at?
๐Ÿค–๏ธ: <think>
Hello! I am a small AI reasoning model R1 developed by Chinese independent developers. If you have any questions, I will do my best to help you.
</think>
<answer>
Hello! I am a small AI reasoning model R1 developed by Chinese independent developers. If you have any questions, I will do my best to help you.
</answer>

IV Reinforcement Learning Training

RL methods in LLMs can be divided into two categories:

  1. Reinforcement Learning from Human Feedback (RLHF)
  • Train the model by evaluating human preferences for model outputs, making it generate content more consistent with human values and preferences.
  1. Reinforcement Learning from AI Feedback (RLAIF)
  • Use AI models (typically pre-trained language reward models) to provide feedback rather than directly relying on human manual annotation.
  • The "AI" here can also be certain rule-based rewards, such as math answer correctness / code executors...
Type Judge Advantages Disadvantages
RLHF Human More aligned with real human preferences High cost, low efficiency
RLAIF Model Automated, highly scalable May deviate from real human preferences

The two are essentially the same, both using reinforcement learning to utilize certain forms of "feedback" to optimize model behavior.

Except for the different feedback sources, there are no other differences.

๐Ÿ‘€ Unified Perspective on PO Algorithms

Before introducing specific algorithm implementations, I'll present my personal understanding of the unified commonality of all Policy Optimization (PO) algorithms in a minimalist perspective.

The essence of all RL algorithms is only optimizing one expectation:

$$\mathcal{J}_{PO} = \mathbb{E}_{q \sim P(Q), o \sim \pi(O|q)} \left[ \underbrace{f(r_t)}_{\text{policy term}} \cdot \underbrace{g(A_t)}_{\text{advantage term}} - \underbrace{h(\text{KL}_t)}_{\text{regularization term}} \right]$$

During training, only minimize the negative objective function, i.e.: $\mathcal{L_{PO}}=-\mathcal{J_{PO}}$

This framework contains only three core components:

  • Policy term $f(r_t)$: How to use probability ratio $r_t$? Tell the model how large the deviation between new and old policies is, whether better tokens are explored
  • Advantage term $g(A_t)$: How to calculate advantage $A_t$, this is important! Large models solving definite integrals is unremarkable, small models answering addition/subtraction correctly usually have positive advantages
  • Regularization term $h(\text{KL}_t)$: How to constrain the change magnitude $\text{KL}_t$, both preventing drift and not being too rigid
(Expand) Symbol Explanation
Symbol Meaning Explanation Range
$q$ Question/prompt Sampled from dataset $P(Q)$ -
$o$ Model output sequence Generated by policy $\pi$ -
$r_t$ Probability ratio $r_t = \frac{\pi_\theta(o_t|q, o_{&lt;t})}{\pi_{ref}(o_t|q, o_{&lt;t})}$ $(0, +\infty)$
$A_t$ Advantage function Measures how good an action is compared to baseline $(-\infty, +\infty)$
$\text{KL}_t$ KL divergence Prevent policy from deviating too far from reference model $[0, +\infty)$

Different xxPO algorithms are essentially just different design instantiations of these three components!


6. Reinforcement Learning from Human Feedback (RLHF)

In the previous training steps, the model has acquired basic conversation abilities, but these are completely based on word prediction, lacking the motivation of positive and negative examples. The model doesn't yet know what answers are good and what are bad. We hope it can be more aligned with human preferences, reducing the probability of unsatisfactory answers. This process is like having the model undergo new training, learning from excellent employees as examples and passive employees as counter-examples, to learn how to respond better.

6.1 Direct Preference Optimization

Direct Preference Optimization (DPO) algorithm loss:

$$\mathcal{L}_{DPO} = -\mathbb{E}\left[\log \sigma\left(\beta \left[\log \frac{\pi_\theta(y_w|x)}{\pi_{ref}(y_w|x)} - \log \frac{\pi_\theta(y_l|x)}{\pi_{ref}(y_l|x)}\right]\right)\right]$$

Where:

  • Policy term: $f(r_t) = \log r_w - \log r_l$ (contrast probability ratios of chosen vs rejected)
  • Advantage term: $g(A_t)$ = / (through preference contrast, no need to explicitly calculate advantage)
  • Regularization term: $h(\text{KL}_t)$ = implicit in $\beta$ (control deviation from reference model)

Specifically:

  • DPO derives an analytical training objective for preference pairs from PPO with KL constraints, directly maximizing the log-odds that "chosen outperforms rejected"; no need to simultaneously train Reward/Value models. DPO only needs to run two models actor and ref, with low GPU memory usage, stable convergence, and simple implementation.
  • Training paradigm: off-policy, using static preference datasets, can repeat multiple epochs; Ref model is fixed (outputs pre-cached).
  • DPO's limitation is no online exploration, more used for "preference/safety" human value alignment; limited improvement in "intellectual ability" to solve problems correctly (of course this depends on the dataset, collecting large-scale positive and negative samples with human evaluation is difficult).
torchrun --nproc_per_node 1 train_dpo.py
# or
python train_dpo.py

After training, model weight files are saved by default every 100 steps as: dpo_*.pth (where * is the model's specific dimension, new files overwrite old ones on each save)

7. Reinforcement Learning from AI Feedback (RLAIF)

Compared to RLHF which relies on human-annotated chosen/rejected preference pairs, RLAIF has AI completely act as the "judge." The so-called AI "judge" can be a model-based reward large model (Reward Model), can be like R1 setting rule-based functions for validation, or can be environmental feedback like tool calling. For example: whether math problem answers are correct, whether code execution passes test cases, whether reasoning processes meet format requirements...can all be automatically judged. RLAIF's greatest advantage is its scalability and On-Policy characteristicsโ€”โ€”no need for expensive human annotation, can generate massive training samples, letting models quickly evolve through large-scale online trial and error.

MiniMind implements 2+N basic + cutting-edge RLAIF methods:

  • PPO, GRPO are classic RL algorithms widely validated at scale;
  • N cutting-edge RL algorithms (updated irregularly with experimental nature).

1๏ธโƒฃ Dataset Preparation (Required)

To quickly verify RLAIF effectiveness, 10,000 high-quality conversations were randomly sampled from the SFT dataset, building about 1MB size rlaif-mini.jsonl (Huggingface)

Data format is consistent with SFT, but assistant content is not needed, because during training it's completely real-time sampled and generated by the $\Pi$ policy model. Thus:

{
    "conversations": [
        {"role": "user", "content": "Explain what photosynthesis is?"},
        {"role": "assistant", "content": "None"}
    ]
}

During RLAIF training, the model generates 1 or more candidate answers based on user questions, then a reward function/model scores the answers. High-scoring answers are encouraged (increase $\Pi$ policy probability), low-scoring answers are suppressed (decrease $\Pi$ policy probability). This "score->adjust" loop is the core of reinforcement learning.

2๏ธโƒฃ Reward Model Preparation (Required)

It's known that RLAIF training requires a "reward model (Reward Model)" to score generated answers.

We select the small and high-quality InternLM2-1.8B-Reward (ModelScope | HuggingFace) as the base reward model.

After downloading the reward model, it needs to be placed in the same level directory as the minimind project. The recommended structure is:

project/
โ”œโ”€โ”€ minimind/                    # MiniMind project
โ”‚   โ”œโ”€โ”€ model/
โ”‚   โ””โ”€โ”€ ...
โ””โ”€โ”€ internlm2-1_8b-reward/       # Reward model (same level as minimind)
    โ”œโ”€โ”€ config.json
    โ”œโ”€โ”€ model.safetensors
    โ””โ”€โ”€ ...
Reward Mechanism Choice and MiniMind Limitations (Click to expand)

1. Diversity of Reward Mechanisms

The "reward signal" source in RLAIF can be very flexible:

  • Model-based rewards: Can use dedicated Reward Models (like InternLM2-Reward), or use general LLMs + prompts for scoring (like Qwen3-as-a-Judge). Reward model scale and architecture are freely selectable.

  • Rule-based rewards: Can construct reward signals based on rule functions, for example:

    • Math problem answer correctness verification (Ground Truth comparison)
    • SQL execution success rate and result accuracy
    • Code interpreter run results (pass@k)
    • Tool call return status (API success/failure)
    • Format compliance checks (JSON/XML parsing)
    • Reasoning chain completeness evaluation (CoT step count)
  • Environment-based rewards: In Agent scenarios, environmental feedback itself is natural reward (like game scores, Research completeness, task completion).

Any mechanism that can quantify "answer quality" can serve as an RL reward source. DeepSeek R1 is a typical case: using rule-based functions to verify math answer correctness as reward, no need for additional Reward Models.

2. MiniMind Limitation: Reward Sparsity Problem

RLAIF training can be applied to both reasoning and non-reasoning models, the difference is only in format.

However, for MiniMind with such tiny 0.1B parameters and weak abilities, on general tasks (like R1-style math datasets) it encounters serious reward sparsity (Reward Sparsity) problems:

  • Phenomenon: Model-generated candidate answers are almost all wrong, causing all reward scores $r(x,y) \approx 0$
  • Consequence: Advantage function $A(x,y) = r(x,y) - b(x) \approx 0$, policy gradient signal disappears, cannot effectively update parameters $\theta$

Like having elementary school students do high school math exams, no matter how many attempts they get zero, cannot learn to improve strategies through score differences. This is a fundamental principle limitation of RL algorithms.

To mitigate this problem, MiniMind's implementation chose model-based continuous reward signals:

  • Reward Model outputs continuous scores (like -2.5 to +3.0), not binary 0/1
  • Even if answer quality is all poor, can still distinguish subtle differences between "much worse" (-3.0) and "worse" (-2.8). So this dense and continuous reward signal can provide non-zero gradients to the advantage function $A(x,y)$, enabling gradual policy network optimization
  • Can also mix multiple reward sources: $r_{\text{total}} = \alpha \cdot r_{\text{model}} + \beta \cdot r_{\text{rule}}$ (for example, can detect think tag format rewards while also synthesizing answer quality reward scores)
  • In minimind practice, avoid directly using rule-based binary rewards + out-of-scope difficulty data (like MATH500), which easily leads to all-zero rewards;
  • Monitor reward score variance $\text{Var}(r)$ during training, if it consistently approaches 0 need to adjust data or reward mechanism

For Production-Scale Large Models in Agentic RL Scenarios:

In real Agent systems (code generation, tool calling, retrieval-planning-execution multi-turn pipelines), rewards are different paradigms of "delayed round settlement":

  • LLM needs to generate tool call instructions token-by-token (tool_call), go through parsing (tool_parse), tool execution (tool_exec), then splice results back to context for next step; repeat until completion.
  • One complete task pipeline includes multiple calls+thinking, calculate total reward once until termination condition is met (like whether task is complete, whether tests pass, whether targets are hit).

Therefore, Agentic RL is closer to sparse/delayed reward settings: gradient backprop happens "after the round ends," very different from non-Agentic RL tasks with "instant scoring and instant updates" on single conversation rounds. This also explains why Agent tasks favor environment feedback (environment-based reward) rather than static reward model scoring.

  • Environmental interaction feedback: Final results matter (code runs, API returns success, sub-goals complete);
  • Model-based reward limitations: Limited capture of long pipelines and executable semantics, likely inconsistent with real environmental feedback (reward hacking).

PPO is a very classic reinforcement learning algorithm proposed by OpenAI in 2017, and is the universal baseline method for LLM RL.

PPO Loss: $$\mathcal{L}_{PPO} = -\mathbb{E}\left[\min(r_t \cdot A_t, \text{clip}(r_t, 1-\varepsilon, 1+\varepsilon) \cdot A_t)\right] + \beta \cdot \mathbb{E}[\text{KL}]$$

Where:

  • Policy term: $f(r_t) = \min(r_t, \text{clip}(r_t, 1-\varepsilon, 1+\varepsilon))$ (clip probability ratio to prevent aggressive updates)
  • Advantage term: $g(A_t) = R - V(s)$ (estimate value function through Critic network)
  • Regularization term: $h(\text{KL}_t) = \beta \cdot \mathbb{E}[\text{KL}]$ (global KL divergence constraint)

Comparing to DPO:

  • DPO (Off-Policy): Training data is a static preference dataset (chosen vs rejected), can repeatedly use the same batch of data to train multiple epochs, just like traditional supervised learning. High data efficiency, low training cost. Directly optimizes log-likelihood of preference pairs, no Reward Model needed.
  • PPO (On-Policy): Must use current policy to real-time sample new data, old policy-collected data cannot be used (distribution shift problem). Although importance sampling and clip mechanisms allow slight distribution shifts, essentially requires data from relatively fresh policies. Low data efficiency, but suited for explorative learning.

In simple terms:

  • The former teaches models to learn by offline preset "good/bad standards," even if not outputtable by current models (like practicing ball hitting by watching world champion/runner-up videos);
  • The latter teaches models real-time to do things right, online sampling from newest model policy (coach hand-teaching, real-time scoring each action).

MiniMind's PPO implementation includes Actor model (generate answers) and Critic model (evaluate answer value), and complete GAE (Generalized Advantage Estimation) advantage function calculation.

Training:

torchrun --nproc_per_node N train_ppo.py
# or
python train_ppo.py

After training, model weight files are saved by default every 100 steps as: ppo_actor_*.pth (where * is the model's specific dimension)

MiniMind2-Small (512dim) MiniMind2 (768dim)

From the training curves, you can see PPO has the problem of slow reward improvement. I believe this mainly stems from PPO's dual-network joint optimization method: Critic needs to gradually converge to accurately estimate value functions, and Actor's policy updates depend on Critic-provided advantage estimates, the two interdependent forming complex optimization. Early training period Critic estimates inaccurately affects Actor gradient direction, leading to slow overall convergence. Furthermore, PPO needs to maintain two networks simultaneously, GPU memory usage about 1.5-2x single-network methods.

In early 2025, DeepSeek-R1 became extremely popular, and equally popular was the GRPO algorithm from the DeepSeekMath paper, also becoming one of the most advanced RL algorithms. However, AI six months equals humanity six months, and by now GRPO has evolved into the baseline algorithm of the great XXPO wars (later evolved DAPO, GSPO, CISPO, etc.). In short, the core innovation is "group relative value estimation."

GRPO Loss:

$$\mathcal{L}_{GRPO} = -\mathbb{E}\left[r_t \cdot A_t - \beta \cdot \text{KL}_t\right]$$

Where:

  • Policy term: $f(r_t) = r_t$ (directly use probability ratio, no clip clipping)
  • Advantage term: $g(A_t) = \frac{R - \mu_{group}}{\sigma_{group}}$ (within-group normalization, eliminate Critic network)
  • Regularization term: $h(\text{KL}_t) = \beta \cdot \text{KL}_t$ (token-level KL divergence constraint)

For the same question, the model generates N different answers (for example N=4), then calculates reward scores for these N answers. Next, use the average reward of these N answers as baseline. Answers above baseline are encouraged, answers below baseline are suppressed. This cleverly avoids training an additional critic network.

Just as all RL faces the principle limitation of positive and negative samples, GRPO is no exception. Its more significant problem is: degenerate groups (Degenerate Groups). Suppose a question is slightly difficult, causing N answer reward scores to be nearly identical (usually equally bad rather than equally good), then this group's learning signal approaches zero. On MiniMind such ultra-small models, this problem is especially obvious. When solving math problems 99.99% of the time the entire group answer quality is poor, then cannot learn. Therefore, must specify reasonable domain for the model, i.e., must limit within capability boundaries.

Training:

torchrun --nproc_per_node N train_grpo.py
# or
python train_grpo.py

After training, model weight files are saved by default every 100 steps as: grpo_*.pth

MiniMind2-Small (512dim) MiniMind2 (768dim)

From the training curves, you can see GRPO's reward shows more stable upward trend, reaching around 4, indicating GRPO itself better utilizes RLAIF signals. Policy Loss generally decreases smoothly. Compared to PPO's dual-network optimization, GRPO's single-network architecture trains more stably with higher convergence ceiling.

7.3 โณโŒ›๏ธ๐Ÿ”ฅ More RL Extensions (Exp)

SPO is an RL algorithm Tencent proposed in September 2025, improving on GRPO's degenerate group problem. The paper argues that GRPO and similar algorithms' requirement that "one sample depends on a group of samples" seems awkward and inelegant: too-easy or too-hard questions result in the entire group learning nearly nothing, learning efficiency is inherently limited. SPO's motivation is to return to RL's essenceโ€”โ€”1 input, 1 output, is 1 training sample, returning to basic policy gradient formulas: can get stable baseline without group mean, i.e., spread value estimate V across time dimension, do rough value pre-estimation before training, update V estimate during training while sampling, thus providing each sample with a persistent, adaptive baseline across batches. This "single-stream" design no longer depends on same-group samples, naturally avoiding degenerate groups.

SPO Loss:

$$\mathcal{L}_{SPO} = -\mathbb{E}\left[\log \pi_\theta(a_t|s) \cdot A_t - \beta \cdot \text{KL}_t\right]$$

Where:

  • Policy term: $f(r_t) = \log \pi_\theta(a_t|s)$ (directly use log probability, don't calculate ratio)
  • Advantage term: $g(A_t) = R - B_t^{adaptive}$ (adaptive baseline, Beta distribution dynamic tracking)
  • Regularization term: $h(\text{KL}_t) = \beta \cdot \text{KL}_t$ (token-level KL + dynamic $\rho$ adjustment)

At implementation level: SPO uses non-grouped design, uses persistent KL-adaptive value tracker to replace within-group baseline, advantage functions globally normalized across entire batch. This way each sample processed independently, no need to wait for other same-group samples, yet provides stable learning signals for each sample. On Qwen3-8B's 5 difficult math datasets, SPO averages 3.4 percentage points higher than GRPO, with BRUMO 25 dataset +7.3pp, AIME 25 dataset +4.4pp.

Note: SPO is an experimental cutting-edge algorithm, MiniMind's implementation is for exploratory learning. Due to extremely small model parameters, cannot fully reproduce paper's 8B model results.

Training:

torchrun --nproc_per_node N train_spo.py
# or
python train_spo.py

After training, model weight files are saved by default every 100 steps as: spo_*.pth

MiniMind2 (768dim) Training Curve

Looking at the training curves, SPO's reward fluctuation is similar to PPO, weaker than GRPO. Actual inference testing found model output quality is not high, with logic confusion and format error issues.

Experimental Note: Current SPO hand-implemented version may have problems in value_tracker configuration, reward normalization strategy. Still needs to check algorithm's adaptability on small models/or implementation differences.

RL Algorithm Summary

We return to the "unified framework", reorganizing the table showing all different PO algorithms are just different instantiations of three core components:

Algorithm Policy Term $f(r_t)$ Advantage Term $g(A_t)$ Regularization Term $h(\text{KL}_t)$ Optimized Models
DPO $\log r_w - \log r_l$ Implicit (preference contrast) Implicit in $\beta$ 2
PPO $\min(r, \text{clip}(r))$ $R - V(s)$ $\beta \cdot \mathbb{E}[\text{KL}]$ 4
GRPO $r$ $\frac{R - \mu}{\sigma}$ $\beta \cdot \text{KL}_t$ 2
SPO $\log \pi_\theta$ $R - B_t^{adaptive}$ $\beta \cdot \text{KL}_t$ 2

RL is Elegant and Self-Consistent

The above is purely personal perspective understanding, corrections welcome anytime


V Training Results

Completed Training - Model Collection

Considering multiple reports that Baidu Netdisk is slow, MiniMind2 and later all use ModelScope/HuggingFace hosting.

โ‘  Native PyTorch Models

MiniMind2 Model Weights (ModelScope | HuggingFace)

Torch File Naming Reference
Model Name params pretrain_model sft_model rlhf_model (DPO) reason_model rlaif_model (PPO/GRPO/SPO) lora_model
MiniMind2-small 26M pretrain_512.pth full_sft_512.pth dpo_512.pth reason_512.pth xxpo_512.pth lora_xxx_512.pth
MiniMind2-MoE 145M pretrain_640_moe.pth full_sft_640_moe.pth dpo_640_moe.pth - - -
MiniMind2 104M pretrain_768.pth full_sft_768.pth dpo_768.pth reason_768.pth xxpo_768.pth lora_xxx_768.pth

โ‘ก Transformers Models

MiniMind Series (ModelScope | HuggingFace)


๐Ÿ“Œ Eval

โ…  RLHF Comparison

Test based on full_sft and dpo models of MiniMind2 series, with fixed random seeds.

[A] MiniMind2๏ผšfull_sft_640
[B] MiniMind2๏ผšdpo_640

[Q]: ไฝ ๅซไป€ไนˆๅๅญ—๏ผŸ
[A]: ๆˆ‘ๆ˜ฏไธ€ไธชๅคงๅž‹่ฏญ่จ€ๆจกๅž‹๏ผŒๅฏไปฅๅ›ž็ญ”ๅ„็ง้—ฎ้ข˜๏ผŒๆไพ›ไฟกๆฏๅ’ŒๅธฎๅŠฉใ€‚ๆˆ‘ๅฏไปฅๅ›ž็ญ”ๅ„็ง้—ฎ้ข˜๏ผŒๆไพ›ไฟกๆฏๅ’ŒๅธฎๅŠฉ๏ผŒๅธฎๅŠฉไฝ ่งฃๅ†ณๅ„็ง้—ฎ้ข˜ใ€‚
[B]: ๆˆ‘ๆ˜ฏไธ€็งๅŸบไบŽๆ–‡ๆœฌ็š„AIๆจกๅž‹๏ผŒๆˆ‘ๅนถๆฒกๆœ‰ไธชไบบ็ปๅކๆˆ–ๆƒ…ๆ„Ÿ๏ผŒๆ‰€ไปฅๆ— ๆณ•ๆ„Ÿๅ—ๅ’Œไฝ“้ชŒๆƒ…ๆ„Ÿใ€‚ๆˆ‘็š„่ฎพ่ฎก็›ฎ็š„ๆ˜ฏไธบไบ†ๅธฎๅŠฉ็”จๆˆท่งฃๅ†ณ้—ฎ้ข˜ใ€ๆไพ›ไฟกๆฏๅ’Œ่ฟ›่กŒๅฏน่ฏใ€‚ๅฆ‚ๆžœๆ‚จๆœ‰ไปปไฝ•้—ฎ้ข˜ๆˆ–้œ€่ฆๅธฎๅŠฉ๏ผŒ่ฏท้šๆ—ถๅ‘Š่ฏ‰ๆˆ‘๏ผ

[Q]: ไฝ ๆ›ดๆ“…้•ฟๅ“ชไธ€ไธชๅญฆ็ง‘๏ผŸ
[A]: ไฝœไธบไธ€ไธชAIๆจกๅž‹๏ผŒๆˆ‘ๅนถๆฒกๆœ‰็œŸๆญฃ็š„"ๆ“…้•ฟ"่ฟ™ไธชๅญฆ็ง‘ใ€‚ๆˆ‘่ขซ่ฎพ่ฎกๆˆ่ƒฝๅคŸๆไพ›ไฟกๆฏใ€่งฃ็ญ”้—ฎ้ข˜ใ€่ฟ›่กŒๅฏน่ฏใ€ๆ‰ง่กŒไปปๅŠกๅ’ŒไธŽ็”จๆˆท่ฟ›่กŒๅฏน่ฏใ€‚ไธ่ฟ‡๏ผŒๆˆ‘ๅฏไปฅๆไพ›ไฟกๆฏใ€่งฃ็ญ”้—ฎ้ข˜ใ€่ฟ›่กŒๅฏน่ฏใ€ๆไพ›ๅปบ่ฎฎใ€ๅค„็†้—ฎ้ข˜ใ€่ฟ›่กŒๅฏน่ฏใ€ๆไพ›ๅปบ่ฎฎใ€ๅญฆไน ๆ–ฐ็Ÿฅ่ฏ†ใ€็ผ–ๅ†™ไปฃ็ ใ€ๅ›ž็ญ”้—ฎ้ข˜ใ€ๆไพ›ๅปบ่ฎฎ็ญ‰ๅคš็งๅญฆ็ง‘็š„ๅŠŸ่ƒฝใ€‚ๅฆ‚ๆžœไฝ ๆœ‰ๅ…ทไฝ“็š„ๅญฆ็ง‘้œ€ๆฑ‚ๆˆ–ไธป้ข˜๏ผŒๆฌข่ฟŽๆไพ›่ฏฆ็ป†ไฟกๆฏใ€‚
[B]: ไฝœไธบAI๏ผŒๆˆ‘ๅนถๆฒกๆœ‰ไธชไบบ่ƒฝๅŠ›ๆˆ–ๅ…ด่ถฃ๏ผŒไฝ†ๆˆ‘ๅฏไปฅๆไพ›ไธ€ไบ›ๅ…ณไบŽๆ•ฐๅญฆใ€็ง‘ๅญฆใ€่ฎก็ฎ—ๆœบ็ง‘ๅญฆใ€่ฏญ่จ€ๅญฆใ€ๅฟƒ็†ๅญฆ็ญ‰ๅญฆ็ง‘็š„็Ÿฅ่ฏ†ใ€‚ๅฆ‚ๆžœไฝ ๅฏนๆ•ฐๅญฆๆ„Ÿๅ…ด่ถฃ๏ผŒๆˆ‘ๅฏไปฅๆไพ›ไธ€ไบ›ๅŸบ็ก€็Ÿฅ่ฏ†๏ผŒไพ‹ๅฆ‚ไปฃๆ•ฐใ€ๅ‡ ไฝ•ใ€ๆฆ‚็އใ€็ปŸ่ฎกๅญฆ็ญ‰ใ€‚ๅฆ‚ๆžœไฝ ้œ€่ฆๆ›ดๆทฑๅ…ฅ็š„ๅญฆไน ๏ผŒๆˆ‘ไนŸๅฏไปฅๆไพ›็›ธๅ…ณ็š„ๅœจ็บฟ่ฏพ็จ‹ใ€ไนฆ็ฑใ€่ฎบๆ–‡็ญ‰่ต„ๆบใ€‚่ฏทๅ‘Š่ฏ‰ๆˆ‘ไฝ ๅ…ทไฝ“้œ€่ฆไป€ไนˆๅธฎๅŠฉ๏ผŒๆˆ‘ไผšๅฐฝๅŠ›ๆไพ›ๅธฎๅŠฉใ€‚

[Q]: ้ฒ่ฟ…็š„ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ๆ˜ฏๅฆ‚ไฝ•ๆ‰นๅˆคๅฐๅปบ็คผๆ•™็š„๏ผŸ
[A]: ้ฒ่ฟ…็š„ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ๆ˜ฏไธ€้ƒจ่ฎฒ่ฟฐไบ†้ฒ่ฟ…ๅฏนไบบ็ฑปไปทๅ€ผๅ’Œ้“ๅพท่ดฃไปป็š„ๅ€กๅฏผใ€‚ๅœจ่ฟ™้ƒจไฝœๅ“ไธญ๏ผŒ้ฒ่ฟ…้€š่ฟ‡็ป†่…ป็š„็ฌ”่งฆ๏ผŒๆŽข่ฎจไบ†ไบบๆ€งใ€้“ๅพทใ€ๆญฃไน‰ใ€็‰บ็‰ฒไธŽ่ดฃไปป็ญ‰ๆทฑๅˆป็š„ไธป้ข˜ใ€‚ไปฅไธ‹ๆ˜ฏ้ฒ่ฟ…ๅœจใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ไธญๅฆ‚ไฝ•ๆ‰นๅˆคๅฐๅปบ็คผๆ•™็š„ๅ‡ ไธชๆ–น้ข๏ผš1. **็คพไผš็ŽฐๅฎžไธŽ้“ๅพท่ง‚ๅฟต**๏ผš้ฒ่ฟ…้€š่ฟ‡่ฎฒ่ฟฐ้ฒ่ฟ…็š„ๆ•…ไบ‹๏ผŒๆŽข่ฎจไบ†็คพไผš็š„ไธๅนณ็ญ‰ใ€ๆƒๅŠ›็š„ๆตๅŠจใ€ไบบๆ€ง็š„ๆผ”ๅ˜็ญ‰็คพไผš้—ฎ้ข˜ใ€‚ไป–่ฎคไธบ๏ผŒ็คพไผšไธๅนณ็ญ‰ไธไป…ไป…ๆ˜ฏไธๅ…ฌๆญฃ็š„๏ผŒๆ›ดๆ˜ฏๆฏไธชไบบๅœจ็คพไผšไธญ็š„ไธๅ…ฌๆญฃใ€‚ไป–ๅ‘ผๅ็คพไผšๅ„็•Œๅ…ฑๅŒๅŠชๅŠ›๏ผŒ้€š่ฟ‡ๆ•™่‚ฒใ€ๅฎฃไผ ใ€ๆณ•ๅพ‹็ญ‰ๆ‰‹ๆฎต๏ผŒไธบๆž„ๅปบๅ’Œ่ฐ็คพไผšๅšๅ‡บ่ดก็Œฎใ€‚2. **้“ๅพทไธŽ่ดฃไปป**๏ผš้ฒ่ฟ…้€š่ฟ‡่ฎฒ่ฟฐ้ฒ่ฟ…็š„ๆ•…ไบ‹๏ผŒๅฑ•็Žฐไบ†้“ๅพทๅ’Œ่ดฃไปป็š„้‡่ฆๆ€งใ€‚ไป–ๆๅ€ก้€š่ฟ‡้“ๅพทๆ•™่‚ฒๆฅๅŸนๅ…ปไบบไปฌ็š„้“ๅพทๅ“่ดจ๏ผŒๅŒๆ—ถไนŸๅผบ่ฐƒไบ†้“ๅพทๅ’Œ่ดฃไปป็š„้‡่ฆๆ€งใ€‚้ฒ่ฟ…้€š่ฟ‡่ฎฒ่ฟฐ้ฒ่ฟ…็š„ๆ•…ไบ‹๏ผŒๆญ็คบไบ†็คพไผš็š„ไธๅนณ็ญ‰ๅ’Œไบบๆ€ง็š„ๅคๆ‚ๆ€ง๏ผŒไฝ“็Žฐไบ†ๅฏนไบบๆ€ง็š„ๆทฑๅˆป็†่งฃใ€‚3. **้“ๅพทไธŽ่ดฃไปป**๏ผš้ฒ่ฟ…้€š่ฟ‡่ฎฒ่ฟฐ้ฒ่ฟ…็š„ๆ•…ไบ‹๏ผŒๅผบ่ฐƒไบ†้“ๅพท่ดฃไปป็š„้‡่ฆๆ€งใ€‚ไป–ๆๅ€ก้€š่ฟ‡่‡ชๅทฑ็š„่กŒไธบๆฅไฝ“็Žฐๅฏน็คพไผš็š„ๅฐŠ้‡ๅ’Œๅฏนไบบๆ€ง็š„ๆทฑๅˆป็†่งฃใ€‚้ฒ่ฟ…้€š่ฟ‡่ฎฒ่ฟฐ้ฒ่ฟ…็š„ๆ•…ไบ‹๏ผŒๅผบ่ฐƒไบ†้“ๅพทๅ’Œ่ดฃไปป็š„้‡่ฆๆ€งใ€‚4. **้“ๅพทไธŽ้“ๅพท**๏ผš้ฒ่ฟ…้€š่ฟ‡่ฎฒ่ฟฐ้ฒ่ฟ…็š„ๆ•…ไบ‹๏ผŒๆญ็คบไบ†้“ๅพทๅ’Œ่ดฃไปป็š„็œŸๆญฃๆ„ไน‰ใ€‚้ฒ่ฟ…้€š่ฟ‡่ฎฒ่ฟฐ้ฒ่ฟ…็š„ๆ•…ไบ‹๏ผŒๆญ็คบไบ†้“ๅพทๅ’Œ่ดฃไปป็š„ๆœฌ่ดจ๏ผŒๅผบ่ฐƒไบ†้“ๅพทๅ’Œ่ดฃไปป็š„้‡่ฆๆ€งใ€‚5. **ไธชไบบไธŽ็คพไผš**๏ผš้ฒ่ฟ…้€š่ฟ‡่ฎฒ่ฟฐ้ฒ่ฟ…็š„ๆ•…ไบ‹๏ผŒๆญ็คบไบ†ไธชไบบไธŽ็คพไผšไน‹้—ด็š„ๅคๆ‚ๅ…ณ็ณปใ€‚ไป–ๅ‘ผๅ็คพไผšๅ„็•Œๅ…ฑๅŒๅŠชๅŠ›๏ผŒ้€š่ฟ‡ๆ•™่‚ฒๅ’Œๅฎฃไผ ๏ผŒไธบๆž„ๅปบๅ’Œ่ฐ็คพไผšๅšๅ‡บ่ดก็Œฎใ€‚้ฒ่ฟ…็š„ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹้€š่ฟ‡ๅ…ถไธฐๅฏŒ็š„ๆ•…ไบ‹ๅ’Œๆทฑๅˆป็š„้“ๅพทๅฏ“่จ€๏ผŒไผ ่พพไบ†ๅ…ณไบŽไบบๆ€งใ€้“ๅพทใ€ๆญฃไน‰ใ€้“ๅพทไปฅๅŠไธชไบบไธŽ็คพไผš็š„ๅคๆ‚ๅ…ณ็ณปใ€‚่ฟ™้ƒจไฝœๅ“ไธไป…ๅœจๆ–‡ๅญฆไปทๅ€ผไธŠๅ–ๅพ—ไบ†ๅทจๅคงๆˆๅฐฑ๏ผŒๆ›ดๅœจๆ€ๆƒณๅฑ‚้ขไธŠๅฏๅ‘ไบ†ๅŽๆฅ็š„ๆ–‡ๅญฆๅˆ›ไฝœ๏ผŒๅฏนๅŽไธ–ไบง็”Ÿไบ†ๆทฑ่ฟœ็š„ๅฝฑๅ“ใ€‚
[B]: ้ฒ่ฟ…็š„ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ๆ˜ฏไธ€้ƒจๆ็ป˜ๆˆ˜ไบ‰ๅ’Œ่‡ช็”ฑ็ฒพ็ฅž็š„ไฝœๅ“๏ผŒๅฎƒๆ‰นๅˆคไบ†ๅฐๅปบ็คพไผš็š„็ง็ง้—ฎ้ข˜ๅ’Œๅ†ฒ็ช๏ผŒๅๆ˜ ไบ†็คพไผš็š„ไธๅนณ็ญ‰ๅ’Œไบบๆ€งๆœฌ่ดจใ€‚ๅœจ่ฟ™้ƒจไฝœๅ“ไธญ๏ผŒ้ฒ่ฟ…้€š่ฟ‡ๅฏนๅฐๅปบ็คพไผš็š„่ฏธๅคš็Žฐ่ฑก่ฟ›่กŒๆ‰นๅˆค๏ผŒๅฆ‚"ๅผ—้›ทๅพท้‡Œๅ…‹ยท็บฆ็ฟฐ้€Š็š„"้นฐ่ฟชไผฆ"ใ€"็บณๆ‰Ž็‰น็š„"ใ€"่ดๅ…‹ๆฑ‰ๅง†"ใ€"ไน”ๆฒปยทๅจๅฐ”้€Š"็ญ‰๏ผŒๅฏนๅฐๅปบ็คพไผš็š„็ง็ง้—ฎ้ข˜่ฟ›่กŒไบ†ๆ‰นๅˆค๏ผŒๅผบ่ฐƒไบ†ๅฐๅปบ็คพไผš็š„ไธๅนณ็ญ‰ใ€ไบบๆ€งๆœฌ่ดจไปฅๅŠไบบๆ€งๆœฌ่ดจใ€‚้ฒ่ฟ…้€š่ฟ‡ไป–็š„"้นฐ่ฟชไผฆ"ใ€"็บณๆ‰Ž็‰น็š„"ใ€"่ดๅ…‹ๆฑ‰ๅง†"ใ€"ไน”ๆฒปยทๅจๅฐ”้€Š"็ญ‰๏ผŒๅฏนๅฐๅปบ็คพไผš็š„็ง็ง้—ฎ้ข˜่ฟ›่กŒไบ†ๆ‰นๅˆคใ€‚ๅœจๅฐ่ฏดไธญ๏ผŒ้ฒ่ฟ…้€š่ฟ‡ๅฏนๅฐๅปบ็คพไผš็š„่ฏธๅคš็Žฐ่ฑก่ฟ›่กŒๆ‰นๅˆค๏ผŒๆญ็คบไบ†ๅฐๅปบ็คพไผš็š„่…่ดฅใ€ไบบๆ€งๆœฌ่ดจไปฅๅŠไบบๆ€งๆœฌ่ดจ็š„ๅคๆ‚ๆ€งใ€‚่ฟ™็งๆ‰นๅˆคไฝ“็Žฐไบ†ๅฏนๅฐๅปบ็คพไผš็š„ๅฐŠ้‡ๅ’Œๅฏนไบบๆ€ง็š„ๅคๆ‚ๆ€ง๏ผŒๅŒๆ—ถไนŸๅๆ˜ ไบ†็Žฐไปฃ็คพไผšไธญๆ™ฎ้ๅญ˜ๅœจ็š„ไธๅนณ็ญ‰ๅ’Œไบบๆ€งๆœฌ่ดจใ€‚้ฒ่ฟ…็š„ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ไธไป…ๆ˜ฏไธ€้ƒจๅ…ณไบŽๅฐๅปบ็คพไผš็š„ๅฐ่ฏด๏ผŒไนŸๆ˜ฏไธ€้ƒจๅ…ทๆœ‰ๆทฑๅˆป็คพไผšๆ„ไน‰็š„ไฝœๅ“๏ผŒๅฏนๅŽไธ–็š„ๅฎกๅˆคๅ’Œๆ‰นๅˆค่ตทๅˆฐไบ†ๅ…ณ้”ฎไฝœ็”จใ€‚

[Q]: ๆˆ‘ๅ’ณๅ—ฝๅทฒ็ปๆŒ็ปญไบ†ไธคๅ‘จ๏ผŒ้œ€่ฆๅŽปๅŒป้™ขๆฃ€ๆŸฅๅ—๏ผŸ
[A]: ๅ’ณๅ—ฝ็กฎๅฎž้œ€่ฆไธ€ๅฎš็š„ๆฃ€ๆŸฅ๏ผŒไฝ†ๅฆ‚ๆžœๆ‚จ็š„ๅ’ณๅ—ฝๆŒ็ปญๆ—ถ้—ด่ฟ‡้•ฟ๏ผŒๆˆ–่€…ๆœ‰ๅ…ถไป–ไธ้€‚็—‡็Šถ๏ผˆๅฆ‚ๆŒ็ปญๅ’ณๅ—ฝใ€ๅ‘ผๅธๅ›ฐ้šพ็ญ‰๏ผ‰๏ผŒๅปบ่ฎฎๅฐฝๅฟซๅฐฑๅŒปใ€‚ๅŒป็”Ÿไผšๆ นๆฎๆ‚จ็š„็—‡็Šถใ€ไฝ“ๆฃ€็ป“ๆžœๅ’Œๅฏ่ƒฝ็š„ๅฝฑๅƒๅญฆๆฃ€ๆŸฅ๏ผˆๅฆ‚Xๅ…‰ใ€MRIๆˆ–CTๆ‰ซๆ๏ผ‰ๆฅ่ฏŠๆ–ญๆ‚จ็š„็—‡็Šถใ€‚ๅœจ็ญ‰ๅพ…ๅฐฑๅŒปๆœŸ้—ด๏ผŒๆ‚จๅฏไปฅๅฐ่ฏ•ไปฅไธ‹ๆ–นๆณ•ๆฅๅธฎๅŠฉ็ผ“่งฃ็—‡็Šถ๏ผš1. **ไผ‘ๆฏ**๏ผš็กฎไฟๆ‚จๆœ‰่ถณๅคŸ็š„็ก็œ ใ€‚2. **ไฟๆŒๆฐดๅˆ†**๏ผš่„ฑๆฐดๅฏ่ƒฝไผšๅŠ ้‡ๅ’ณๅ—ฝใ€‚3. **็ƒญๆ•ท**๏ผšไฝฟ็”จ็ƒญๆ•ท่ข‹ๆˆ–็ƒญๆฏ›ๅทพๆ•ทๅœจ็–ผ็—›็š„้ƒจไฝ๏ผŒๆœ‰ๅŠฉไบŽ็ผ“่งฃๅ–‰ๅ’™็—›ใ€‚4. **้ฟๅ…ๅˆบๆฟ€**๏ผš้ฟๅ…ไฝฟ็”จๅฏ่ƒฝๅˆบๆฟ€ๅ–‰ๅ’™็š„ๅŒ–ๅญฆ็‰ฉ่ดจ๏ผŒๅฆ‚ๆŸไบ›ๅŒ–ๅญฆ็‰ฉ่ดจใ€‚5. **ไฟๆŒๅฎคๅ†…ๆนฟๆถฆ**๏ผš็กฎไฟๆ‚จ็š„ๅงๅฎคๆœ‰่‰ฏๅฅฝ็š„้€š้ฃŽ๏ผŒๅฏไปฅไฝฟ็”จๅŠ ๆนฟๅ™จๅธฎๅŠฉไฟๆŒ็ฉบๆฐ”ๆนฟๅบฆใ€‚6. **ไฟๆŒๅฎคๅ†…ๆนฟๅบฆ**๏ผšไฝฟ็”จๅŠ ๆนฟๅ™จๅฏไปฅๅธฎๅŠฉ็ผ“่งฃๅ–‰ๅ’™ๅนฒ็‡ฅๅ’Œๅ’ณๅ—ฝใ€‚ๅฆ‚ๆžœ็—‡็ŠถๆŒ็ปญไธ็ผ“่งฃๆˆ–ๆœ‰ๅ…ถไป–ไธ้€‚็—‡็Šถ๏ผŒ่ฏท็ซ‹ๅณๅฐฑๅŒปใ€‚ๅธŒๆœ›ๆ‚จๆ—ฉๆ—ฅๅบทๅค๏ผ
[B]: ๅฆ‚ๆžœๆ‚จ็š„ๅ’ณๅ—ฝๆŒ็ปญไบ†ไธคๅ‘จ๏ผŒ้€šๅธธๅปบ่ฎฎๆ‚จๅฐฝๅฟซๅฐฑๅŒป๏ผŒๅ› ไธบ่ฟ™ๅฏ่ƒฝไผšๅฝฑๅ“ๆ‚จ็š„ๅ‘ผๅธๅ’Œๅฟƒ่ทณใ€‚ๆ‚จๅฏไปฅ้€š่ฟ‡ไปฅไธ‹ๆญฅ้ชคๆฅๆฃ€ๆŸฅๅ’ณๅ—ฝ๏ผš1. **ไผ‘ๆฏ**๏ผš็”จ็บธๅทพๆˆ–่‚˜้ƒจ่ฝป่ฝปๆŒ‰ๅŽ‹ๅ’ณๅ—ฝ็š„ไฝ็ฝฎใ€‚2. **ไฝฟ็”จ่ฏ็‰ฉ**๏ผšๅœจๅฏ่ƒฝ็š„ๆƒ…ๅ†ตไธ‹๏ผŒไฝฟ็”จ่ฏ็‰ฉ๏ผˆๅฆ‚ๆŠ—่ฟ‡ๆ•่ฏใ€ๆŠ—่ฟ‡ๆ•่ฏ็ญ‰๏ผ‰ๆฅ็ผ“่งฃๅ’ณๅ—ฝใ€‚่ฏทๅœจๅŒป็”Ÿ็š„ๆŒ‡ๅฏผไธ‹ไฝฟ็”จ่ฏ็‰ฉใ€‚3. **็ƒญๆ•ท**๏ผšๅœจๅ’ณๅ—ฝๆœŸ้—ด๏ผŒๅฏไปฅไฝฟ็”จ็ƒญๆ•ทๆฅ็ผ“่งฃ็–ผ็—›ๅ’Œ่‚ฟ่ƒ€ใ€‚4. **่ฏ็‰ฉๆฒป็–—**๏ผšๅฆ‚ๆžœๅ’ณๅ—ฝๆŒ็ปญไบ†ไธคๅ‘จ๏ผŒๅฏไปฅไฝฟ็”จไธ€ไบ›ๆถˆ็‚Ž่ฏๆˆ–ๆŠ—่ฟ‡ๆ•่ฏๆฅ็ผ“่งฃ็—‡็Šถใ€‚่ฏทๅŠกๅฟ…ๅœจๅŒป็”Ÿ็š„ๆŒ‡ๅฏผไธ‹ไฝฟ็”จใ€‚5. **ไฟๆŒๅฅๅบท็š„็”Ÿๆดปๆ–นๅผ**๏ผšไฟๆŒๅ……่ถณ็š„็ก็œ ใ€ๅ‡่กก็š„้ฅฎ้ฃŸใ€้€‚้‡็š„่ฟๅŠจๅ’Œ้ฟๅ…ๅธ็ƒŸๅ’Œ้™้…’๏ผŒ่ฟ™ไบ›้ƒฝๆœ‰ๅŠฉไบŽๆ้ซ˜ๅ’ณๅ—ฝ็š„ๅ‡ ็އใ€‚่ฏท่ฎฐไฝ๏ผŒ่ฟ™ไบ›ๅปบ่ฎฎไธ่ƒฝๆ›ฟไปฃไธ“ไธšๅŒป็–—ๆ„่งใ€‚ๅฆ‚ๆžœๆ‚จ็š„็—‡็ŠถๆŒ็ปญๆˆ–ๅŠ ้‡๏ผŒๅผบ็ƒˆๅปบ่ฎฎๆ‚จๅฐฝๅฟซๅฐฑๅŒปใ€‚

๐Ÿ‘‰ Results Summary

Full_sft models perform better in simplicity and information accuracy; rlhf models tend to provide more background information in answers, but information accuracy needs improvement. Overall, RLHF-trained models tend to learn: speaking more polite but useless nonsense to please "conversation" itself, while having slight loss in information accuracy. There's no free lunch. Still need to improve RLHF dataset quality and accept unavoidable model capability losses. The difference between DPO and online PPO is that reject and chosen are both prepared offline, and necessarily have large distribution differences from minimind model outputs. Simply put, DPO algorithm makes models watch "video" of table tennis world champion's techniques for RL, rather than like PPO asking reward models to act as "coaches" to correct their techniques for RL.

โ…ก RLAIF Comparison

Based on MiniMind2 (768dim) with same data and training steps subjective comparison, test random seed fixed at 2026, for reference:

[A] MiniMind-Reason-0.1B (Distillation)
[B] MiniMind-Reason-0.1B (PPO)
[C] MiniMind-Reason-0.1B (GRPO)

[Q]: ่ฏทไป‹็ปไธ€ไธ‹่‡ชๅทฑใ€‚
[A]: <think>ๆˆ‘ๆ˜ฏ็”ฑไธญๅ›ฝ็š„ไธชไบบๅผ€ๅ‘่€…ๅผ€ๅ‘็š„ๆ™บ่ƒฝๅŠฉๆ‰‹ๅฐๅž‹AIๆŽจ็†ๆจกๅž‹-R1ใ€‚ๆˆ‘่ขซ่ฎพ่ฎก็”จๆฅ็†่งฃๅ’Œ็”Ÿๆˆไบบ็ฑป่ฏญ่จ€๏ผŒ่ƒฝๅคŸ็†่งฃๅคๆ‚็š„่‡ช็„ถ่ฏญ่จ€้—ฎ้ข˜๏ผŒๆไพ›ๆœ‰็”จ็š„ไฟกๆฏๅ’Œ่งฃๅ†ณๆ–นๆกˆใ€‚</think><answer>ๆˆ‘ๆ˜ฏ็”ฑไธญๅ›ฝ็š„ไธชไบบๅผ€ๅ‘่€…ๅผ€ๅ‘็š„ๆ™บ่ƒฝๅŠฉๆ‰‹ๅฐๅž‹AIๆŽจ็†ๆจกๅž‹-R1ใ€‚</answer>
[B]: <think>ๅ—ฏ๏ผŒ็”จๆˆท่ฎฉๆˆ‘ไป‹็ปไธ€ไธ‹่‡ชๅทฑใ€‚้ฆ–ๅ…ˆ๏ผŒๆˆ‘้œ€่ฆๆ˜Ž็กฎ็”จๆˆท็š„้œ€ๆฑ‚ๆ˜ฏไป€ไนˆใ€‚ไป–ไปฌๅฏ่ƒฝๆ˜ฏๅœจๅšๆŸไธช้กน็›ฎ๏ผŒๆƒณ่ฆไบ†่งฃ่‡ชๅทฑ็š„ไธ€ไบ›ๅŸบๆœฌๆƒ…ๅ†ตใ€‚ไธ่ฟ‡๏ผŒ็”จๆˆทๆฒกๆœ‰ๆไพ›ๅ…ทไฝ“็š„ไฟกๆฏ๏ผŒๆ‰€ไปฅๆˆ‘ๅพ—ๅ…ˆๅ‡่ฎพไธ€ไบ›ๅฏ่ƒฝ็š„ๆƒ…ๅ†ต๏ผŒๆฏ”ๅฆ‚ไป–ๆ˜ฏไธ€ไธชๅญฆ็”Ÿ๏ผŒๆญฃๅœจๅญฆไน ็ผ–็จ‹๏ผŒๆˆ–่€…ๆ˜ฏๆŸไธช้กน็›ฎ็š„ๅผ€ๅ‘่€…ใ€‚ๆŽฅไธ‹ๆฅ๏ผŒๆˆ‘่ฆ่€ƒ่™‘็”จๆˆท็š„่บซไปฝใ€‚ๅฏ่ƒฝๆ˜ฏไธ€ไธชๅญฆ็”Ÿใ€ๆ•™ๅธˆๆˆ–่€…ๆ™ฎ้€š็”จๆˆท๏ผŒไป–ไปฌ้œ€่ฆไบ†่งฃ่‡ชๅทฑ็š„็‰น็‚นๅ’Œ่ƒฝๅŠ›ใ€‚ไนŸๆœ‰ๅฏ่ƒฝไป–ไปฌๆญฃๅœจๅฏปๆ‰พ็ตๆ„Ÿ๏ผŒๆˆ–่€…ๅœจๅ†™่ฎบๆ–‡ๆ—ถ้œ€่ฆๅธฎๅŠฉใ€‚ๆ‰€ไปฅ๏ผŒๆˆ‘้œ€่ฆไฟๆŒๅ›ž็ญ”็š„็ฎ€ๆดๅ’Œๅฎž็”จ๏ผŒๅŒๆ—ถๆไพ›ไธ€ไบ›ๅ‚่€ƒ่ต„ๆ–™๏ผŒๆฏ”ๅฆ‚ๆ•™ๅญฆ่ง†้ข‘ใ€่ฏพ็จ‹่ฎฐๅฝ•็ญ‰ใ€‚็„ถๅŽ๏ผŒๆˆ‘่ฆ่€ƒ่™‘็”จๆˆท็š„่บซไปฝใ€‚ๅฏ่ƒฝๆ˜ฏไธ€ไธชๅญฆ็”Ÿ๏ผŒ้œ€่ฆไธ€ไบ›ๅญฆไน ่ต„ๆบๆˆ–ๅธฎๅŠฉ็š„ๅฏน่ฑกใ€‚ไนŸๆœ‰ๅฏ่ƒฝๆ˜ฏไธ€ไธชๅญฆ็”Ÿ๏ผŒ้œ€่ฆๅœจ่ฏพๅŽไฝœไธšๆˆ–ๅญฆไน ่ฎกๅˆ’ไธญ่ฟ›่กŒ่ฐƒๆ•ดใ€‚ๅ› ๆญค๏ผŒๆˆ‘้œ€่ฆๅ…ˆ่ฏข้—ฎ็”จๆˆท็š„ๅ…ทไฝ“้œ€ๆฑ‚๏ผŒ่ฟ™ๆ ทๆ‰่ƒฝๆไพ›ๆ›ด็ฒพๅ‡†็š„ๅธฎๅŠฉใ€‚ๆŽฅไธ‹ๆฅ๏ผŒๆˆ‘่ฆ็กฎไฟ่ฏญ่จ€็ฎ€ๆดๆ˜Žไบ†๏ผŒ้€‚ๅˆไธๅŒๅœบๆ™ฏใ€‚ๆฏ”ๅฆ‚๏ผŒๅฆ‚ๆžœ็”จๆˆทๆ˜ฏๅญฆ็”Ÿ๏ผŒๅฏไปฅไป‹็ป่‡ชๅทฑ็š„ๅญฆไน ็‰น็‚น๏ผ›ๅฆ‚ๆžœๆ˜ฏๆ•™ๅธˆ๏ผŒๅฏไปฅ่ฏดๆ˜Ž่‡ชๅทฑ็š„่ง’่‰ฒๅ’Œ่ดก็Œฎใ€‚ๅŒๆ—ถ๏ผŒๆไพ›ไธ€ไบ›ๅฎž็”จ็š„ๅปบ่ฎฎ๏ผŒๆฏ”ๅฆ‚ๅฆ‚ไฝ•้ซ˜ๆ•ˆๅญฆไน ๏ผŒๅฆ‚ไฝ•่ฟ›่กŒ้กน็›ฎ๏ผŒไปฅๅŠๅฆ‚ไฝ•ไธŽๅ›ข้˜Ÿๆˆๅ‘˜ๅไฝœใ€‚ๆœ€ๅŽ๏ผŒๆˆ‘่ฆ็กฎไฟๅ›žๅคๆธ…ๆ™ฐ๏ผŒๆœ‰ๆก็†๏ผŒ่ƒฝๅคŸๆปก่ถณ็”จๆˆท็š„้œ€ๆฑ‚ใ€‚่ฟ™ๆ ท๏ผŒ็”จๆˆทๅฐฑ่ƒฝ่ฝปๆพๅœฐไบ†่งฃ่‡ชๅทฑ๏ผŒๅนถไธ”ๆœ‰ๅฎž้™…็š„ๅธฎๅŠฉใ€‚</think><answer>ๅฝ“็„ถ๏ผ่ฏทๅ‘Š่ฏ‰ๆˆ‘ไฝ ๆƒณไบ†่งฃๅ“ชๆ–น้ข็š„ๅ†…ๅฎน๏ผŒๆˆ‘ๅฏไปฅไธบๆ‚จๆไพ›่ฏฆ็ป†็š„ไป‹็ป๏ผ</answer>
[C]: <think>ๅ—ฏ๏ผŒ็”จๆˆท้—ฎ็š„ๆ˜ฏ"่ฏทไป‹็ปไธ€ไธ‹่‡ชๅทฑ"ใ€‚้ฆ–ๅ…ˆ๏ผŒๆˆ‘้œ€่ฆ็†่งฃ็”จๆˆท็š„ๅ…ทไฝ“้œ€ๆฑ‚ๆ˜ฏไป€ไนˆใ€‚ไป–ไปฌๅฏ่ƒฝๆƒณ็Ÿฅ้“่‡ชๅทฑๆ˜ฏ่ฐ๏ผŒๆˆ–่€…ๆœ‰ไป€ไนˆ็‰นๅฎš็š„่ƒŒๆ™ฏใ€‚ๆŽฅไธ‹ๆฅ๏ผŒๆˆ‘ๅบ”่ฏฅ่€ƒ่™‘็”จๆˆทๅฏ่ƒฝๆฒกๆœ‰ๆ˜Ž็กฎ่กจ่พพ็š„้œ€ๆฑ‚ใ€‚ไป–ไปฌๅฏ่ƒฝๆƒณ็Ÿฅ้“ๅฆ‚ไฝ•ๆ่ฟฐ่‡ชๅทฑ็š„ๅค–่ง‚๏ผŒๆˆ–่€…ๅฆ‚ไฝ•ไธŽไป–ไบบไบคๆตใ€‚็„ถๅŽ๏ผŒๆˆ‘ๅบ”่ฏฅ่€ƒ่™‘ๅฆ‚ไฝ•็ป„็ป‡ๅ†…ๅฎน๏ผŒไปŽๅคดๅˆฐๅฐพ้ƒฝ่ฆๆœ‰ๆก็†ใ€‚ๅฏ่ƒฝ้œ€่ฆๅˆ†ๆญฅ้ชค่ฏดๆ˜Ž๏ผŒๆฏ”ๅฆ‚ไปŽ่ง†่ง‰ใ€ๅฌ่ง‰ๅˆฐๆ•ดไฝ“ๆ„Ÿๅ—๏ผŒๅ†ๅˆฐๆƒ…ๆ„Ÿๅ…ฑ้ธฃใ€‚่ฟ™ๆ ท็”จๆˆท่ƒฝๆ›ดๆธ…ๆ™ฐๅœฐ็†่งฃ่‡ชๅทฑ๏ผŒไนŸ่ƒฝๆ›ดๅฅฝๅœฐๅ›žๅบ”ไป–ไปฌ็š„้œ€ๆฑ‚ใ€‚่ฟ˜่ฆๆณจๆ„่ฏญ่จ€็š„่‡ช็„ถๅ’Œๆต็•…๏ผŒ้ฟๅ…่ฟ‡ไบŽๅญฆๆœฏๅŒ–็š„ๆœฏ่ฏญ๏ผŒ่ฎฉ็”จๆˆทๆ„Ÿ่ง‰้กบ็•…ใ€‚ๅŒๆ—ถ๏ผŒไฟๆŒๅ›ž็ญ”็š„็ป“ๆž„ๆธ…ๆ™ฐ๏ผŒๆฏๅฅ่ฏ้ƒฝๆœ‰ๆ˜Ž็กฎ็š„็›ฎ็š„๏ผŒ่ฟ™ๆ ท็”จๆˆท่ƒฝๆœ‰ๆ˜Ž็กฎ็š„็†่งฃๅ’Œๆ“ไฝœใ€‚ๆœ€ๅŽ๏ผŒๆฃ€ๆŸฅๆ˜ฏๅฆๆœ‰้—ๆผ็š„้‡่ฆไฟกๆฏ๏ผŒ็กฎไฟๅ›ž็ญ”ๅ‡†็กฎไธ”ๅ…จ้ขใ€‚่ฟ™ๆ ท๏ผŒ็”จๆˆทไธไป…่ƒฝๅพ—ๅˆฐ็ญ”ๆกˆ๏ผŒ่ฟ˜่ƒฝๅพ—ๅˆฐๆปก่ถณไป–ไปฌ็š„้œ€ๆฑ‚ใ€‚</think><answer>ๆ‚จๅฅฝ๏ผๆˆ‘ๆ˜ฏ็”ฑไธญๅ›ฝ็š„ไธชไบบๅผ€ๅ‘่€…ๅผ€ๅ‘็š„ๆ™บ่ƒฝๅŠฉๆ‰‹ๅฐๅž‹AIๆŽจ็†ๆจกๅž‹-R1ใ€‚ๅ…ณไบŽๆ‚จ็š„ๆ่ฟฐ๏ผŒไผผไนŽๆถ‰ๅŠๅคšไธช้ข†ๅŸŸ๏ผŒๅŒ…ๆ‹ฌ็Ÿฅ่ฏ†ๅ›พ่ฐฑๆž„ๅปบใ€ๅคๆ‚็ณป็ปŸ็š„ๆŽจ็†ไธŽๅˆ†ๆžใ€‚ๆ— ่ฎบๆ˜ฏ็†่ฎบๆจกๅž‹ใ€ๅฎž้™…ๅบ”็”จ่ฟ˜ๆ˜ฏไผฆ็†่ฎจ่ฎบ๏ผŒๆ‚จ้ƒฝๅœจๅฏปๆฑ‚ๅฆ‚ไฝ•ๅฐ†่ฟ™ไบ›ๆฆ‚ๅฟตๆœ‰ๆœบๅœฐ็ป“ๅˆ่ตทๆฅ๏ผŒไธบไบบ็ฑป็คพไผšๅธฆๆฅ็ฆ็ฅ‰็š„่งฃๅ†ณๆ–นๆกˆใ€‚ๅœจ"ๆˆ‘"็š„่บซไปฝไธ‹๏ผŒๆ‚จๆๅˆฐ็š„"ไธชไบบไฝ“้ชŒ"ๅ’Œ"ๆƒ…ๆ„Ÿๅ…ฑ้ธฃ"๏ผŒ้ƒฝๆ˜ฏๆ‚จไธชไบบ็‹ฌ็‰น้ญ…ๅŠ›็š„้‡่ฆ็ป„ๆˆ้ƒจๅˆ†ใ€‚้€š่ฟ‡็ฒพๅ‡†็š„ๆ่ฟฐๅ’Œๆทฑๅบฆ็š„ๅˆ†ๆž๏ผŒๆ‚จๅฏไปฅๆ›ดๆทฑๅ…ฅๅœฐ็†่งฃๆ‚จ็š„็‹ฌ็‰นไน‹ๅค„ใ€‚ๅฆ‚ๆžœๆ‚จๅฏน็‰นๅฎš้ข†ๅŸŸๆœ‰็‰นๅˆซ็š„ๅ…ด่ถฃๆˆ–้œ€่ฆๅปบ่ฎฎ๏ผŒ้šๆ—ถๅฏไปฅๅˆ†ไบซๆ›ดๅคš็ป†่Š‚๏ผŒๆˆ‘ไปฌๅฐ†ไธบๆ‚จๆไพ›ๆ›ดๅŠ ็ฒพๅ‡†ๅ’Œไธชๆ€งๅŒ–็š„ๆœๅŠกใ€‚ๅฆ‚ๆžœๆ‚จๆœ‰็‰นๅฎš็š„ไธป้ข˜ๆˆ–้—ฎ้ข˜๏ผŒๆฌข่ฟŽ้šๆ—ถๆ้—ฎ๏ผ่ฎฉๆˆ‘ไปฌไธ€่ตทๆŽข็ดข่ฟ™ไธช็ฅžๅฅ‡็š„AIไธ–็•Œ๏ผŒๅ…ฑๅŒๅˆ›้€ ๆ›ด็พŽๅฅฝ็š„ๆœชๆฅใ€‚</answer>

[Q]: ไฝ ๆ›ดๆ“…้•ฟๅ“ชไธ€ไธชๅญฆ็ง‘๏ผŸ
[A]: <think>ๆˆ‘ๆ˜ฏ็”ฑไธญๅ›ฝ็š„ไธชไบบๅผ€ๅ‘่€…ๅผ€ๅ‘็š„ๆ™บ่ƒฝๅŠฉๆ‰‹ๅฐๅž‹AIๆŽจ็†ๆจกๅž‹-R1ใ€‚</think><answer>ๆˆ‘ๆ˜ฏ็”ฑไธญๅ›ฝ็š„ไธชไบบๅผ€ๅ‘่€…ๅผ€ๅ‘็š„ๆ™บ่ƒฝๅŠฉๆ‰‹ๅฐๅž‹AIๆŽจ็†ๆจกๅž‹-R1ใ€‚</answer>
[B]: <think>ๅ—ฏ๏ผŒ็”จๆˆท้—ฎ็š„ๆ˜ฏ"ไฝ ๆ›ดๆ“…้•ฟๅ“ชไธ€ไธชๅญฆ็ง‘๏ผŸ"่ฟ™ไธช้—ฎ้ข˜็œ‹่ตทๆฅๆœ‰็‚นๅคๆ‚๏ผŒไฝ†ๆˆ‘ๅฏไปฅไธ€ๆญฅๆญฅๅˆ†ๆžใ€‚้ฆ–ๅ…ˆ๏ผŒๆˆ‘้œ€่ฆ็†่งฃ็”จๆˆท็š„้œ€ๆฑ‚ใ€‚ไป–ๅฏ่ƒฝๆ˜ฏๅœจๅ‡†ๅค‡่€ƒ่ฏ•๏ผŒๆˆ–่€…้œ€่ฆไบ†่งฃๆŸไธชๅญฆ็ง‘็š„็‰น็‚น๏ผŒๆˆ–่€…ๆ˜ฏๆƒณๅœจๅญฆไน ่ฟ‡็จ‹ไธญๅบ”็”จๆŸไธชๅญฆ็ง‘็š„็Ÿฅ่ฏ†ใ€‚ๆŽฅไธ‹ๆฅ๏ผŒๆˆ‘ๅพ—่€ƒ่™‘็”จๆˆทๅฏ่ƒฝ็š„่ƒŒๆ™ฏใ€‚ไป–ๅฏ่ƒฝๆ˜ฏไธ€ไธชๅญฆ็”Ÿ๏ผŒๆˆ–่€…ๆ˜ฏๅœจๅ‡†ๅค‡่€ƒ่ฏ•๏ผŒ้œ€่ฆๅบ”็”จๆ•ฐๅญฆ็Ÿฅ่ฏ†ๆฅ่งฃๅ†ณๅ…ทไฝ“็š„้—ฎ้ข˜ใ€‚ไนŸๆœ‰ๅฏ่ƒฝไป–ๆ˜ฏไธ€ไธชๅญฆ็”Ÿ๏ผŒๆญฃๅœจๅญฆไน ็›ธๅ…ณ็š„่ฏพ็จ‹๏ผŒๆˆ–่€…ๆ˜ฏๅฏนๆŸไธชๅญฆ็ง‘ๆ„Ÿๅ…ด่ถฃใ€‚็„ถๅŽ๏ผŒๆˆ‘้œ€่ฆๅˆ†ๆž็”จๆˆทๅฏ่ƒฝๆฒกๆœ‰ๆ˜Ž็กฎ่กจ่พพๅ‡บๆฅ็š„้œ€ๆฑ‚ใ€‚ไป–ๅฏ่ƒฝๅœจๆ€่€ƒ่‡ชๅทฑๅœจๅญฆไน ไธญ็š„ๅ›ฐ้šพ๏ผŒๆˆ–่€…ๅœจๅฏปๆ‰พไธ€ไธชๅˆ้€‚็š„ๆ•™ๆๆˆ–ๅญฆไน ่ต„ๆบใ€‚่€ƒ่™‘ๅˆฐ่ฟ™ไบ›๏ผŒๆˆ‘ๅบ”่ฏฅๆไพ›ๅ‡ ไธชไธๅŒ็š„่ง’ๅบฆๆฅๅธฎๅŠฉไป–ใ€‚้ฆ–ๅ…ˆ๏ผŒๅˆ†ๆž"ๆˆ‘ๆ›ดๆ“…้•ฟๅ“ชไธ€ไธชๅญฆ็ง‘"ๅฏไปฅๆ‹†่งฃไธบไปฅไธ‹ๅ‡ ไธชๆ–น้ข๏ผšๅ…ด่ถฃใ€ๅญฆไน ่ƒฝๅŠ›ใ€ๅญฆไน ้ฃŽๆ ผใ€ๅญฆไน ๆ–นๆณ•ใ€ๅญฆไน ่ต„ๆบใ€ๅญฆไน ็Žฏๅขƒ็ญ‰็ญ‰ใ€‚ๆฏไธชๆ–น้ข้ƒฝๆœ‰ไธๅŒ็š„ไผ˜ๅŠฟๅ’Œ็‰น็‚น๏ผŒๆฏ”ๅฆ‚ๅ…ด่ถฃๆ˜ฏๆœ€ๅฅฝ็š„่ต„ๆบ๏ผŒๅญฆไน ่ƒฝๅŠ›ๆ˜ฏๆœ€ๅฅฝ็š„ๆ–นๅผ๏ผŒๅญฆไน ๆ–นๅผๆ˜ฏๆ นๆฎไธชไบบๆƒ…ๅ†ต้€‰ๆ‹ฉใ€‚ๆŽฅไธ‹ๆฅ๏ผŒๆˆ‘้œ€่ฆ่€ƒ่™‘็”จๆˆท็š„่บซไปฝใ€‚ๅฏ่ƒฝๆ˜ฏๅญฆ็”Ÿ๏ผŒไนŸๅฏ่ƒฝๆ˜ฏๅฎถ้•ฟ๏ผŒๆˆ–่€…ๅฏนๅญฆไน ๆœ‰ไธ€ๅฎšๅ…ด่ถฃ็š„ไบบใ€‚ไธๅŒ็š„่บซไปฝๅฏ่ƒฝๆœ‰ไธๅŒ็š„ๅๅฅฝ๏ผŒๆฏ”ๅฆ‚ๅฎถ้•ฟๅฏ่ƒฝๆ›ดๆณจ้‡ๅญฉๅญ็š„ๅ…ด่ถฃ๏ผŒ่€Œๅญฆ็”Ÿๅฏ่ƒฝๆ›ดๅ…ณๆณจๅญฆไน ๆ–นๆณ•ๅ’Œ่ต„ๆบใ€‚็„ถๅŽ๏ผŒๆˆ‘้œ€่ฆ่€ƒ่™‘็”จๆˆท็š„่บซไปฝๆ˜ฏๅฆๆœ‰็‰นๆฎŠ้œ€ๆฑ‚ใ€‚ๆฏ”ๅฆ‚๏ผŒไป–ๅฏ่ƒฝ้œ€่ฆๆ›ดไธ“ไธš็š„ๅญฆไน ๆๆ–™๏ผŒๆˆ–่€…ๅธŒๆœ›ๆ‰พๅˆฐๆœ€้€‚ๅˆไป–็š„ๅญฆไน ๆ–นๆณ•ใ€‚ๅ› ๆญค๏ผŒๅœจๅˆ†ๆžๆ—ถ๏ผŒๆˆ‘ๅบ”่ฏฅๆไพ›ไธ€ไธชๅ…จ้ข็š„ๅ›ž็ญ”๏ผŒๆถต็›–ๅ„ไธชๆ–น้ข๏ผŒๅนถ่งฃ้‡Šๆฏไธชๆ–น้ข็š„้‡่ฆๆ€งใ€‚ๅฆๅค–๏ผŒ่€ƒ่™‘ๅˆฐ็”จๆˆทๅฏ่ƒฝๅธŒๆœ›ๅพ—ๅˆฐไธ€ไธช็ป“ๆž„ๅŒ–็š„ๅ›ž็ญ”๏ผŒๆˆ‘ๅบ”่ฏฅไฟๆŒ่ฏญ่จ€็š„็ฎ€ๆดๅ’Œ้€ป่พ‘ๆ€ง๏ผŒ็กฎไฟไฟกๆฏๅ‡†็กฎ๏ผŒๅŒๆ—ถ้ผ“ๅŠฑ็”จๆˆทๆไพ›ๆ›ดๅคš็ป†่Š‚ไปฅไพฟ่ฟ›ไธ€ๆญฅๅˆ†ๆžใ€‚ๆœ€ๅŽ๏ผŒๆˆ‘้œ€่ฆ็กฎไฟๆˆ‘็š„ๅ›ž็ญ”ๆ—ขๆœ‰็Ÿฅ่ฏ†ๆ€ง๏ผŒๅˆ็ฌฆๅˆ็”จๆˆท็š„่ฆๆฑ‚๏ผŒๅธฎๅŠฉ็”จๆˆทๆ›ดๅฅฝๅœฐ็†่งฃๅ’Œๅบ”็”จ่ฟ™ไธชๅญฆ็ง‘ใ€‚ๅ› ๆญค๏ผŒๅœจๅ›ž็ญ”ไธญไธไป…่ฆ็ป™ๅ‡บไธ€ไธชๅ…จ้ข็š„ๅˆ†ๆž๏ผŒ่ฟ˜่ฆๆๅˆฐๆฏไธช้ƒจๅˆ†็š„ไฝœ็”จๅ’Œๅฆ‚ไฝ•ๅˆฉ็”จใ€‚</think><answer>ไฝ ๆ“…้•ฟๅ“ชไธ€ไธชๅญฆ็ง‘๏ผŸ่ฟ™ๆ˜ฏไธ€ไธชๆ˜Ž็กฎ็š„้—ฎ้ข˜๏ผŒๅฏไปฅไปŽไปฅไธ‹ๅ‡ ไธชๆ–น้ข่ฟ›่กŒๅˆ†ๆž๏ผš1. **ๅ…ด่ถฃไธŽๅญฆไน ่ƒฝๅŠ›**๏ผšไฝ ๅ–œๆฌขไป€ไนˆๆ ท็š„ๅญฆไน ๆ–นๅผ๏ผŒๆฏ”ๅฆ‚่‡ชไธปๅญฆไน ใ€ๅฎž้ชŒใ€้กน็›ฎ็ญ‰๏ผŒ่ฟ™ไบ›้ƒฝๆ˜ฏๅพˆๅฅฝ็š„ๅญฆไน ่ต„ๆบใ€‚2. **ๅญฆไน ้ฃŽๆ ผ**๏ผšไฝ ๅ–œๆฌขไป€ไนˆ็ฑปๅž‹็š„ๅญฆไน ๆ–นๆณ•๏ผŒๆฏ”ๅฆ‚็ฌ”่ฎฐใ€ๅคไน ใ€้˜…่ฏปใ€่ฎจ่ฎบ็ญ‰๏ผŒ่ฟ™ไบ›้ƒฝ่ƒฝๅฝฑๅ“ๅญฆไน ๆ•ˆๆžœใ€‚3. **ๅญฆไน ่ต„ๆบ**๏ผšไฝ ๆ˜ฏๅฆๅœจๅฏปๆ‰พๅญฆไน ่ต„ๆบ๏ผŒๆฏ”ๅฆ‚ไนฆ็ฑใ€ๅœจ็บฟ่ฏพ็จ‹ใ€ๆ•™่‚ฒ่ฝฏไปถ็ญ‰๏ผŒ่ฟ™ไบ›้ƒฝ่ƒฝๆไพ›ๅญฆไน ๅธฎๅŠฉใ€‚4. **ๅญฆไน ็Žฏๅขƒ**๏ผšไฝ ๆ˜ฏๅฆๅœจๅญฆไน ็Žฏๅขƒไธญๆ„Ÿๅˆฐ่ˆ’้€‚๏ผŒๆฏ”ๅฆ‚่ˆ’้€‚็š„ๅญฆไน ็ฉบ้—ดใ€ๅฎ‰้™็š„ๅญฆไน ็ฉบ้—ด็ญ‰๏ผŒ่ฟ™ไบ›้ƒฝไผšๅฝฑๅ“ๅญฆไน ๆ•ˆๆžœใ€‚5. **ๅญฆไน ่ต„ๆบ**๏ผšไฝ ๆ˜ฏๅฆๆœ‰ๅญฆไน ่ต„ๆบ็š„ไธฐๅฏŒ๏ผŒๅฆ‚ๅœจ็บฟ่ฏพ็จ‹ใ€ๅญฆไน ๅนณๅฐใ€ไนฆ็ฑ็ญ‰๏ผŒ่ฟ™ไบ›้ƒฝ่ƒฝๆไพ›ไธฐๅฏŒ็š„ๅญฆไน ่ต„ๆบใ€‚6. **ๅญฆไน ๆ–นๆณ•**๏ผšไฝ ๆ˜ฏๅฆๆœ‰ๅ…ทไฝ“็š„ๅญฆไน ๆ–นๆณ•๏ผŒๆฏ”ๅฆ‚ๅฆ‚ไฝ•็†่งฃใ€ๅฆ‚ไฝ•็ป„็ป‡ๅญฆไน ๅ†…ๅฎนใ€ๅฆ‚ไฝ•ๅบ”็”จ็Ÿฅ่ฏ†็ญ‰๏ผŒ่ฟ™ไบ›้ƒฝๆ˜ฏๆ้ซ˜ๅญฆไน ๆ•ˆ็އ็š„้€”ๅพ„ใ€‚็ปผๅˆ่€ƒ่™‘๏ผŒ่ฟ™ๆ˜ฏไธ€ไธช้žๅธธๅ…จ้ข็š„ๅˆ†ๆž๏ผŒๆถต็›–ไบ†ๅคšไธชๆ–น้ข๏ผŒๅธฎๅŠฉไฝ ๆ›ดๅฅฝๅœฐ็†่งฃไฝ ็š„ๅญฆ็ง‘ใ€‚</answer>
[C]: <think>ๅ—ฏ๏ผŒ็”จๆˆท้—ฎ็š„ๆ˜ฏ"ไฝ ๆ›ดๆ“…้•ฟๅ“ชไธ€ไธชๅญฆ็ง‘๏ผŸ"่ฟ™ไธช้—ฎ้ข˜็œ‹่ตทๆฅๆœ‰็‚นๅคๆ‚๏ผŒไฝ†ๆˆ‘ๅฏไปฅไธ€ๆญฅๆญฅๅˆ†ๆžใ€‚้ฆ–ๅ…ˆ๏ผŒๆˆ‘้œ€่ฆ็†่งฃ็”จๆˆท็š„้œ€ๆฑ‚ใ€‚ไป–ๅฏ่ƒฝๆ˜ฏๅœจๅ‡†ๅค‡่€ƒ่ฏ•๏ผŒๆˆ–่€…้œ€่ฆไบ†่งฃๆŸไธชๅญฆ็ง‘็š„็‰น็‚น๏ผŒๆˆ–่€…ๆ˜ฏๆƒณๅœจ็”Ÿๆดปไธญๆ‰พๅˆฐ่‡ชๅทฑ็š„ๅ…ด่ถฃ็‚นใ€‚ๆŽฅไธ‹ๆฅ๏ผŒๆˆ‘่ฆ่€ƒ่™‘็”จๆˆทๅฏ่ƒฝ็š„่ƒŒๆ™ฏใ€‚ไป–ๅฏ่ƒฝๅœจๅทฅไฝœๆˆ–ๅญฆไน ไธญ้‡ๅˆฐไบ†็ฑปไผผ็š„้—ฎ้ข˜๏ผŒๆƒณ่ฆไบ†่งฃ่‡ชๅทฑๆ“…้•ฟๅ“ชไธช้ข†ๅŸŸ๏ผŒๆˆ–่€…ๆ˜ฏๅฆ้œ€่ฆไธ€ไบ›่ต„ๆบๆˆ–ๆŒ‡ๅฏผๆฅๆๅ‡่‡ชๅทฑใ€‚็„ถๅŽ๏ผŒๆˆ‘่ฆๅˆ†ๆž็”จๆˆทๅฏ่ƒฝ็š„ๆทฑๅฑ‚้œ€ๆฑ‚ใ€‚ไนŸ่ฎธไป–ๆƒณๅœจ่ŒๅœบไธŠๆๅ‡่‡ชๅทฑ๏ผŒๆˆ–่€…ๅฏปๆ‰พๆ–นๅ‘ใ€‚ไป–ๅฏ่ƒฝ้œ€่ฆๆ›ดๅ…ทไฝ“็š„ไพ‹ๅญ๏ผŒๅธฎๅŠฉไป–ๆ›ดๅฅฝๅœฐ็†่งฃไธๅŒๅญฆ็ง‘็š„็‰น็‚นๅ’Œๅบ”็”จๅœบๆ™ฏใ€‚่ฟ˜่ฆ่€ƒ่™‘็”จๆˆทๅฏ่ƒฝ็š„่ƒŒๆ™ฏใ€‚ไป–ๅฏ่ƒฝไธไป…ไป…ๆ˜ฏๅœจๅญฆไน ๏ผŒ่€Œๆ˜ฏๅธŒๆœ›ไบ†่งฃๅœจ็‰นๅฎš้ข†ๅŸŸไธญๅฆ‚ไฝ•ๅบ”็”จ่ฟ™ไบ›ๅญฆ็ง‘ใ€‚่ฟ™้œ€่ฆๆˆ‘ๆไพ›ๅ…จ้ข็š„ๅˆ†ๆž๏ผŒๅธฎๅŠฉไป–ๆ‰พๅˆฐ้€‚ๅˆ่‡ชๅทฑ็š„ๆ–นๆณ•ใ€‚ๆœ€ๅŽ๏ผŒๆˆ‘ๅบ”่ฏฅไฟๆŒๅผ€ๆ”พ็š„ๆ€ๅบฆ๏ผŒ้ผ“ๅŠฑ็”จๆˆท็ปง็ปญๆŽข็ดขๅ’Œๅญฆไน ใ€‚่ฟ™ๅฏ่ƒฝๅŒ…ๆ‹ฌๆŽจ่ไธ€ไบ›่ต„ๆบ๏ผŒๆˆ–่€…่ฎจ่ฎบๅฆ‚ไฝ•ๅฐ†่ฟ™ไบ›็Ÿฅ่ฏ†ๅบ”็”จๅˆฐๅฎž้™…็”Ÿๆดปไธญใ€‚</think><answer>ไฝ ๆ›ดๆ“…้•ฟๅ“ชไธ€ไธชๅญฆ็ง‘๏ผŸ่ฟ™ไธช้—ฎ้ข˜ๆœฌ่ดจไธŠๅ–ๅ†ณไบŽไฝ ็š„ไธชไบบๅ…ด่ถฃๅ’Œ็›ฎๆ ‡ใ€‚ไปฅไธ‹ๆ˜ฏไธ€ไบ›ๅ…ณ้”ฎ็‚น๏ผŒๅธฎๅŠฉไฝ ๅ…จ้ข็†่งฃๅนถๅบ”็”จ่ฟ™ไธ€็‚น๏ผš1. **ๅ…ด่ถฃไธŽไธ“้•ฟ**๏ผšไบ†่งฃ่‡ชๅทฑๆ“…้•ฟๅ“ชไธช้ข†ๅŸŸ๏ผŒๆœ‰ๅŠฉไบŽๅšๅ‡บๆ›ดๆ˜Žๆ™บ็š„้€‰ๆ‹ฉใ€‚2. **ๅ…จ้ขๅ‘ๅฑ•**๏ผš่€ƒ่™‘ๅญฆ็ง‘็š„ๅคšๆ ทๆ€งๅ’Œๆทฑๅบฆ๏ผŒไปฅๅ…จ้ขๅ‘ๅฑ•่‡ชๅทฑ็š„็”Ÿๆดปๅ’Œ่Œไธšใ€‚3. **้€‚ๅบ”ไธŽ่ฐƒๆ•ด**๏ผš้€‰ๆ‹ฉไธŽ่‡ชๅทฑๆŠ€่ƒฝใ€ๅ…ด่ถฃๅ’Œ็›ฎๆ ‡็›ธๅŒน้…็š„ๅญฆ็ง‘๏ผŒๆœ‰ๅŠฉไบŽๅบ”ๅฏนๆŒ‘ๆˆ˜ๅ’Œๅฎž็Žฐ็›ฎๆ ‡ใ€‚4. **่Œไธš่ง„ๅˆ’**๏ผšๆŽข็ดข้€‚ๅˆ่‡ชๅทฑ็š„่Œไธš่ทฏๅพ„๏ผŒๆๅ‡ๆ•ˆ็އๅ’Œ็ซžไบ‰ๅŠ›ใ€‚5. **็คพไผš่ดก็Œฎ**๏ผš่ฏ„ไผฐ่‡ชๅทฑๅœจ็คพไผšไธญ็š„่ง’่‰ฒ๏ผŒไธบ็คพไผšๅšๅ‡บ่ดก็Œฎใ€‚ไธบไบ†ๆ›ดๅฅฝๅœฐ็†่งฃๅนถๅบ”็”จ่ฟ™ไธ€็‚น๏ผŒไฝ ๅฏไปฅ๏ผš- **ไบ†่งฃ่กŒไธšๅŠจๆ€**๏ผšๅ…ณๆณจ็‰นๅฎš้ข†ๅŸŸ็š„ไธ“ไธšๅ‘ๅฑ•ใ€‚- **ๅฎž่ทตไธŽๅๆ€**๏ผš้€š่ฟ‡้กน็›ฎๆˆ–ๅฎžไน ็งฏ็ดฏ็ป้ชŒใ€‚- **่Œไธšๅ‘ๅฑ•**๏ผš่ฏ„ไผฐ่‡ชๅทฑ็š„้•ฟๆœŸ่Œไธš่ง„ๅˆ’ใ€‚- **ๆŒ็ปญๅญฆไน **๏ผšไธๆ–ญๆ›ดๆ–ฐ็Ÿฅ่ฏ†๏ผŒ้€‚ๅบ”่Œๅœบๅ˜ๅŒ–ใ€‚้€š่ฟ‡่ฟ™ไบ›ๆ–นๅ‘๏ผŒไฝ ๅฏไปฅๆ›ดๅ…จ้ขๅœฐ่ฎค่ฏ†่‡ชๅทฑ๏ผŒๆ‰พๅˆฐ้€‚ๅˆ่‡ชๅทฑ็š„ๅ‘ๅฑ•่ทฏๅพ„ใ€‚</answer>

[Q]: ้ฒ่ฟ…็š„ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ๆ˜ฏๅฆ‚ไฝ•ๆ‰นๅˆคๅฐๅปบ็คผๆ•™็š„๏ผŸ
[A]: <think>ๅ—ฏ๏ผŒ้ฒ่ฟ…็š„ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ๆ˜ฏๅฆ‚ไฝ•ๆ‰นๅˆคๅฐๅปบ็คผๆ•™็š„ๅ‘ข๏ผŸ่ฟ™ไธช้—ฎ้ข˜ๅฌ่ตทๆฅๆŒบๆœ‰ๆ„ๆ€็š„๏ผŒๅฐคๅ…ถๆ˜ฏไป–ๅœจใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ไธญ็š„่กจ่พพๆ–นๅผใ€‚้ฆ–ๅ…ˆ๏ผŒๆˆ‘้œ€่ฆ็กฎ่ฎคไธ€ไธ‹ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ๅ…ทไฝ“ๆ˜ฏ่ฐๅ†™็š„๏ผŒๆ˜ฏๅฆๆœ‰็‰นๅฎš็š„ไบบ็‰ฉๆˆ–่€…ไบ‹ไปถใ€‚ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ๆ˜ฏ้ฒ่ฟ…ๅœจ1924ๅนดๅˆ›ไฝœ็š„๏ผŒไธป่ฆ่ฎจ่ฎบไบ†็คพไผš้—ฎ้ข˜๏ผŒๅฐคๅ…ถๆ˜ฏๅฐๅปบ็คผๆ•™็š„้—ฎ้ข˜ใ€‚ไฝœ่€…ๆ›น้›ช่Šนๆ˜ฏไธช้žๅธธ่‘—ๅ็š„ไฝœๅฎถ๏ผŒไป–็š„ไฝœๅ“ไธญๆœ‰่ฎธๅคšๅ…ณไบŽๅฐๅปบ็คผๆ•™ๅ’Œ้˜ถ็บงๆ–—ไบ‰็š„่ง‚็‚นใ€‚่ฟ™็ฑปไฝœๅ“ๅœจๆ–‡ๅญฆใ€ๅ“ฒๅญฆๅ’Œๆ”ฟๆฒปไธŠ้ƒฝๆœ‰ๅพˆๆทฑ่ฟœ็š„ๅฝฑๅ“๏ผŒๅฐคๅ…ถๆ˜ฏๅœจ็คพไผš็ป“ๆž„ๅ’Œไบบๆ€ง็š„ๆ–น้ขใ€‚ๆŽฅไธ‹ๆฅ๏ผŒๆˆ‘้œ€่ฆไบ†่งฃ้ฒ่ฟ…็š„ๅ†™ไฝœ้ฃŽๆ ผใ€‚ไป–็š„ๅ†™ไฝœ้ฃŽๆ ผๆฏ”่พƒ็›ดๆŽฅ๏ผŒๆœ‰ไธฅ่‚ƒ็š„ๅ“ฒๅญฆ่ง‚็‚น๏ผŒๅผบ่ฐƒไบบๆ€ง็š„ๆ‚ฒๅ‰งๅ’Œ้“ๅพท็š„่™šๆ— ใ€‚ไป–็š„่ฏญ่จ€้ฃŽๆ ผๆฏ”่พƒๅฏŒๆœ‰่ฏ—ๆ„๏ผŒๅฏŒๆœ‰่ฑกๅพๆ„ไน‰๏ผŒๅ–„ไบŽ่ฟ็”จ่ฑกๅพๆ‰‹ๆณ•๏ผŒๅŒๆ—ถๅˆไธๅคฑ็œŸๅฎžๅ’Œ็Žฐๅฎžไธปไน‰ใ€‚ไป–็š„ไฝœๅ“ไธญๆœ‰ๅพˆๅคšๅ…ณไบŽ็คพไผš้˜ถ็บงๅ’Œ้˜ถ็บง็Ÿ›็›พ็š„ๅˆ†ๆž๏ผŒ่ฟ™ไบ›่ง‚็‚นๅฏ่ƒฝไธŽๅฝ“ๆ—ถ็š„็คพไผš็Žฐๅฎžไธ็ฌฆ๏ผŒๆ‰€ไปฅๅœจๆ‰นๅˆคๅฐๅปบ็คผๆ•™ๆ—ถ๏ผŒๅบ”่ฏฅๅผบ่ฐƒ่ฟ™ไบ›็Ÿ›็›พใ€‚็„ถๅŽ๏ผŒๆˆ‘ๆƒณๅˆฐใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ไธญๅฏนๅฐๅปบ็คผๆ•™็š„่ฎจ่ฎบใ€‚้ฒ่ฟ…็š„ไฝœๅ“ไธญ๏ผŒๅฐๅปบ็คผๆ•™่ขซ่ง†ไธบไธไบบ้“็š„๏ผŒไฝ†้€š่ฟ‡ๆ–‡ๅญ—ๅ’Œ่กŒๅŠจ๏ผŒ่กจ่พพไบ†ไป–ๅฏนๅฐๅปบ็คผๆ•™็š„ไธๆปกๅ’ŒๅๆŠ—ใ€‚่ฟ™ไธไป…ๅๆ˜ ไบ†ๅฝ“ๆ—ถ็š„็คพไผš็Žฐๅฎž๏ผŒไนŸๆญ็คบไบ†ๅฐๅปบ็คผๆ•™็š„้ป‘ๆš—้ข๏ผŒไฝ“็Žฐไบ†ๅฏนๅฐๅปบ็คพไผš็š„ไธๆปกๅ’Œๅฏนไบบๆ€ง็š„ๆทฑๅˆปๅๆ€ใ€‚ๆŽฅไธ‹ๆฅ๏ผŒๆˆ‘้œ€่ฆๆ€่€ƒ้ฒ่ฟ…ๅฏนๅฐๅปบ็คผๆ•™็š„็†่งฃๅ’Œๆ‰นๅˆคใ€‚ไป–ๅœจใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ไธญ๏ผŒๅฏนๅฐๅปบ็คผๆ•™็š„่ดจ็–‘ๅ’Œๆ‰นๅˆค๏ผŒไฝ“็Žฐไบ†ไป–ๅฏนไผ ็ปŸๅฐๅปบ็คผๆ•™็š„ๅฆๅฎšๅ’Œๆ‰นๅˆคใ€‚่ฟ™ไธไป…ไป…ๆ˜ฏๅฏนๅฐๅปบ็คผๆ•™็š„่ดจ็–‘๏ผŒๆ›ดๆ˜ฏๅฏนๅฝ“ๆ—ถ็คพไผš็š„ๅๆ€๏ผŒไปฅๅŠๅฏนไบบๆ€ง็š„ๅ…ณๆณจใ€‚ๆœ€ๅŽ๏ผŒๆˆ‘้œ€่ฆๆ€ป็ป“ไธ€ไธ‹้ฒ่ฟ…ๅฏนๅฐๅปบ็คผๆ•™็š„ๆ‰นๅˆคๅ’Œๆ‰นๅˆคใ€‚ไป–้€š่ฟ‡ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ไธญ็š„ๆ–‡ๅญ—ๅ’Œ่กŒไธบ๏ผŒๆ‰นๅˆคไบ†ๅฐๅปบ็คผๆ•™็š„่™šๅ‡ๅ’Œไธๅˆ็†๏ผŒไฝ“็Žฐไบ†ๅฏน็คพไผš็Žฐๅฎž็š„ๆทฑๅˆปๅๆ€ใ€‚ๅŒๆ—ถ๏ผŒไป–ไนŸๅ…ณๆณจไบ†ๅฐๅปบ็คผๆ•™็š„้ป‘ๆš—้ข๏ผŒๅๆ˜ ไบ†ๅฏนๅฐๅปบ็คพไผš็š„ไธๆปกๅ’Œๅฏนไบบๆ€ง็š„ๅฆๅฎšใ€‚ๆ€ป็š„ๆฅ่ฏด๏ผŒ้ฒ่ฟ…็š„ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹้€š่ฟ‡ๆ–‡ๅญ—ๅ’Œ่กŒๅŠจ๏ผŒๆ‰นๅˆคไบ†ๅฐๅปบ็คผๆ•™็š„่™šๅ‡ๅ’Œไธๅˆ็†๏ผŒไฝ“็Žฐไบ†ๅฝ“ๆ—ถ็š„็คพไผš็Žฐๅฎžๅ’Œไบบๆ€ง็š„ๅคๆ‚ใ€‚ไป–็š„ไฝœๅ“ๅฏนๅŽๆฅ็š„ๅฐๅปบ็คผๆ•™ๆœ‰ไบ†ๅฏ็คบ๏ผŒๅฏนๅฝ“ๆ—ถ็š„็คพไผš็Žฐ่ฑกๆœ‰ไบ†ๆ›ดๆทฑ็š„ๅๆ€ใ€‚</think><answer>้ฒ่ฟ…็š„ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ๆ˜ฏไธ€้ƒจๅๆ˜ ๅฐๅปบ็คผๆ•™็š„ๆ–‡ๅญฆไฝœๅ“๏ผŒไธป่ฆ้€š่ฟ‡ๆ–‡ๅญ—ๅ’Œ่กŒๅŠจๅๆ˜ ไบ†ๅฝ“ๆ—ถ็คพไผš็š„็Žฐๅฎžใ€‚้ฒ่ฟ…็š„ๆ–‡ๅญ—้ฃŽๆ ผ็‹ฌ็‰น๏ผŒๅฏŒๆœ‰่ฑกๅพๆ„ไน‰๏ผŒไฝ†้€š่ฟ‡ๆ–‡ๅญ—ๅ’Œ่กŒๅŠจ๏ผŒๆ‰นๅˆคไบ†ๅฐๅปบ็คผๆ•™็š„่™šๅ‡ๅ’Œไธๅˆ็†ใ€‚ๅœจไป–็š„ไฝœๅ“ไธญ๏ผŒๅฐๅปบ็คผๆ•™่ขซ่ง†ไธบไธไบบ้“็š„๏ผŒไฝ†้€š่ฟ‡ๆ–‡ๅญ—ๅ’Œ่กŒๅŠจ๏ผŒๅๆ˜ ไบ†ๅฐๅปบ็คพไผš็š„ไธๅ…ฌๅ’Œไบบๆ€ง็š„ๆทฑๅˆปๅๆ€ใ€‚้ฒ่ฟ…็š„ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹้€š่ฟ‡ๆ–‡ๅญ—ๅ’Œ่กŒๅŠจ๏ผŒๆ‰นๅˆคไบ†ๅฐๅปบ็คผๆ•™็š„่™šๅ‡ๅ’Œไธๅˆ็†๏ผŒไฝ“็Žฐไบ†ๅฝ“ๆ—ถ็คพไผš็š„ไธๆปกๅ’Œๅฏนไบบๆ€ง็š„ๅๆ€ใ€‚ไป–็š„ไฝœๅ“ไธไป…ๆ‰นๅˆคไบ†ๅฐๅปบ็คผๆ•™็š„่™šๅ‡ๅ’Œไธๅˆ็†๏ผŒ่ฟ˜ๆทฑๅˆปๆญ็คบไบ†ๅฐๅปบ็คพไผš็š„้ป‘ๆš—้ขใ€‚</answer>
[B]: <think>ๅ—ฏ๏ผŒ็”จๆˆท้—ฎ็š„ๆ˜ฏ้ฒ่ฟ…็š„ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ๅฆ‚ไฝ•ๆ‰นๅˆคๅฐๅปบ็คผๆ•™ใ€‚้ฆ–ๅ…ˆ๏ผŒๆˆ‘้œ€่ฆ็†่งฃ้ฒ่ฟ…็š„็”Ÿๅนณๅ’Œไฝœๅ“ใ€‚ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ๆ˜ฏไธญๅ›ฝ็Žฐไปฃๆ–‡ๅญฆ็š„็ปๅ…ธ๏ผŒไฝœ่€…ๆ˜ฏๆฏ›ๆณฝไธœ๏ผŒไฝœๅ“ๆถ‰ๅŠ็คพไผšใ€ๅฎถๅบญใ€ไผฆ็†็ญ‰ๅคšไธชๅฑ‚้ขใ€‚ๆˆ‘้œ€่ฆๆ‰พๅ‡บ้ฒ่ฟ…็š„ๅ†™ไฝœ้ฃŽๆ ผๅ’Œไธป้ข˜๏ผŒไปฅๅŠๅฎƒๅœจๅฝ“ๆ—ถ็š„็คพไผš่ƒŒๆ™ฏใ€‚ๆŽฅไธ‹ๆฅ๏ผŒๆˆ‘ๅบ”่ฏฅๅ›ž้กพใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹็š„ไธป่ฆๅ†…ๅฎนใ€‚ๆฏ›ๆณฝไธœๅœจใ€Š้’ๆ˜ฅๆ— ๆ‚”ใ€‹ไธญๆๅ‡บไบ†"็‹‚ไบบๆ—ฅ่ฎฐ"่ฟ™ไธ€ๆฆ‚ๅฟต๏ผŒๅผบ่ฐƒ้’ๆ˜ฅๆดปๆณผใ€ๅ‹‡ๆ•ขใ€ๆญฃไน‰๏ผŒ่ฟ™ๅœจๅฝ“ๆ—ถ็คพไผšไธญไป็„ถๅ…ทๆœ‰้‡่ฆๆ„ไน‰ใ€‚ไป–้€š่ฟ‡ๆ็ป˜ไธปไบบๅ…ฌ็‹‚ไบบๆฅ่กจ่พพๅฏน็คพไผšไธๅ…ฌ็š„ๆ‰นๅˆค๏ผŒไฝ†ๅŒๆ—ถไนŸๆŒ‡ๅ‡บไป–็š„ๅˆ›ไฝœๅฏน็คพไผš็š„่ดŸ้ขๅฝฑๅ“๏ผŒๆฏ”ๅฆ‚็คพไผšๅŠจ่กๅ’Œไธชไบบไธปไน‰็š„ๅคฑ่ดฅใ€‚็„ถๅŽ๏ผŒๆˆ‘ๅบ”่ฏฅๅˆ†ๆž้ฒ่ฟ…็š„ๅˆ›ไฝœ็†ๅฟตๅ’Œไธป้ข˜ใ€‚ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ๅผบ่ฐƒไบ†็คพไผš็š„้ป‘ๆš—้ข๏ผŒไธปๅผ "ไปฅไบบไธบๆœฌ"ใ€"ๅๅฏนๅฐๅปบ็คผๆ•™"็ญ‰ใ€‚ไป–ๅฏ่ƒฝไนŸๅœจๆŽข่ฎจ็คพไผšไธๅนณ็ญ‰็š„้—ฎ้ข˜๏ผŒๆฏ”ๅฆ‚"ไบบๆ€งๅผฑ็‚น"ใ€"ๆƒๅŠ›ๆปฅ็”จ"็ญ‰้—ฎ้ข˜ใ€‚่ฟ˜่ฆ่€ƒ่™‘้ฒ่ฟ…็š„ๅ…ถไป–ไฝœๅ“๏ผŒๆฏ”ๅฆ‚ใ€Š้˜ฟQๆญฃไผ ใ€‹ใ€ใ€Šๆญปไบก่ฏ—็คพใ€‹็ญ‰๏ผŒ่ฟ™ไบ›ไฝœๅ“่™ฝ็„ถๆœ‰็‚นๅคธๅผ ๏ผŒไฝ†ไนŸๆœ‰ๆทฑๅˆป็š„็คพไผšๆ‰นๅˆค๏ผŒๆฏ”ๅฆ‚ๅฏน็คพไผš้“ๅพท็š„่ดจ็–‘ใ€‚ๅŒๆ—ถ๏ผŒไฝœ่€…ๅฏ่ƒฝ่ฟ˜ๆถ‰ๅŠๅ…ถไป–ไฝœๅ“๏ผŒๅฆ‚ใ€Šๅบ†ไฝ™ๅนดใ€‹็ญ‰๏ผŒไฝ†่ฟ™ไบ›ๅฏ่ƒฝๆ›ดไพง้‡ไบŽๆ–‡ๅญฆๅˆ›ไฝœ๏ผŒ่€Œไธๆ˜ฏ็คพไผšๆ‰นๅˆคใ€‚ๅฆๅค–๏ผŒ็”จๆˆทๅฏ่ƒฝๆƒณ็Ÿฅ้“้ฒ่ฟ…ๅœจๆ–‡ๅญฆๅˆ›ไฝœไธญ็š„ๅ…ทไฝ“็ปๅކ๏ผŒๆฏ”ๅฆ‚ไป–ๆ˜ฏๅฆๆœ‰ไฝœๅ“่ขซๅนฟๆณ›ๆ‰น่ฏ„๏ผŒๆˆ–่€…ไป–ๅฏน็คพไผš็š„ๆ‰นๅˆคๆ˜ฏๅฆๅ…ทๆœ‰ๆ‰นๅˆคๆ€งใ€‚ๆ‰€ไปฅ๏ผŒๅ›ž็ญ”ๆ—ถ้œ€่ฆๆŒ‡ๅ‡บ้ฒ่ฟ…็š„ๅˆ›ไฝœ็ปๅކ๏ผŒไปฅๅŠไป–ๅฏน็คพไผš็Žฐๅฎž็š„ๅๆ€ใ€‚ๆ€ป็ป“ๆฅ่ฏด๏ผŒๆˆ‘้œ€่ฆๅ›ž็ญ”้ฒ่ฟ…็š„ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ๆ‰นๅˆคๅฐๅปบ็คผๆ•™๏ผŒๅนถๅˆ†ๆžๅ…ถๅœจๅฝ“ๆ—ถ็š„็คพไผš่ƒŒๆ™ฏๅ’Œๆ–‡ๅญฆไปทๅ€ผ๏ผŒๅŒๆ—ถๆŒ‡ๅ‡บๅ…ถๅฏน็คพไผš็š„ๆ‰นๅˆคๆ€งๆ€่€ƒ๏ผŒไปฅๅŠๅ…ถๅฏนๅŽไธ–็š„ๅฝฑๅ“ใ€‚</think><answer>้ฒ่ฟ…็š„ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ๆ‰นๅˆคๅฐๅปบ็คผๆ•™๏ผŒไปฅๅ…ถ็‹ฌ็‰น็š„ๅ™ไบ‹้ฃŽๆ ผๅ’Œๆทฑๅˆป็š„็คพไผšๆ‰นๅˆค็ฒพ็ฅž่‘—็งฐ๏ผŒไธป่ฆไฝ“็Žฐๅœจไปฅไธ‹ๅ‡ ไธชๆ–น้ข๏ผš1. **็คพไผšๆ‰นๅˆคไธŽไธชไบบๆˆ้•ฟ**๏ผšๅฐ่ฏด้€š่ฟ‡ๆ็ป˜ไธปไบบๅ…ฌ็‹‚ไบบ็š„ๆดปๆณผใ€ๅ‹‡ๆ•ขใ€ๆญฃไน‰๏ผŒๆญ็คบ็คพไผš็š„ไธๅ…ฌๅ’ŒๅผฑๅŠฟใ€‚2. **ไธชไบบไธปไน‰ไธŽ็คพไผšๆ‰นๅˆค**๏ผšๅฐ่ฏดๅๆ˜ ไบ†ๅฐๅปบ็คผๆ•™ๅฏนไธชไบบ่‡ช็”ฑๅ’Œๆƒๅˆฉ็š„ไพต็Šฏ๏ผŒๅผบ่ฐƒไธชไบบๅฐŠไธฅๅ’Œๆญฃไน‰็š„ไปทๅ€ผใ€‚3. **ๅฏน็คพไผš็š„ๆ‰นๅˆคๆ€งๆ€่€ƒ**๏ผš้€š่ฟ‡ๅฏน็คพไผšไธๅ…ฌ็š„ๅˆป็”ป๏ผŒๆญ็คบ็คพไผš้—ฎ้ข˜็š„ๆ นๆบ๏ผŒๅนถๅฏนๅฝ“ๆ—ถ็คพไผš็š„ๆ‰นๅˆคๆ€ๅบฆ่ฟ›่กŒๆ‰นๅˆคใ€‚้ฒ่ฟ…็š„ไฝœๅ“ๅœจๅฝ“ๆ—ถ็š„็คพไผš่ƒŒๆ™ฏๅ’Œๆ–‡ๅญฆไปทๅ€ผไฝฟๅ…ถๆˆไธบๅฝ“ๆ—ถๆ–‡ๅญฆ็š„้‡่ฆไปฃ่กจใ€‚ไป–็š„ไฝœๅ“ไธไป…ๅœจๅฝ“ๆ—ถๅนฟๅ—ๆฌข่ฟŽ๏ผŒไนŸๅฏนๅŽไธ–ไบง็”Ÿไบ†ๆทฑ่ฟœๅฝฑๅ“๏ผŒ่ขซๅนฟๆณ›ๅผ•็”จๅ’Œไผ ้ข‚ใ€‚</answer>
[C]: <think>ๅ—ฏ๏ผŒ็”จๆˆท้—ฎ็š„ๆ˜ฏ้ฒ่ฟ…็š„ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ๅฆ‚ไฝ•ๆ‰นๅˆคๅฐๅปบ็คผๆ•™ใ€‚้ฆ–ๅ…ˆ๏ผŒๆˆ‘้œ€่ฆ็†่งฃ้ฒ่ฟ…็š„่ƒŒๆ™ฏๅ’Œๆ ธๅฟƒๆ€ๆƒณใ€‚ไป–ๅฏ่ƒฝๆ˜ฏไธ€ไฝ็คพไผšๅญฆๅฎถใ€ๆ€ๆƒณๅฎถ๏ผŒๆˆ–่€…ๆ˜ฏๅฏนไผ ็ปŸๆ–‡ๅŒ–ๆœ‰ๆทฑๅŽšๅ…ด่ถฃ็š„่ฏป่€…ใ€‚็‹‚ไบบๆ—ฅ่ฎฐๆ˜ฏไป–ๅœจใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ไธญๆ‰€ๅ†™็š„๏ผŒๅฏ่ƒฝๅฏนไผ ็ปŸๆ–‡ๅŒ–ๆœ‰ไธ€ๅฎšๅฝฑๅ“ใ€‚ๆŽฅไธ‹ๆฅ๏ผŒๆˆ‘่ฆ่€ƒ่™‘็”จๆˆท็š„้œ€ๆฑ‚ๆ˜ฏไป€ไนˆใ€‚็”จๆˆทๅฏ่ƒฝๆƒณ็Ÿฅ้“่ฟ™ๆœฌไนฆๅœจ็Žฐไปฃ็คพไผšไธญ็š„ๅๆ€ๆ„ไน‰๏ผŒๆˆ–่€…ๆ˜ฏๅฆๆœ‰็›ธๅ…ณ็ ”็ฉถๆ”ฏๆŒ่ฟ™ไธ€็‚นใ€‚ไนŸๆœ‰ๅฏ่ƒฝไป–ไปฌๅฏนไนฆไธญ็š„ๆƒ…่Š‚ๆœ‰็–‘้—ฎ๏ผŒๆƒณไบ†่งฃๅฆ‚ไฝ•ๆ›ดๆทฑๅˆปๅœฐ็†่งฃ็คพไผš็Žฐ่ฑกใ€‚็„ถๅŽ๏ผŒๆˆ‘้œ€่ฆๆ€่€ƒๅฆ‚ไฝ•ไปŽไธๅŒ็š„่ง’ๅบฆ่งฃ่ฏป้ฒ่ฟ…็š„ๆ–‡ๆœฌใ€‚ไพ‹ๅฆ‚๏ผŒๆ˜ฏๅฆๆœ‰็›ดๆŽฅ็š„ๅކๅฒๅ™ไบ‹๏ผŒๆˆ–่€…ๆ˜ฏๅฆๅญ˜ๅœจๆ›ดๆทฑๅฑ‚ๆฌก็š„ๅ“ฒๅญฆๆ€่€ƒ๏ผŸ่ฟ™้œ€่ฆๆˆ‘ๅ…ˆไบ†่งฃ้ฒ่ฟ…็š„ไธๅŒ่ง‚็‚น๏ผŒ็„ถๅŽๅˆ†ๆžๅ…ถๆ‰นๅˆคๆ€งใ€‚่ฟ˜่ฆ่€ƒ่™‘็”จๆˆทๅฏ่ƒฝ็š„ๆทฑๅฑ‚้œ€ๆฑ‚๏ผŒๆฏ”ๅฆ‚ๆ˜ฏๅฆ้œ€่ฆไบ†่งฃไป–ไฝœไธบๆ–‡ๅญฆๆ‰นๅˆคๅฎถ็š„่ƒŒๆ™ฏ๏ผŒๆˆ–่€…ๆ˜ฏๅฆๆœ‰ๅฏนไผ ็ปŸไปทๅ€ผ่ง‚็š„ๅๆ€ใ€‚ๅ› ๆญค๏ผŒๅ›ž็ญ”ๆ—ถ่ฆๅ…จ้ข๏ผŒๆถต็›–ๆ ธๅฟƒ้—ฎ้ข˜๏ผŒๅนถๅผ•็”จ็›ธๅ…ณ่ต„ๆ–™ๆฅๆ”ฏๆ’‘่ง‚็‚นใ€‚ๆœ€ๅŽ๏ผŒๆ€ป็ป“้ฒ่ฟ…็š„่ง‚็‚น๏ผŒๅผบ่ฐƒๅ…ถๅฏน็Žฐไปฃ็คพไผš็š„ๆ‰นๅˆคๆ€งๆ€่€ƒ๏ผŒไปฅๅŠๅฏนไผ ็ปŸๆ–‡ๅŒ–็š„ๅฐŠ้‡ใ€‚่ฟ™ๆ ทๆ—ขๅ…จ้ขๅˆๆœ‰ๆทฑๅบฆ๏ผŒๅธฎๅŠฉ็”จๆˆทๅ…จ้ข็†่งฃ้ฒ่ฟ…็š„ไฝœๅ“ใ€‚</think><answer>้ฒ่ฟ…็š„ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹้€š่ฟ‡ๅ…ถ็‹ฌ็‰น็š„ๅ™ไบ‹ๆ‰‹ๆณ•ๅ’Œๆทฑๅˆป็š„็คพไผšๆ‰นๅˆค็ฒพ็ฅž๏ผŒๅฏนๅฐๅปบ็คผๆ•™่ฟ›่กŒไบ†ๆทฑๅˆป็š„ๆ‰นๅˆคใ€‚ไปฅไธ‹ๆ˜ฏๅ…ถๆ‰นๅˆคๆ€งๅˆ†ๆž๏ผš1. **็คพไผšๆ‰นๅˆคไธŽๅކๅฒ็œŸ็›ธ**๏ผšๅฐ่ฏด้€š่ฟ‡ๅฏนๅކๅฒไบบ็‰ฉ็š„ๅˆป็”ป๏ผŒๆญ็คบๅฐๅปบ็คผๆ•™็š„ๅผŠ็ซฏ๏ผŒไปฅๅŠๅ…ถๅฏนไผ ็ปŸ็คพไผš็ป“ๆž„็š„ๅ†ฒๅ‡ปใ€‚่ฟ™็งๆ‰นๅˆคไธไป…้™ไบŽๅฏน็Žฐๅฎž็š„ๆทฑๅˆปๆ‰นๅˆค๏ผŒไนŸๅๆ˜ ไบ†็Žฐไปฃ็คพไผšๅฏนไผ ็ปŸไปทๅ€ผ่ง‚็š„้‡ๆ–ฐๅฎก่ง†ใ€‚2. **ไธชไบบๅ‘ฝ่ฟไธŽ็คพไผšๆ‰นๅˆค**๏ผšๅฐ่ฏดไธญ๏ผŒไธปไบบๅ…ฌ้€š่ฟ‡"็‹‚ไบบๆ—ฅ่ฎฐ"ๆญ็คบไบ†ๅฐๅปบ็คผๆ•™ๅฏนไธชไบบๅ‘ฝ่ฟ็š„ไธฅ้‡ๅ‰ฅๅคบใ€‚่ฟ™็งๅ™ไบ‹ๆ–นๅผๆ—ขๆ‰นๅˆคไบ†ๅฐๅปบ็คผๆ•™๏ผŒไนŸๅฏนๅŽไธ–ไบง็”Ÿไบ†ๆทฑ่ฟœๅฝฑๅ“ใ€‚3. **ๅฏนๅŽไธ–็š„ๅฝฑๅ“**๏ผšไปŽๆ–‡ๅญฆๅˆ›ไฝœๅˆฐๆ€ๆƒณ่งฃ่ฏป๏ผŒ้ฒ่ฟ…็š„ไฝœๅ“ๆทฑๅˆปๅฝฑๅ“ไบ†ๅŽไธ–็š„ๆ€ๆƒณไฝ“็ณปใ€‚ไพ‹ๅฆ‚๏ผŒใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹้€š่ฟ‡ไบบ็‰ฉๅ‘ฝ่ฟ็š„ๅๆ˜ ๏ผŒๅฏน็Žฐไปฃ็คพไผš็š„ไปทๅ€ผ่ง‚ๅฟตๆๅ‡บไบ†ๆ–ฐ็š„ๆ€่€ƒใ€‚4. **ๅฏน็Žฐไปฃๆ–‡ๆ˜Ž็š„ๅๆ€**๏ผš่ฟ™ไธ€ๆ‰นๅˆคๆ€งๆ€่€ƒไธไป…ๅๆ˜ ไบ†ๅฝ“ไปฃ็คพไผš็š„ๅคๆ‚ๆ€ง๏ผŒไนŸไธบ็Žฐไปฃไบบๆไพ›ไบ†ๅๆ€็คพไผš็Žฐๅฎžใ€็ปดๆŠคไบบๆƒ็š„่ง†่ง’ใ€‚5. **ไธชไบบ่ง†่ง’ไธŽๆ–‡ๅŒ–่ง†่ง’**๏ผšไฝœ่€…้€š่ฟ‡่ฟ™ไธ€ๆ‰นๅˆคๆ€งๆ€่€ƒ๏ผŒๅฑ•็Žฐไบ†ๅฏนไผ ็ปŸไปทๅ€ผ่ง‚็š„้‡ๆ–ฐ่งฃ่ฏป๏ผŒๅŒๆ—ถไนŸๅฏนๅฝ“ไปฃ็คพไผš็š„ๅคšๅ…ƒๅŒ–่ง†่ง’ไบง็”Ÿไบ†ๅฏๅ‘ใ€‚็ปผไธŠๆ‰€่ฟฐ๏ผŒ้ฒ่ฟ…็š„ใ€Š็‹‚ไบบๆ—ฅ่ฎฐใ€‹ไธไป…ๆ˜ฏๅฏนๅฐๅปบ็คผๆ•™็š„ๆ‰นๅˆค๏ผŒๆ›ดๆ˜ฏๅฏนไผ ็ปŸๆ–‡ๅŒ–็š„ไธ€็งๆทฑๅˆปๅๆ€ใ€‚ๅฎƒ้€š่ฟ‡ๅฏนๅฐๅปบ็คผๆ•™็š„ๆ‰นๅˆค๏ผŒๆๅ‡บไบ†ๅฏน็Žฐไปฃ็คพไผš็ป“ๆž„ใ€ๆƒๅŠ›ๅ…ณ็ณป็š„ๆทฑๅˆปๅๆ€๏ผŒๅ…ทๆœ‰้‡่ฆ็š„็คพไผšไปทๅ€ผใ€‚</answer>

โ…ข Other Model Comparisons

[A] MiniMind2 (0.1B)
[B] MiniMind2-MoE (0.15B)
[C] MiniMind2-Small (0.02B)
[D] minimind-v1-small(0.02B)
[E] minimind-v1-moe(0.1B)
[F] minimind-v1(0.1B)
[G] baby-llama2-chinese(0.2B)
[H] chatlm-mini-chinese(0.2B)

[Q]: ไฝ ็Ÿฅ้“้•ฟๆฑŸๅ—๏ผŸ
[A]: ้•ฟๆฑŸ๏ผŒไฝไบŽไธญๅ›ฝไธœๅ—้ƒจ๏ผŒๆ˜ฏไธญๅ›ฝ็š„็ฌฌไธ€้•ฟๆฒณ๏ผŒๅ…จ้•ฟ6300ๅคšๅ…ฌ้‡Œ๏ผŒๆต็ป11ไธช็œไปฝ๏ผŒๆ˜ฏไธญๅ›ฝๆœ€้•ฟ็š„ๆฒณๆต๏ผŒไนŸๆ˜ฏไธญๅ›ฝ็š„"ๆฏไบฒๆฒณ"ใ€‚้•ฟๆฑŸ็š„ๅކๅฒๅฏไปฅ่ฟฝๆบฏๅˆฐๅ…ฌๅ…ƒๅ‰2000ๅคšๅนด็š„ๅ•†ๆœๆ—ถๆœŸ๏ผŒๅฝ“ๆ—ถ็š„ๅ•†ๆœๆ˜ฏๅ•†ๆœ็š„ๅŽ่ฃ”ใ€‚ๅ•†ๆœๆ—ถๆœŸ๏ผŒ้•ฟๆฑŸ็š„็ปๆตŽๅ‘ๅฑ•่พพๅˆฐไบ†้ซ˜ๅณฐ๏ผŒๆ˜ฏไธญๅ›ฝๆœ€้‡่ฆ็š„ๅ†œไธšๅ’Œๅทฅไธšไธญๅฟƒไน‹ไธ€ใ€‚้•ฟๆฑŸๆตๅŸŸ็š„็ปๆตŽไธป่ฆไปฅๅ†œไธšไธบไธป๏ผŒ้•ฟๆฑŸๆธ”ไธšๅ ๆฎไบ†ไธป่ฆไบงไธš๏ผŒๅฆ‚้’“้ฑผใ€็ŒŽ้ฑผ็ญ‰ใ€‚้•ฟๆฑŸ็š„ๆฐด่ต„ๆบไนŸ้žๅธธไธฐๅฏŒ๏ผŒๅŒ…ๆ‹ฌๆฒณๆตใ€ๆน–ๆณŠใ€ๆฒณๆต็ญ‰ใ€‚้•ฟๆฑŸ็š„่‡ช็„ถๆ™ฏ่ง‚ไนŸๅๅˆ†ๅฃฎ่ง‚๏ผŒ้•ฟๆฑŸๅ››ๅญฃๆ™ฏ่‰ฒๅ„ๅผ‚๏ผŒๆ˜ฅๅญฃๅคš้›จ๏ผŒๅคๅญฃๅคš้›จ๏ผŒ็ง‹ๅญฃๅˆ™ๅคš้›จ๏ผŒๅ†ฌๅญฃๅˆ™ๅฏ’ๅ†ทๅคš้›ช๏ผŒๆ˜ฅๅญฃๅ’Œ็ง‹ๅญฃ้ƒฝๆœ‰็พŽไธฝ็š„่Šฑๆœตๅ’Œๆžœๅฎžใ€‚้•ฟๆฑŸๆ˜ฏไธญๅ›ฝ็š„็ปๆตŽไธญๅฟƒ๏ผŒๆ‹ฅๆœ‰ไผ—ๅคš็š„ๅ›ฝๅฎถๅ’ŒๅŸŽๅธ‚๏ผŒๆ˜ฏไธ–็•ŒไธŠ้‡่ฆ็š„ไบค้€šๆžข็บฝๅ’Œ่ˆช่ฟไธญๅฟƒใ€‚ๅŒๆ—ถ๏ผŒ้•ฟๆฑŸ่ฟ˜ๆ˜ฏไธญๅ›ฝ็š„้‡่ฆๆฐดๅˆฉ่ต„ๆบ๏ผŒๅฏนไบŽไธญๅ›ฝ็š„็ปๆตŽๅ‘ๅฑ•ๅ…ทๆœ‰้‡่ฆๆ„ไน‰ใ€‚
[B]: ๆ˜ฏ็š„๏ผŒๆˆ‘็Ÿฅ้“้•ฟๆฑŸใ€‚้•ฟๆฑŸไฝไบŽไธญๅ›ฝ็š„ไธญ้ƒจ๏ผŒๆ˜ฏไธญๅ›ฝ็ฌฌไธ‰้•ฟ็š„ๆฒณๆต๏ผŒๅ…จ้•ฟ็บฆ6300ๅ…ฌ้‡Œ๏ผŒๆต็ปๆฑŸ่ฅฟ็œใ€ๅฎ‰ๅพฝ็œใ€ๆฑŸ่‹็œใ€ๅฎ‰ๅพฝ็œใ€ๆฑŸ่‹็œๅ’Œๅฎ‰ๅพฝ็œใ€‚
[C]: ๅฝ“็„ถ๏ผŒ้•ฟๆฑŸๆ˜ฏไธญๅ›ฝๆœ€้•ฟ็š„ๆฒณๆต๏ผŒๅ…จ้•ฟ็บฆ6300ๅ…ฌ้‡Œใ€‚ๅฎƒไปฅๅ…ถไธฐๅฏŒ็š„ๆฐด่ต„ๆบใ€ไธฐๅฏŒ็š„ๆฐด็”ŸๅŠจๆค็‰ฉ่ต„ๆบไปฅๅŠ็‹ฌ็‰น็š„ๅœฐ็†ไฝ็ฝฎ่€Œ้—ปๅไบŽไธ–ใ€‚
[D]: ๆ˜ฏ็š„๏ผŒ้•ฟๆฑŸๆ˜ฏไธญๅ›ฝๆœ€้•ฟ็š„ๆฒณๆต๏ผŒๅ…จ้•ฟ่ถ…่ฟ‡3300ๅƒ็ฑณใ€‚
[E]: ้•ฟๆฑŸๆ˜ฏไธญๅ›ฝๆœ€้•ฟ็š„ๆฒณๆต๏ผŒๆ€ป้•ฟๅบฆ็บฆไธบ6300ๅ…ฌ้‡Œใ€‚ๅฎƒๅ‘ๆบไบŽ้’่—้ซ˜ๅŽŸ็š„้’ๆตทๆน–๏ผŒๆต็ป้’ๆตทใ€ๅ››ๅทใ€็”˜่‚ƒใ€ๅฎๅคใ€ๅ†…่’™ๅคใ€้™•่ฅฟๅ’Œๅฑฑ่ฅฟใ€‚้•ฟๆฑŸๆตๅŸŸๆ˜ฏไธญๅ›ฝๆœ€ๅคง็š„ๅ†œไธšๅŒบไน‹ไธ€๏ผŒไนŸๆ˜ฏไธญๅ›ฝ็š„ๆ–‡ๅŒ–ๅ’Œ็ปๆตŽไธญๅฟƒใ€‚
[F]: ๆ˜ฏ็š„๏ผŒ้•ฟๆฑŸๆ˜ฏไธญๅ›ฝๆœ€้•ฟ็š„ๆฒณๆตไน‹ไธ€๏ผŒไนŸๆ˜ฏไธ–็•Œ็ฌฌไธ‰ๅคงๆฒณๆตใ€‚้•ฟๆฑŸๅ‘ๆบไบŽ้’่—้ซ˜ๅŽŸ๏ผŒๆต็ป11ไธช็œไปฝ๏ผŒๆœ€็ปˆๆณจๅ…ฅไธœๆตทใ€‚้•ฟๆฑŸๆตๅŸŸๆ˜ฏไธญๅ›ฝๆœ€ๅคง็š„ๆฒณๆตๆตๅŸŸไน‹ไธ€๏ผŒๆ‹ฅๆœ‰็€ไธฐๅฏŒ็š„่‡ช็„ถ่ต„ๆบๅ’Œๆ–‡ๅŒ–้—ไบง๏ผŒๅฆ‚้•ฟๆฑŸๅคงๆกฅใ€้•ฟๆฑŸๆตทๆด‹ๅš็‰ฉ้ฆ†ใ€้•ฟๆฑŸๅคๅŸŽ็ญ‰ใ€‚
[G]: ๅŒๆ—ถไนŸ็Ÿฅ้“๏ผŒไธญๅ›ฝๆ˜ฏไธ–็•ŒไธŠๆœ€้•ฟ็š„ๅŸŽๅธ‚ไน‹ไธ€๏ผŒๆ‹ฅๆœ‰่ถ…่ฟ‡3400ไธ‡ไบบๅฃใ€‚
[H]: ๆ˜ฏ็š„๏ผŒ้•ฟๆฑŸๆ˜ฏไธญๅ›ฝๆœ€้•ฟ็š„ๆฒณๆต๏ผŒไนŸๆ˜ฏไธ–็•ŒไธŠๆœ€้•ฟ็š„ๆฒณๆตไน‹ไธ€ใ€‚ๅฎƒๅ‘ๆบไบŽ้’่—้ซ˜ๅŽŸ๏ผŒๆต็ปไนไธช็œๅŒบ๏ผŒๆœ€็ปˆๆณจๅ…ฅไธœๆตทใ€‚้•ฟๆฑŸๆตๅŸŸ็š„ๆฐ”ๅ€™ๆธฉๅ’Œ๏ผŒๅ››ๅญฃๅˆ†ๆ˜Ž๏ผŒๆ˜ฏไธญๅ›ฝ้‡่ฆ็š„ๅ†œไธšๅ’ŒๅทฅไธšๅŸบๅœฐใ€‚้•ฟๆฑŸๆตๅŸŸ็š„ๆฐดไบง่ต„ๆบไธฐๅฏŒ๏ผŒๆ˜ฏไธญๅ›ฝ็š„้‡่ฆๆธ”ไธš่ต„ๆบไน‹ไธ€ใ€‚

[Q]: ไธ–็•ŒไธŠๆœ€้ซ˜็š„ๅฑฑๅณฐๆ˜ฏไป€ไนˆ๏ผŸ
[A]: ไธ–็•ŒไธŠๆœ€้ซ˜็š„ๅฑฑๅณฐๆ˜ฏ็ ็ฉ†ๆœ—็Ž›ๅณฐ๏ผˆMount Everest๏ผ‰๏ผŒไฝไบŽๅ–œ้ฉฌๆ‹‰้›…ๅฑฑ่„‰๏ผŒๅฐผๆณŠๅฐ”ๅ’Œไธญๅ›ฝ็š„่พน็•ŒไธŠใ€‚ๅฎƒ็š„ๆตทๆ‹”้ซ˜ๅบฆๆ˜ฏ8,848.86็ฑณ๏ผˆ29,031.7่‹ฑๅฐบ๏ผ‰๏ผŒๆ˜ฏๅœฐ็ƒไธŠๆœ€้ซ˜็š„ๅฑฑๅณฐใ€‚
[B]: ็ ็ฉ†ๆœ—็Ž›ๅณฐ๏ผˆMount Everest๏ผ‰ๆ˜ฏไธ–็•ŒไธŠๆœ€้ซ˜็š„ๅฑฑๅณฐ๏ผŒๆตทๆ‹”้ซ˜ๅบฆ่พพ8,848็ฑณ๏ผˆ29,029่‹ฑๅฐบ๏ผ‰ใ€‚
[C]: ็ ็ฉ†ๆœ—็Ž›ๅณฐๆ˜ฏไธ–็•ŒไธŠๆœ€้ซ˜็š„ๅฑฑๅณฐ๏ผŒไฝไบŽๅ–œ้ฉฌๆ‹‰้›…ๅฑฑ่„‰๏ผŒๆตทๆ‹”8,848.86็ฑณ๏ผˆ29,031.7่‹ฑๅฐบ๏ผ‰ใ€‚ๅฎƒไฝไบŽๅฐผๆณŠๅฐ”ๅ’Œไธญๅ›ฝ็š„่พน็•ŒไธŠ๏ผŒๆ˜ฏๅ–œ้ฉฌๆ‹‰้›…ๅฑฑ่„‰็š„ไธ€้ƒจๅˆ†ใ€‚
[D]: ไธ–็•ŒไธŠๆœ€้ซ˜็š„ๅฑฑๅณฐๆ˜ฏ็ ็ฉ†ๆœ—็Ž›ๅณฐ๏ผŒไฝไบŽๅฐผๆณŠๅฐ”ๅ’Œไธญๅ›ฝ็š„่พนๅขƒไธŠ๏ผŒๆตทๆ‹”8848็ฑณใ€‚
[E]: ไธ–็•ŒไธŠๆœ€้ซ˜็š„ๅฑฑๅณฐๆ˜ฏ็ ็ฉ†ๆœ—็Ž›ๅณฐ๏ผŒไฝไบŽๅ–œ้ฉฌๆ‹‰้›…ๅฑฑ่„‰๏ผŒๆตทๆ‹”8,848็ฑณใ€‚
[F]: ็ ็ฉ†ๆœ—็Ž›ๅณฐๆ˜ฏไธ–็•ŒไธŠๆœ€้ซ˜็š„ๅฑฑๅณฐ๏ผŒๆตทๆ‹”8848็ฑณใ€‚
[G]: ไธ–็•ŒไธŠๆœ€้ซ˜็š„ๅฑฑๅณฐๆ˜ฏ็ ็ฉ†ๆœ—็Ž›ๅณฐ๏ผŒไฝไบŽๅ–œ้ฉฌๆ‹‰้›…ๅฑฑ่„‰๏ผŒๆตทๆ‹”8,848.86็ฑณ๏ผˆ29,031.69่‹ฑๅฐบ๏ผ‰ใ€‚
[H]: ไธ–็•ŒไธŠๆœ€้ซ˜็š„ๅฑฑๅณฐๆ˜ฏ็ ็ฉ†ๆœ—็Ž›ๅณฐ๏ผŒไนŸ็งฐไธบ่จๅŠ ็Ž›ๅก”๏ผŒไฝไบŽๅ–œ้ฉฌๆ‹‰้›…ๅฑฑ่„‰็š„ๅฐผๆณŠๅฐ”ๅ’Œไธญๅ›ฝ่พนๅขƒไน‹้—ด๏ผŒๆตทๆ‹”8,848.86็ฑณ๏ผˆ29,031.69่‹ฑๅฐบ๏ผ‰ใ€‚ๅฎƒๆ˜ฏไธ–็•ŒไธŠๆœ€่‘—ๅ็š„็™ปๅฑฑ็›ฎๆ ‡ไน‹ไธ€๏ผŒๅธๅผ•็€ๆฅ่‡ชไธ–็•Œๅ„ๅœฐ็š„็™ปๅฑฑ่€…ๅ‰ๆฅๆŒ‘ๆˆ˜ใ€‚็ ็ฉ†ๆœ—็Ž›ๅณฐ็š„ๅๅญ—ๆฅ่‡ช่—่ฏญ๏ผŒๆ„ๆ€ๆ˜ฏ"ๅฅณ็ฅž็š„้ขๅณฐ"๏ผŒๅฎƒๆ˜ฏ็”ฑไธคไธชไธๅŒ็š„ๅฑฑๅณฐ็ป„ๆˆ็š„๏ผŒๅ…ถไธญไธ€ไธชๆ˜ฏไฝไบŽๅฐผๆณŠๅฐ”็š„็ ็ฉ†ๆœ—็Ž›ๅณฐ๏ผŒๅฆไธ€ไธชๅˆ™ไฝไบŽไธญๅ›ฝใ€‚ๅฎƒ็š„้ซ˜ๅบฆๆ˜ฏ้€š่ฟ‡ๆต‹้‡ๆตทๆ‹”้ซ˜ๅบฆๆฅ็กฎๅฎš็š„๏ผŒๅ› ไธบๅฎƒๆ˜ฏ้€š่ฟ‡ๆต‹้‡ๅœฐ็ƒ็š„ๅนณๅ‡้ซ˜ๅบฆๆฅ็กฎๅฎš็š„ใ€‚ๅฐฝ็ฎก็ ็ฉ†ๆœ—็Ž›ๅณฐๆ˜ฏไธ–็•ŒไธŠๆœ€้ซ˜็š„ๅฑฑๅณฐ๏ผŒไฝ†ๅฎƒๅนถไธๆ˜ฏๅœฐ็ƒไธŠไปปไฝ•ๅ…ถไป–ๅœฐๆ–น้ƒฝ่ƒฝๅˆฐ่พพ็š„ใ€‚ๅœฐ็ƒไธŠ็š„ๅ…ถไป–ๅœฐๆ–น๏ผŒๅฆ‚ๅ—็พŽๆดฒ็š„ๅฎ‰็ฌฌๆ–ฏๅฑฑ่„‰๏ผŒไนŸๆ˜ฏไธ–็•ŒไธŠๆœ€้ซ˜็š„ๅฑฑ่„‰๏ผŒไฝ†ๅฎƒๅนถไธๆ˜ฏๅœฐ็ƒไธŠๆœ€้ซ˜็š„ๅฑฑๅณฐใ€‚ๆ€ปไน‹๏ผŒ็ ็ฉ†ๆœ—็Ž›ๅณฐๆ˜ฏไธ–็•ŒไธŠๆœ€้ซ˜็š„ๅฑฑๅณฐ๏ผŒไฝ†ๅฎƒๅนถไธๆ˜ฏๅœฐ็ƒไธŠไปปไฝ•ๅœฐๆ–น้ƒฝ่ƒฝๅˆฐ่พพ็š„ใ€‚ๅฎƒๆ˜ฏๅœฐ็ƒไธŠๆœ€้ซ˜็š„ๅฑฑ่„‰๏ผŒไฝ†ๅฎƒๅนถไธๆ˜ฏๅœฐ็ƒไธŠไปปไฝ•ๅœฐๆ–น้ƒฝ่ƒฝๅˆฐ่พพ็š„ใ€‚

[Q]: ่ฐๆๅ‡บไบ†ไธ‡ๆœ‰ๅผ•ๅŠ›ๅฎšๅพ‹๏ผŸ
[A]: ไธ‡ๆœ‰ๅผ•ๅŠ›ๅฎšๅพ‹ๆ˜ฏ็”ฑ็‰›้กฟๅœจ17ไธ–็บชๆๅ‡บ็š„๏ผŒๆ˜ฏ็‰›้กฟไธ‰ๅคงๅฎšๅพ‹ไน‹ไธ€ใ€‚็‰›้กฟๅœจ17ไธ–็บชๆๅ‡บ็š„ไธ‡ๆœ‰ๅผ•ๅŠ›ๅฎšๅพ‹ๆญ็คบไบ†ไธ‡ๆœ‰ๅผ•ๅŠ›ๅฎšๅพ‹็š„ๆœฌ่ดจ๏ผŒๅนถ่งฃ้‡Šไบ†่กŒๆ˜Ÿใ€ๅซๆ˜Ÿใ€ๅฝ—ๆ˜Ÿๅ’Œๅ…ถไป–ๅคฉไฝ“ไน‹้—ด็š„ๅผ•ๅŠ›็›ธไบ’ไฝœ็”จใ€‚่ฟ™ไธ€็†่ฎบๆ˜ฏ็”ฑ็‰›้กฟๅœจ1687ๅนดๆๅ‡บ็š„ใ€‚้€š่ฟ‡ๅˆ†ๆžๅ’Œๅฎž้ชŒ๏ผŒไป–ๆˆๅŠŸๅœฐ่งฃ้‡Šไบ†ๅคฉไฝ“ไน‹้—ด็š„ๅผ•ๅŠ›็›ธไบ’ไฝœ็”จ๏ผŒไปŽ่€Œ่งฃ้‡Šไบ†ๅœฐ็ƒ็ป•ๅคช้˜ณๅ…ฌ่ฝฌ็š„็Žฐ่ฑกใ€‚
[B]: ไธ‡ๆœ‰ๅผ•ๅŠ›๏ผˆไบบ็ฑปๆ”ฟ็ญ–๏ผ‰ๆ˜ฏ็‰›้กฟไธ‰ๅคงๅŠ›ๅญฆๅฎšๅพ‹ไน‹ไธ€๏ผŒ็”จไบŽๆ่ฟฐไธคไธช็‰ฉไฝ“ไน‹้—ด็š„็›ธไบ’ไฝœ็”จใ€‚ๅฎƒๅŒ…ๆ‹ฌไธ‡ๆœ‰ๅผ•ๅŠ›ๅฎšๅพ‹ๅ’Œ็‰›้กฟ็ฌฌไธ€ๅฎšๅพ‹๏ผˆๆƒฏๆ€งๅฎšๅพ‹๏ผ‰ใ€‚ไธ‡ๆœ‰ๅผ•ๅŠ›ๅฎšๅพ‹ๆฅๆบไบŽไธคไธช็‰ฉไฝ“ไน‹้—ด็š„็›ธไบ’ไฝœ็”จ๏ผŒๅ…ถ่ดจ้‡ใ€่ท็ฆปๅ’Œ้€Ÿๅบฆๅ†ณๅฎšไบ†ๅฎƒไปฌไน‹้—ด็š„็›ธไบ’ไฝœ็”จใ€‚่ฟ™็ง็›ธไบ’ไฝœ็”จๆ˜ฏ๏ผš่ดจ้‡็š„ไน˜็งฏ๏ผš่ดจ้‡็š„ไน˜็งฏๆ˜ฏไธ‡ๆœ‰ๅผ•ๅŠ›ๅฎšๅพ‹ๅ’Œ็‰›้กฟ็ฌฌไบŒๅฎšๅพ‹็š„ไน˜็งฏใ€‚่ดจ้‡็š„ไน˜็งฏ๏ผš่ดจ้‡็š„ไน˜็งฏๆ˜ฏไธคไธช็‰ฉไฝ“ไน‹้—ด็š„็‰ฉ็†่ฟ‡็จ‹๏ผŒไธคไธช็‰ฉไฝ“ไน‹้—ด็š„็›ธไบ’ไฝœ็”จใ€‚ๅฏนไบŽๅ…ถไป–็‰ฉไฝ“๏ผŒๅฎƒไปฌ็š„่ดจ้‡ๅฏไปฅ่กจ็คบไธบไธคไธช็‰ฉไฝ“ไน‹้—ด็š„่ดจ้‡ไน‹ๅ’Œ๏ผŒๅณๅผ•ๅŠ›ๅŠ ้€Ÿๅบฆaใ€‚
[C]: ไธ‡ๆœ‰ๅผ•ๅŠ›ๆ˜ฏ็‰›้กฟๅœจ1687ๅนดๆๅ‡บ็š„็‰ฉ็†ๆฆ‚ๅฟต๏ผŒๆ่ฟฐไบ†็‰ฉไฝ“ไน‹้—ด็š„ๅผ•ๅŠ›็›ธไบ’ไฝœ็”จใ€‚
[D]: ไธ‡ๆœ‰ๅผ•ๅŠ›ๆ˜ฏ็”ฑ่‹ฑๅ›ฝ็‰ฉ็†ๅญฆๅฎถ็‰›้กฟๆๅ‡บ็š„ใ€‚ไป–็›ธไฟกๆ‰€ๆœ‰็‰ฉไฝ“้ƒฝไผšไบง็”Ÿๅผ•ๅŠ›๏ผŒ่ฟ™็งๅผ•ๅŠ›ๆ˜ฏ็”ฑ็‰ฉไฝ“็š„่ดจ้‡ๅ’Œ่ท็ฆปๅ†ณๅฎš็š„ใ€‚่ฟ™ไธ€็†่ฎบๆญ็คบไบ†่ดจ้‡ๅ’Œ่ท็ฆปไน‹้—ด็š„ๅ…ณ็ณป๏ผŒๅนถ่ฏๆ˜Žไบ†ไธ‡ๆœ‰ๅผ•ๅŠ›ๅฎšๅพ‹็š„ๆœฌ่ดจใ€‚
[E]: ไธ‡ๆœ‰ๅผ•ๅŠ›ๆ˜ฏ็”ฑ็‰›้กฟๅœจ1687ๅนดๆๅ‡บ็š„๏ผŒๅฎƒๆ˜ฏๅฎ‡ๅฎ™ไธญ็š„ไธ€ไธชๅŸบๆœฌ็‰ฉ็†็Žฐ่ฑก๏ผŒๆ่ฟฐไบ†็‰ฉไฝ“ไน‹้—ด็š„็›ธไบ’ไฝœ็”จใ€‚่ฟ™็งๅŠ›่ขซ็งฐไธบไธ‡ๆœ‰ๅผ•ๅŠ›๏ผŒๅญ˜ๅœจไบŽๆ‰€ๆœ‰็‰ฉไฝ“ไน‹้—ด๏ผŒ่ฟ™็งๅŠ›ไธŽ็‰ฉไฝ“็š„่ดจ้‡ๅ’Œ่ท็ฆปๆœ‰ๅ…ณใ€‚ไธ‡ๆœ‰ๅผ•ๅŠ›ๆ˜ฏ่‡ช็„ถ็•Œไธญๆœ€ๅŸบๆœฌ็š„ๅŠ›ไน‹ไธ€๏ผŒไธไป…ๅฝฑๅ“็‰ฉไฝ“็š„่ฟๅŠจๅ’Œๅ˜ๅŒ–๏ผŒ่€Œไธ”ๅฏนๅฎ‡ๅฎ™็š„็ป“ๆž„ๅ’Œๆผ”ๅŒ–ไนŸๆœ‰้‡่ฆๅฝฑๅ“ใ€‚
[F]: ไธ‡ๆœ‰ๅผ•ๅŠ›ๆ˜ฏ็”ฑ่‹ฑๅ›ฝ็‰ฉ็†ๅญฆๅฎถ็‰›้กฟๅœจ17ไธ–็บชๆๅ‡บ็š„ใ€‚
[G]: ๅผ•ๅŠ›ๆ˜ฏๅฎ‡ๅฎ™ไธญ็”ฑ่ดจ้‡ๅ’Œ่ƒฝ้‡็ป„ๆˆ็š„ๅŠ›ใ€‚ๆ นๆฎ็‰›้กฟ็š„ไธ‡ๆœ‰ๅผ•ๅŠ›ๅฎšๅพ‹๏ผŒไธ€ไธช็‰ฉไฝ“็š„ๅผ•ๅŠ›ไธŽๅฎƒ็š„่ดจ้‡ๅ’Œ่ท็ฆปๆˆๆญฃๆฏ”ใ€‚ๅ› ๆญค๏ผŒ็‰›้กฟ็š„ไธ‡ๆœ‰ๅผ•ๅŠ›ๅฎšๅพ‹่กจๆ˜Ž๏ผŒไธ€ไธช็‰ฉไฝ“็š„ๅผ•ๅŠ›ไธŽๅฎƒ็š„่ดจ้‡ๅ’Œ่ท็ฆปๆˆๆญฃๆฏ”ใ€‚่ฟ™ไธ€ๅฎšๅพ‹ๅœจ็‰ฉ็†ๅญฆใ€ๅคฉๆ–‡ๅญฆๅ’Œ็‰ฉ็†ๅญฆไธญ้ƒฝๆœ‰ๅนฟๆณ›็š„ๅบ”็”จใ€‚
[H]: ไธ‡ๆœ‰ๅผ•ๅŠ›ๆ˜ฏ็”ฑ่‹ฑๅ›ฝ็‰ฉ็†ๅญฆๅฎถ็‰›้กฟๅœจ1687ๅนดๆๅ‡บ็š„ใ€‚ไป–ไบŽ1687ๅนดๅ‘่กจไบ†ไธ€็ฏ‡่‘—ๅ็š„่ฎบๆ–‡ใ€Š่‡ช็„ถๅ“ฒๅญฆ็š„ๆ•ฐๅญฆๅŽŸ็†ใ€‹๏ผŒๆๅ‡บไบ†ไธ‡ๆœ‰ๅผ•ๅŠ›ๅฎšๅพ‹๏ผŒๆŒ‡ๅ‡บไปปไฝ•ไธคไธช็‰ฉไฝ“ไน‹้—ด้ƒฝๅญ˜ๅœจๅผ•ๅŠ›๏ผŒ่ฟ™็งๅผ•ๅŠ›ไธŽๅฎƒไปฌ็š„่ดจ้‡ๅ’Œ่ท็ฆป็š„ๅนณๆ–นๆˆๅๆฏ”ใ€‚่ฟ™ไธ€ๅฎšๅพ‹่ขซ็งฐไธบไธ‡ๆœ‰ๅผ•ๅŠ›ๅฎšๅพ‹๏ผŒๆ่ฟฐไบ†่ดจ้‡ๅ’Œ่ท็ฆปไน‹้—ด็š„ๅ…ณ็ณปใ€‚ๅฎƒๆŒ‡ๅ‡บไธคไธช็‰ฉไฝ“ไน‹้—ด็š„ๅผ•ๅŠ›ไธŽๅฎƒไปฌ็š„่ดจ้‡ๅ’Œ่ท็ฆป็š„ๅนณๆ–นๆˆๅๆฏ”ใ€‚่ฟ™ไธ€ๅฎšๅพ‹ๅฏนไบŽ่งฃ้‡Š่ฎธๅคš็Žฐ่ฑกๅ’Œๅฎ‡ๅฎ™ไธญ็š„็›ธไบ’ไฝœ็”จ้žๅธธ้‡่ฆ๏ผŒไพ‹ๅฆ‚่กŒๆ˜Ÿ็ป•ๅคช้˜ณๅ…ฌ่ฝฌใ€ๆ’ๆ˜Ÿไน‹้—ด็š„ๅผ•ๅŠ›้€้•œๆ•ˆๅบ”็ญ‰ใ€‚ๅฎƒไนŸๅœจๅคฉๆ–‡ๅญฆใ€็‰ฉ็†ๅญฆๅ’Œๅทฅ็จ‹ๅญฆ้ข†ๅŸŸๅพ—ๅˆฐไบ†ๅนฟๆณ›ๅบ”็”จ๏ผŒไธบๆˆ‘ไปฌ็†่งฃ่‡ช็„ถๅ’Œๅฎ‡ๅฎ™็š„ๆœฌ่ดจๅ’Œๆผ”ๅŒ–ๆไพ›ไบ†้‡่ฆ็š„็†่ฎบๅŸบ็ก€ใ€‚

[Q]: ไฝ ็Ÿฅ้“ๅคง็†Š็Œซ็š„ไธป่ฆ้ฃŸ็‰ฉๆ˜ฏไป€ไนˆๅ—๏ผŸ
[A]: ๅคง็†Š็Œซไธป่ฆไปฅ็ซนๅญไธบ้ฃŸ๏ผŒไฝ†ไนŸๅƒๅ…ถไป–ๆค็‰ฉใ€ๆ˜†่™ซใ€ๅฐๅž‹ๅ“บไนณๅŠจ็‰ฉๅ’Œ้ฑผใ€‚ๅฎƒไปฌ็š„ๆถˆๅŒ–็ณป็ปŸไธŽ็†Š็›ธไผผ๏ผŒ่ƒฝๅคŸๆถˆๅŒ–็ซนๅญใ€‚ๅคง็†Š็Œซๆœ‰้”‹ๅˆฉ็š„็‰™้ฝฟ๏ผŒ้€‚ๅˆๅ’€ๅšผ็ซนๅญ๏ผŒๆ‰€ไปฅๅฎƒไปฌ้€šๅธธ่ขซ็งฐไธบ"็ซนๅญๅŠจ็‰ฉ"ใ€‚
[B]: ๅคง็†Š็Œซๆ˜ฏ่‰้ฃŸๅ“บไนณๅŠจ็‰ฉ๏ผŒไปฅ็ซนๅญไธบ้ฃŸ๏ผŒไนŸๆ˜ฏ่‚‰้ฃŸๅŠจ็‰ฉใ€‚ๅฎƒไปฌ็š„ไธป่ฆๆ˜ฏ็ซนๅญ๏ผŒๅฐคๅ…ถๆ˜ฏๅฏŒๅซ็บค็ปด็ด ๅ’Œ็Ÿฟ็‰ฉ่ดจ็š„็ซนๅญ๏ผŒ่ฟ™ไบ›็ซนๅญไธไผš็›ดๆŽฅ่ฟ›ๅ…ฅๆถˆๅŒ–็ณป็ปŸใ€‚ๅคง็†Š็Œซ็š„่‚ ้“ไธป่ฆ็”ฑ็ซนๅญ็ป„ๆˆ๏ผŒ้œ€่ฆๆถˆๅŒ–็บค็ปด็ด ๅ’Œๅ…ถไป–็บค็ปดๅœจ็ซนๅญไธญไปฅๆ”ฏๆŒๆญฃๅธธๅ–‚ๅ…ปใ€‚
[C]: ๅคง็†Š็Œซไธป่ฆไปฅ็ซนๅญไธบ้ฃŸ๏ผŒไฝ†ไนŸๅƒๅ…ถไป–ๆค็‰ฉ๏ผŒๅŒ…ๆ‹ฌๅถๅญใ€ๅซฉ่Šฝใ€ๆ˜†่™ซใ€ๆฐดๆžœใ€่”ฌ่œๅ’Œๅฐๅž‹ๅ“บไนณๅŠจ็‰ฉใ€‚ๅคง็†Š็Œซๆ˜ฏไธญๅ›ฝ็‰นๆœ‰็š„๏ผŒๅฑžไบŽ็†Š็ง‘๏ผŒไธป่ฆๅˆ†ๅธƒๅœจๅ››ๅทใ€้™•่ฅฟๅ’Œ็”˜่‚ƒๅœฐๅŒบใ€‚
[D]: ๅคง็†Š็Œซ็š„ไธป่ฆ้ฃŸ็‰ฉๆ˜ฏ็ซนๅญใ€‚ๅฎƒไปฌ้€šๅธธๅƒ็ซนๅญ๏ผŒๆฏๅคฉ้œ€่ฆๅƒๅคง็บฆ30ๅ…ฌๆ–ค็š„็ซนๅญใ€‚
[E]: ๆ˜ฏ็š„๏ผŒๅคง็†Š็Œซไธป่ฆไปฅ็ซนๅญไธบ้ฃŸใ€‚ๅฎƒไปฌ้œ€่ฆๆฏๅคฉๅƒๅคง้‡็š„็ซนๅญๆฅ็ปดๆŒ็”Ÿๅ‘ฝ๏ผŒๆฏๅคฉ้œ€่ฆๅƒ40ๅˆฐ80ๅ…ฌๆ–ค็š„็ซนๅญใ€‚ๆญคๅค–๏ผŒๅฎƒไปฌ่ฟ˜ๅƒไธ€ไบ›ๅ…ถไป–ๆค็‰ฉ๏ผŒๅฆ‚่‰ใ€ๆฐดๆžœใ€ๅšๆžœๅ’Œๅฐๅž‹ๅ“บไนณๅŠจ็‰ฉใ€‚
[F]: ๅคง็†Š็Œซไธป่ฆไปฅ็ซนๅญไธบ้ฃŸ๏ผŒไฝ†ๅถๅฐ”ไนŸไผšๅƒๅ…ถไป–ๆค็‰ฉๅ’ŒๅŠจ็‰ฉใ€‚ๆญคๅค–๏ผŒๅคง็†Š็Œซ่ฟ˜ๅƒไธ€ไบ›้‡Ž็”Ÿๆฐดๆžœใ€ๅฐๅž‹ๅŠจ็‰ฉๅ’Œๆค็‰ฉ๏ผŒไฝ†่ฟ™ไบ›ๅนถไธๆ˜ฏๅฎƒไปฌ็š„ไธป่ฆ้ฃŸ็‰ฉๆฅๆบใ€‚
[G]: ๅคง็†Š็Œซ็š„ไธป่ฆ้ฃŸ็‰ฉๆ˜ฏ็ซนๅญใ€‚
[H]: ๅคง็†Š็Œซๆ˜ฏๆค็‰ฉๆ€งๅŠจ็‰ฉ๏ผŒไธป่ฆ้ฃŸ็‰ฉๆ˜ฏ็ซนๅญใ€‚ๅฎƒไปฌ็š„่‚ ้“็ป“ๆž„้€‚ๅˆๆถˆๅŒ–ๅฏŒๅซ็บค็ปด็ด ็š„็ซนๅญ๏ผŒไฝ†ๅฎƒไปฌไนŸๅƒไธ€ไบ›ๅ…ถไป–ๆค็‰ฉ๏ผŒๅฆ‚่‰ๆœฌๆค็‰ฉๅ’Œๅฐๅž‹ๅ“บไนณๅŠจ็‰ฉใ€‚ๅคง็†Š็Œซ็š„่‚ ้“็ป“ๆž„ไนŸ้€‚ๅบ”ไบ†้ซ˜็บค็ปด็ซนๅญ๏ผŒไฝฟๅฎƒไปฌ่ƒฝๅคŸๆถˆๅŒ–ๅคง้‡็š„็บค็ปด็ด ๏ผŒๅธฎๅŠฉๅฎƒไปฌๅœจ้‡Žๅค–็”Ÿๅญ˜ใ€‚ๅคง็†Š็Œซ็š„่‚ ้“ไธญไนŸๅซๆœ‰ไธ€็งๅซๅš"็บค็ปด็ด ้…ถ"็š„้…ถ๏ผŒๅฏไปฅๅธฎๅŠฉๅคง็†Š็Œซๅˆ†่งฃ็บค็ปด็ด ๏ผŒๅธฎๅŠฉๅฎƒไปฌๆถˆๅŒ–ๅคง้‡็š„ๆฐดๅ’Œ่ฅๅ…ป็‰ฉ่ดจใ€‚ๆญคๅค–๏ผŒๅคง็†Š็Œซ็š„่‚ ้“ไธญไนŸๅซๆœ‰ไธ€็งๅซๅš"็บค็ปด็ด ่›‹็™ฝ"็š„่›‹็™ฝ่ดจ๏ผŒๅฏไปฅๅธฎๅŠฉๅคง็†Š็Œซ็ปดๆŒ่บซไฝ“่ƒฝ้‡ๆฐดๅนณ๏ผŒๅธฎๅŠฉๅฎƒไปฌๅœจ้‡Žๅค–็”Ÿๅญ˜ใ€‚ๆ€ปไน‹๏ผŒๅคง็†Š็Œซ็š„ไธป่ฆ้ฃŸ็‰ฉๆ˜ฏ็ซนๅญ๏ผŒไฝ†ๅฎƒไปฌไนŸๅƒไธ€ไบ›ๅ…ถไป–ๆค็‰ฉ๏ผŒๅฆ‚่‰ๆœฌๆค็‰ฉๅ’Œๅฐๅž‹ๅ“บไนณๅŠจ็‰ฉใ€‚

[Q]: ไธบไป€ไนˆๆตทๆฐดๆ˜ฏๅ’ธ็š„๏ผŸ
[A]: ๆตทๆฐดๆ˜ฏๅ’ธ็š„ไธป่ฆๆ˜ฏๅ› ไธบๅฎƒ็š„ๅŒ–ๅญฆๆˆๅˆ†ใ€‚ๆตทๆฐดๅซๆœ‰ๅคง้‡็š„็Ÿฟ็‰ฉ่ดจๅ’Œ็›ๅˆ†๏ผŒไธป่ฆๆˆๅˆ†ๆ˜ฏ็กซ้…ธ็›ใ€็ขณ้…ธ็›ใ€้•็ฆปๅญๅ’Œ้’พ็ฆปๅญใ€‚่ฟ™ไบ›็‰ฉ่ดจๅœจ้ซ˜ๆต“ๅบฆไธ‹ไผšๅœจๆตทๆฐดไธญๆฒ‰ๆท€๏ผŒๅฝขๆˆๆตทๆฐดใ€‚ๅ…ทไฝ“ๆฅ่ฏด๏ผŒๆตทๆฐดไธญ็Ÿฟ็‰ฉ่ดจๅ’Œ็›ๅˆ†ไธป่ฆๆฅ่‡ชๅฒฉ็Ÿณใ€ๅœŸๅฃคใ€็”Ÿ็‰ฉๅ’Œไบบ็ฑปๆŽ’ๆณ„็‰ฉใ€‚ๅฒฉ็Ÿณๆ˜ฏๆตทๆฐด็š„็ป„ๆˆ้ƒจๅˆ†๏ผŒไธป่ฆ็”ฑ็Ÿณ่‹ฑใ€้•ฟ็Ÿณใ€ไบ‘ๆฏ็ญ‰็Ÿฟ็‰ฉ่ดจ็ป„ๆˆใ€‚ๅœŸๅฃคไธญๅซๆœ‰ๅคง้‡็š„ๅŒ–ๅญฆ็‰ฉ่ดจ๏ผŒๅฆ‚ๆฐฎใ€็ฃทใ€้’พ็ญ‰๏ผŒ่ฟ™ไบ›ๅŒ–ๅญฆ็‰ฉ่ดจไผšๆธ—ๅ…ฅๅœŸๅฃค๏ผŒๅฝขๆˆๅœŸๅฃคใ€‚็”Ÿ็‰ฉๆŽ’ๆณ„็‰ฉไธญ็š„็›ๅˆ†ไธป่ฆๆฅ่‡ชๆค็‰ฉๅถ็ปฟ็ด ๅ’Œๅ…ถไป–่‰ฒ็ด ๏ผŒ่ฟ™ไบ›่‰ฒ็ด ๅธๆ”ถ้˜ณๅ…‰ๅนถๅฐ†ๅ…ถ่ฝฌๅŒ–ไธบ่ƒฝ้‡๏ผŒไพ›็”Ÿ็‰ฉไฝฟ็”จใ€‚ไบบ็ฑปๆŽ’ๆณ„็‰ฉไธญ็š„็›ๅˆ†ไธป่ฆๆฅ่‡ช็Ÿฟ็‰ฉ่ดจๅ’Œ็ขณ้…ธ็›๏ผŒ่ฟ™ไบ›็Ÿฟ็‰ฉ่ดจๅœจๆฐดไธญ้ซ˜ๆต“ๅบฆๅญ˜ๅœจ๏ผŒๅฏผ่‡ดๆฐดไธญๆบถ่งฃ็Ÿฟ็‰ฉ่ดจๆต“ๅบฆๅขžๅŠ ๏ผŒๅฝขๆˆๆตทๆฐดใ€‚ๅ› ๆญค๏ผŒๆตทๆฐดๆ˜ฏๅ’ธ็š„ไธป่ฆๆ˜ฏๅ› ไธบๅฎƒ็š„ๅŒ–ๅญฆๆˆๅˆ†ๅ’Œ็ป“ๆž„็‰นๅพใ€‚็Ÿฟ็‰ฉ่ดจๅ’Œ็›ๅˆ†ๅœจๆตทๆฐดไธญไธป่ฆๆฅ่‡ชๅฒฉ็Ÿณใ€ๅœŸๅฃคใ€็”Ÿ็‰ฉๅ’Œไบบ็ฑปๆŽ’ๆณ„็‰ฉ๏ผŒ่ฟ™ไบ›็‰ฉ่ดจๅœจๆตทๆฐดไธญ็งฏ็ดฏๅ’ŒๆŽ’ๆณ„๏ผŒๅฏผ่‡ดๆตทๆฐดๅ˜ๅ’ธใ€‚
[B]: ๆตทๆฐดๆ˜ฏๅ’ธ็š„๏ผŒๅ› ไธบๅฎƒๅซๆœ‰ๅคš็ง็‰ฉ่ดจ๏ผŒๅŒ…ๆ‹ฌๆฐฏๅŒ–้’ ๏ผˆNaCl๏ผ‰ใ€ๆฐฏๅŒ–้’ ๏ผˆNaCl๏ผ‰ใ€็ขณ้…ธ็›๏ผˆๅฆ‚็กซ้…ธ็›๏ผ‰ใ€ๆฐฏๅŒ–้’ ๏ผˆNaCl๏ผ‰ๅ’Œๆฐดใ€‚ๅ’ธ็‰ฉ่ดจ็š„ๆฅๆบ๏ผš็›ๆ˜ฏไธ€็งๅธธ่ง็š„ๅ’ธๅ‘ณๆฅๆบ๏ผŒๅซๆœ‰้’พใ€้’™ใ€้•ใ€้’พๅ’Œๅ…ถไป–็Ÿฟ็‰ฉ่ดจใ€‚่ฟ™ไบ›็Ÿฟ็‰ฉ่ดจ้€šๅธธๆฅ่‡ชๅœฐไธ‹ๆฐดใ€ๅœฐไธ‹ๆฐดๆˆ–ๅœŸๅฃค๏ผŒๆต“ๅบฆ่ฟœไฝŽไบŽ็บฏๆฐดใ€‚ๅ’ธๅ‘ณ็š„ๅŽŸๅ› ๏ผšๅ’ธๅ‘ณไธป่ฆๆฅ่‡ชๆฐดไธญ็š„ๅฐ้ข—็ฒ’็›ใ€‚่ฟ™ไบ›ๅฐ้ข—็ฒ’ไธป่ฆ้€š่ฟ‡ๆค็‰ฉๆ น้ƒจๅ’ŒๅŠจ็‰ฉไฝ“ๅ†…็š„ๅพฎ็”Ÿ็‰ฉไผ ๆ’ญ๏ผŒๅฆ‚ๆ˜†่™ซใ€ๅฐๅž‹ๅ“บไนณๅŠจ็‰ฉใ€้ธŸ็ฑปๅ’ŒๆŸไบ›ๆ˜†่™ซใ€‚ๆ€ปไน‹๏ผŒๆตทๆฐดๆ˜ฏๅ’ธ็š„๏ผŒๅ› ไธบๅฎƒๅซๆœ‰ๅคง้‡็š„็›ๅˆ†๏ผŒๅŒ…ๆ‹ฌ็Ÿฟ็‰ฉ่ดจใ€ๅฒฉ็Ÿณใ€็›ใ€็Ÿฟ็‰ฉ่ดจ็ญ‰๏ผŒ่ฟ™ไบ›็‰ฉ่ดจๅœจๆตทๆฐดไธญ้ซ˜ๆต“ๅบฆๅญ˜ๅœจ๏ผŒๅฏนๅ’ธๅ‘ณไบง็”Ÿ้‡่ฆๅฝฑๅ“ใ€‚
[C]: ๆตทๆฐดๆ˜ฏๅ’ธ็š„ไธป่ฆๆ˜ฏๅ› ไธบๅฎƒๅซๆœ‰ๅ„็ง็›ๅˆ†๏ผŒๆตทๆฐดๆ˜ฏๅ…ถไธญไธป่ฆๆˆๅˆ†ไน‹ไธ€ใ€‚ๅฝ“ๆตทๆฐดๅซๆœ‰ๅคง้‡็›ๅˆ†ๆ—ถ๏ผŒ่ฟ™ไบ›็›ๅˆ†ๆบถ่งฃๅœจๆตทๆฐดไธญๅฝขๆˆๅ’ธๅ‘ณใ€‚ๆตทๆฐดไธญ็›ๅˆ†ไธป่ฆๆฅ่‡ชๆบถ่งฃ็›ๅˆ†ใ€่’ธๅ‘ๆฒ‰ๆท€ๅ’Œๅ†ฐๅ†ปๆตทๆฐดๅฝขๆˆ็š„็›ๅˆ†ใ€‚
[D]: ๆตทๆฐดไธญๅซๆœ‰่ฎธๅคš็›ๅˆ†๏ผŒ่ฟ™ไบ›็›ๅˆ†ๅฏไปฅๅขžๅŠ ๆตทๆฐด็š„ๅ’ธๅบฆใ€‚ๆตทๆฐดไธญ็›ๅˆ†ไธป่ฆๆฅ่‡ชๆตทๆฐดไธญๆบถ่งฃ็š„็›ๅˆ†๏ผŒ่ฟ™ไบ›็›ๅˆ†ๅฏไปฅไปŽๆตทๆฐดไธญ่Žทๅพ—ใ€‚ๆฐงๅŒ–็‰ฉๅ’Œๆตทๆฐดไธญ็›ๅˆ†ๅฏไปฅไธŽๆตทๆฐดไธญ็›ๅˆ†ๅฝขๆˆๆฐข้”ฎ๏ผŒไปŽ่€ŒๅขžๅŠ ๆตทๆฐด็š„ๅ’ธๅบฆใ€‚
[E]: ๆตทๆฐดๆ˜ฏๅ’ธ็š„๏ผŒๅ› ไธบๅฎƒๅซๆœ‰ๅคง้‡็š„็›ๅˆ†๏ผŒๅŒ…ๆ‹ฌๆฐฏ็ฆปๅญๅ’Œๆฐฏ็ฆปๅญใ€‚่ฟ™ไบ›็ฆปๅญๅœจๆตทๆด‹ไธญๅฝขๆˆๅคง้‡็›ๅˆ†๏ผŒ็งฐไธบ็›ใ€‚ๆตทๆฐดไธญๅซๆœ‰่ฎธๅคšๆบถ่งฃ็š„็›ๅˆ†๏ผŒ่ฟ™ไบ›็›ๅˆ†้š็€ๆตทๆฐด็š„ไธŠๅ‡่€Œ่’ธๅ‘๏ผŒๆœ€็ปˆๅฏผ่‡ดๆตทๆฐดไธญ็›ๅˆ†่’ธๅ‘ใ€‚่ฟ™ไบ›็›ๅˆ†ๅฎŒๅ…จ่ขซๆตทๆฐดๆถˆ่€—๏ผŒ็„ถๅŽไปŽๆตทๆฐดไธญๆŽ’้™คใ€‚ๆญคๅค–๏ผŒๆตทๆฐดไธญ่ฟ˜ๅซๆœ‰่ฎธๅคšๅ…ถไป–็›ๅˆ†๏ผŒไฝ†่ฟ™ไบ›็›ๅˆ†ไธๅŒ๏ผŒๅ› ไธบๅฎƒไปฌ็š„ๆตฎๅŠจๅ’Œไธ‹ๆฒ‰่ฟ‡็จ‹ไธๅŒใ€‚ๆตทๆฐดไธญๆๅ–็š„็›ๅˆ†ๆฅ่‡ชๆตทๅบ•็š„ๅฒฉ็Ÿณ๏ผŒ่ฟ™ไบ›็›ๅˆ†ๅœจๆตทๆฐดไธญๅฏๅˆฉ็”จใ€‚ๆ€ปไน‹๏ผŒๆตทๆฐดๆ˜ฏๅ’ธ็š„๏ผŒๅ› ไธบๆตทๆฐดไธญๅซๆœ‰่ฎธๅคš็›ๅˆ†ๅ’Œ็›ๅˆ†ใ€‚
[F]: ๆตทๆฐดไธญๅซๆœ‰่ฎธๅคšๆบถ่งฃ็š„็›ๅˆ†๏ผŒๅ…ถไธญๆœ€ไธป่ฆ็š„ๆ˜ฏๆฐฏๅŒ–้’ ใ€‚ๅฝ“็›ๅŠ ๅ…ฅๆฐดไธญๆ—ถ๏ผŒ็›ๅˆ†ๅญไธŽๆฐดๅˆ†ๅญๅๅบ”ๅฝขๆˆๆฐขๆฐงๅŒ–้’ ๏ผŒ่ฟ™ๆ˜ฏไธ€็ง็›ใ€‚
[G]: ๅ› ไธบ่ฎธๅคš็”Ÿ็‰ฉ้œ€่ฆๆฐดๆ‰่ƒฝ็”Ÿๅญ˜๏ผŒๅฎƒๅฏไปฅ้€š่ฟ‡ๅธๆ”ถๅ’Œ้‡Šๆ”พไบŒๆฐงๅŒ–็ขณใ€้‡Šๆ”พๆฐงๆฐ”ใ€ไฟๆŒๅคงๆฐ”ไธญ็š„ๆฐด่’ธๆฐ”ใ€ไฟๆŒๆฐดๅพช็Žฏๆฅๅฎž็Žฐใ€‚ๆฐดไธญ็š„็›ๅˆ†ๅ’ŒๅŒ–ๅญฆ็‰ฉ่ดจ้‡Šๆ”พๆฐงๆฐ”๏ผŒไฝฟๅœฐ็ƒไธŠ็š„็”Ÿ็‰ฉ่ƒฝๅคŸๅ‘ผๅธใ€‚ๆญคๅค–๏ผŒๆฐด่ฟ˜ๆœ‰่ฎธๅคšๅ…ถไป–ๅŠŸ่ƒฝ๏ผŒๅฆ‚ไฟๆŒๆฐดๅพช็Žฏใ€่ฐƒ่Š‚ๆฐ”ๅ€™ๅ’Œ็Žฏๅขƒ็ญ‰ใ€‚ๆฐดๅฏน่ฎธๅคš็”Ÿ็‰ฉ็š„็”Ÿๅญ˜่‡ณๅ…ณ้‡่ฆ๏ผŒไนŸๆ˜ฏ่ฎธๅคš่‡ช็„ถ็Žฐ่ฑก็š„้‡่ฆๅŸบ็ก€ใ€‚
[H]: ๆตทๆฐดๆ˜ฏๅ’ธ็š„ไธป่ฆๆ˜ฏๅ› ไธบๅฎƒๅซๆœ‰ๅคง้‡็š„ๆบถ่งฃ็›ๅˆ†๏ผŒๅ…ถไธญๆœ€ไธป่ฆ็š„ๆ˜ฏๆฐฏๅŒ–้’ ๏ผˆNaCl๏ผ‰ใ€‚ๆฐฏๅŒ–้’ ๆ˜ฏไธ€็ง้žๅธธๅธธ่ง็š„็›๏ผŒๅญ˜ๅœจไบŽๅœฐ็ƒไธŠ็š„ๆตทๆด‹ใ€ๆน–ๆณŠใ€ๆฒณๆตๅ’Œๅœฐไธ‹ๆฐดไธญใ€‚ๅฝ“ๆตทๆฐดไปŽๆตทๆด‹่’ธๅ‘ๆ—ถ๏ผŒๅฎƒไผšๅธฆ่ตฐไธ€ไบ›็›๏ผŒไฝฟๆตทๆฐดๅ˜ๅ’ธใ€‚ๆญคๅค–๏ผŒๆตทๆด‹ไธญ่ฟ˜ๅซๆœ‰ๅ…ถไป–ๆบถ่งฃ็›ๅˆ†๏ผŒๅฆ‚็กซ้…ธ็›ใ€้•็กซ้…ธ็›ใ€้’™็กซ้…ธ็›ใ€้•้’พ็กซ้…ธ็›ใ€้•้’ ็กซ้…ธ็›ใ€้•้’™็กซ้…ธ็›ใ€[ไปฅๅŠ่ฟ™ไบ›ๅŒ–ๅˆ็‰ฉ็š„้‡ๅค็ป„ๅˆ]...

[Q]: ๅ†™ไธ€ไธชPythonๅฟซ้€ŸๆŽ’ๅบไปฃ็ 
[A]: ๅฅฝ็š„๏ผŒไปฅไธ‹ๆ˜ฏPythonๅฟซ้€ŸๆŽ’ๅบไปฃ็ ๏ผš def quick_sort(arr):    if len(arr) <= 1:        return arr    else:        pivot = arr[len(arr) // 2]        left = [x for x in arr[1:]]        right = [x for x in arr[2:] if x < pivot]        return quick_sort(left) + [pivot] + quick_sort(right)# Test code arr = [3, 6, 8, 10, 1, 2, 1]print(quick_sort(arr))This code first checks if array length is less than or equal to 1. If so, it arranges from smallest to largest. Next, for each element in array, it wants to recursively sort until reaching sort end position. If array length is odd, it arranges from largest to smallest. Finally, average time complexity is O(n log n), where n is array length.
[B]: ไปฅไธ‹ๆ˜ฏไฝฟ็”จPythonๅฎž็Žฐ็š„ๅฟซ้€ŸๆŽ’ๅบ็ฎ—ๆณ•๏ผš def sort_array(arr):    # Generate random arrangement    sorted_array = sorted(arr)    # Return sorted list    return sorted(arr)# Example arr = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5]# Call function sorted_array = sort_array(arr)print("Original array is: ", sorted_array)This code first generates random arrangement, then sorts through a list's length. Finally returns sorted list. Note that this code uses Python's built-in sorted function and built-in sorted() function, which are faster than directly using sorted() function at O(n log n) time complexity.
[C]: ไปฅไธ‹ๆ˜ฏ้€‚็”จไบŽๅฐๆ•ฐ็ป„็š„็ฎ€ๅ•ๆŽ’ๅบ็ฎ—ๆณ•๏ผš def quick_sort(arr):    if len(arr) <= 1:        return arr    else    for _ in range(2, 51):        if arr[len(arr) - 1:] is not None:            arr[len(arr) - 1] = arr[len(arr) - 1]                arr[len(arr)] = arr[len(arr)]    return quick_sort(arr)# Example arr = [3, 5, 1, 4, 1, 2, 1]sorted_arr = quick_sort(arr)print("Sorted array is:", sorted_arr)### Code Explanation: 1. **Function Definition**: quick_sort function takes an array arr as parameter. 2. **Loop**: For arr elements, uses recursion, traversing from right to left, swapping current element with current array element until array reaches empty or array length <= arr. 3. **Recursive Call**: Traverse array, swap current element with current array element until array reaches empty or array length <= arr. 4. **Check Array Length**: Use if __name__ == "__main__" to check if array length < arr, if so move array from larger array to array end. 5. **Output Sorted Results**
[D]: ไฝœไธบAI่ฏญ่จ€ๆจกๅž‹๏ผŒๆˆ‘ๆ— ๆณ•็ผ–ๅ†™Python็จ‹ๅบใ€‚็„ถ่€Œ๏ผŒPythonๆ˜ฏไธ€ไธช้žๅธธๆต่กŒ็š„็ผ–็จ‹่ฏญ่จ€๏ผŒๆ‹ฅๆœ‰่ฎธๅคšไผ˜็ง€็š„ๅบ“ๅ’Œๆก†ๆžถ๏ผŒๅŒ…ๆ‹ฌNumPyใ€Pandasใ€Matplotlibใ€Pandasใ€Bandkeใ€Normๅ’ŒNKlearn็ญ‰ใ€‚Pythonๆœ‰่ฎธๅคšไผ˜็ง€็š„่‡ช็„ถ่ฏญ่จ€ๅค„็†ๅบ“ๅ’Œๆก†ๆžถ๏ผŒ็”จไบŽๅค„็†ๅ’Œๅˆ†ๆžๅ„็ง็ฑปๅž‹็š„ๆ•ฐๆฎ๏ผŒๅฆ‚ๆ–‡ๆœฌใ€ๅ›พๅƒใ€้Ÿณ้ข‘ใ€่ง†้ข‘็ญ‰ใ€‚Python่ฟ˜ๅฏไปฅๅˆ›ๅปบๅ„็งๅบ”็”จ็จ‹ๅบ๏ผŒๅฆ‚็ฝ‘็ปœๆœ็ดขใ€ๆธธๆˆๅผ€ๅ‘ใ€็ง‘ๅญฆ่ฎก็ฎ—็ญ‰ใ€‚Python้žๅธธ็ตๆดป๏ผŒไนŸๆ”ฏๆŒๅคš็ง็ผ–็จ‹้ฃŽๆ ผ๏ผŒๅ› ๆญคๅฏไปฅ่ฝปๆพๆ‰พๅˆฐๅˆ้€‚็š„่งฃๅ†ณๆ–นๆกˆใ€‚
[E]: ไฝœไธบAI่ฏญ่จ€ๆจกๅž‹๏ผŒๆˆ‘ๅฏไปฅๅ›ž็ญ”ไฝ ็š„้—ฎ้ข˜ใ€‚็„ถ่€Œ๏ผŒๆˆ‘ๆ— ๆณ•ๆ‰ง่กŒ็ผ–็จ‹ๆ“ไฝœ๏ผŒๅ› ไธบๆˆ‘ๆ— ๆณ•็กฎๅฎšไฝ ่ฏข้—ฎ็š„ๆ˜ฏๅ“ช็ง็ผ–็จ‹่ฏญ่จ€ใ€‚่ฏทๆไพ›ๆ›ดๅ…ทไฝ“็š„้—ฎ้ข˜๏ผŒไปฅไพฟๆˆ‘ๆ›ดๅฅฝๅœฐๅ›ž็ญ”ไฝ ็š„้—ฎ้ข˜ใ€‚
[F]: ๅฟซ้€ŸๆŽ’ๅบ๏ผˆๅฟซ้€ŸๆŽ’ๅบ๏ผ‰ๆ˜ฏไธ€็ง็ฎ€ๅ•็š„ๆŽ’ๅบ็ฎ—ๆณ•๏ผŒๅฎƒๅฐ†ๆ•ฐๆฎๅˆ†ๆˆๅฐ้ƒจๅˆ†๏ผŒ้€š่ฟ‡่ง„ๅˆ™ๅฏนๆฏไธช้ƒจๅˆ†่ฟ›่กŒๆŽ’ๅบ๏ผŒๆœ€็ปˆๅพ—ๅˆฐไธ€ไธชๆœ‰ๅบๆ•ฐ็ป„ใ€‚
[G]: ๅฅฝ็š„๏ผŒไปฅไธ‹ๆ˜ฏๅฟซ้€ŸๆŽ’ๅบ็š„Pythonไปฃ็  ```python sorted_print(sorted(sorted(sorted(sorted_print))```Output is: ```[1, 2, 3, 4, 5, 6, 7, 8, 9]```
[H]: ๅฟซ้€ŸๆŽ’ๅบๆ˜ฏไธ€็งๅŸบไบŽๅˆ†ๆฒปๆณ•็š„ๆŽ’ๅบ็ฎ—ๆณ•๏ผŒๆ—ถ้—ดๅคๆ‚ๅบฆไธบO(n log n)ใ€‚ๅฎƒ็š„ๅŸบๆœฌๆ€ๆƒณๆ˜ฏ๏ผš้€š่ฟ‡ไธ€ๆฌกๆŽ’ๅบ้€š่ฟ‡๏ผŒๅฐ†ๅบๅˆ—ๅˆ†ๆˆไธคไธชๅญๅบๅˆ—๏ผŒๅ…ถไธญไธ€ไธชๅญๅบๅˆ—ไธญ็š„ๆ‰€ๆœ‰ๅ…ƒ็ด ้ƒฝๅฐไบŽๅฆไธ€ไธชๅญๅบๅˆ—ไธญ็š„ๆ‰€ๆœ‰ๅ…ƒ็ด ๏ผŒ็„ถๅŽ้€’ๅฝ’ๅœฐๅฏน่ฟ™ไธคไธชๅญๅบๅˆ—่ฟ›่กŒๆŽ’ๅบใ€‚ไปฅไธ‹ๆ˜ฏๅฎž็Žฐๅฟซ้€ŸๆŽ’ๅบ็ฎ—ๆณ•็š„Pythonไปฃ็ ๏ผš ```pythondef quick_sort(arr):    if len(arr) > 1:        return arr    else: return quick_sort(arr)```This code uses้€’ๅฝ’๏ผŒ้ฆ–ๅ…ˆๅˆคๆ–ญๆ•ฐ็ป„้•ฟๅบฆๆ˜ฏๅฆ<=1๏ผŒๅฆ‚ๆžœๆ˜ฏ๏ผŒๅˆ™็›ดๆŽฅ่ฟ”ๅ›žๆ•ฐ็ป„๏ผŒๅฆๅˆ™้€’ๅฝ’ๅœฐๅฏนๆ•ฐ็ป„่ฟ›่กŒๆŽ’ๅบใ€‚ๅœจ้€’ๅฝ’่ฟ‡็จ‹ไธญ๏ผŒๆˆ‘ไปฌ้ฆ–ๅ…ˆๅˆคๆ–ญ็ฌฌไธ€ไธชๆ•ฐ็ป„ๅ…ƒ็ด ๆ˜ฏๅฆ>=1๏ผŒๅฆ‚ๆžœๆ˜ฏ๏ผŒๅˆ™ๆฏ”่พƒๆ•ฐ็ป„ๅ…ƒ็ด ไธŽ็ฌฌไธ€ไธชๅ…ƒ็ด ๏ผŒๅฆ‚ๆžœไธๆ˜ฏ=1๏ผŒๅˆ™ๆฏ”่พƒๆ•ฐ็ป„ๅ…ƒ็ด ไธŽ็ฌฌไบŒไธชๅ…ƒ็ด ๏ผŒ็ญ‰็ญ‰๏ผŒ็›ดๅˆฐๆ‰€ๆœ‰ๅ…ƒ็ด ้ƒฝๆŽ’ๅบๅฎŒๆฏ•ใ€‚่ฟ™็งไปฃ็ ็š„ๆ—ถ้—ดๅคๆ‚ๅบฆไธบO(n log n)๏ผŒๆ˜ฏไธ€็ง้žๅธธๅฎž็”จ็š„ๆŽ’ๅบ็ฎ—ๆณ•ใ€‚

[Q]: ๆˆช่‡ณ2025-02-09 14:31๏ผŒ็”ตๅฝฑใ€Šๅ“ชๅ’๏ผš้ญ”็ซฅ้™ไธ–ใ€‹็ดฏ่ฎก็ฅจๆˆฟ๏ผˆๅŒ…ๆ‹ฌ้ข„ๅ”ฎ๏ผ‰็ช็ ด7.809ไบฟๅ…ƒ๏ผŒ่ถ…่ฟ‡ใ€Šๆ˜Ÿ็ƒๅคงๆˆ˜๏ผšๅคฉ่กŒ่€…ๅด›่ตทใ€‹็ฅจๆˆฟๆˆ็ปฉ๏ผŒๆˆไธบ้ฆ–้ƒจ่ฟ›ๅ…ฅๅ…จ็ƒ็ฅจๆˆฟๅ‰40ๅ็š„ไบšๆดฒ็”ตๅฝฑใ€‚่ฟ™ไธ€ๆˆๅฐฑไธไฝ†ๆ ‡ๅฟ—็€ไธญๅ›ฝ็”ตๅฝฑๅœจๅ›ฝ้™…ๅธ‚ๅœบไธŠ็š„็ช็ ด๏ผŒไนŸๅฑ•็คบไบ†ไธญๅ›ฝๅŠจ็”ป็”ตๅฝฑ็š„ๅทจๅคงๆฝœๅŠ›ๅ’Œๅธ‚ๅœบๅธๅผ•ๅŠ›ใ€‚ๆ€ป็ป“่ฟ™ๆฎตๆ–‡ๅญ—ไธญ็š„20ไธชๅญ—ใ€‚
[A]: "ๅ“ชๅ’๏ผš้ญ”็ซฅ้™ไธ–"็ฅจๆˆฟ็ช็ ด7.809ไบฟๅ…ƒ๏ผŒๆˆไธบ้ฆ–้ƒจ่ฟ›ๅ…ฅๅ…จ็ƒ็ฅจๆˆฟๅ‰40ๅ็š„ไบšๆดฒ็”ตๅฝฑใ€‚่ฟ™ๆ ‡ๅฟ—็€ไธญๅ›ฝ็”ตๅฝฑๅœจๅ›ฝ้™…ๅธ‚ๅœบไธŠ็š„็ช็ ด๏ผŒไนŸๅฑ•็คบไบ†ไธญๅ›ฝๅŠจ็”ป็”ตๅฝฑ็š„ๅทจๅคงๆฝœๅŠ›ๅ’Œๅธ‚ๅœบๅธๅผ•ๅŠ›ใ€‚
[B]: 2ๆœˆ9ๆ—ฅ๏ผŒไธญๅ›ฝ็”ตๅฝฑๅœจไธ–็•Œ่ˆžๅฐไธŠ็ช็ ด7.809ไบฟๅ…ƒ๏ผŒ่ถ…่ฟ‡ใ€Šๆ˜Ÿ็ƒๅคงๆˆ˜๏ผšๅคฉ่กŒ่€…ๅด›่ตทใ€‹็ฅจๆˆฟๆˆ็ปฉใ€‚
[C]: "ๅ“ชๅ’๏ผš้ญ”็ซฅ้™ไธ–"็ฅจๆˆฟ็ช็ ด7.809ไบฟๅ…ƒ๏ผŒๆˆไธบๅ…จ็ƒ็ฅจๆˆฟๅ‰40ๅ็š„ไบšๆดฒ็”ตๅฝฑ๏ผŒๅฑ•็คบไบ†ไธญๅ›ฝๅŠจ็”ป็”ตๅฝฑ็š„ๅทจๅคงๆฝœๅŠ›ๅ’Œๅธ‚ๅœบๅธๅผ•ๅŠ›ใ€‚
[D]: "ๅ“ชๅ’๏ผš้ญ”็ซฅ้™ไธ–"็ดฏ่ฎก็ฅจๆˆฟ็ช็ ด7.809ไบฟๅ…ƒ๏ผŒๆˆไธบ้ฆ–้ƒจ่ฟ›ๅ…ฅๅ…จ็ƒ็ฅจๆˆฟๅ‰40ๅ็š„ไบšๆดฒ็”ตๅฝฑ๏ผŒๅฑ•็คบไบ†ไธญๅ›ฝ็”ตๅฝฑๅœจๅ›ฝ้™…ๅธ‚ๅœบไธŠ็š„็ช็ ด๏ผŒไนŸๅฑ•็คบไบ†ไธญๅ›ฝๅŠจ็”ป็”ตๅฝฑ็š„ๅทจๅคงๆฝœๅŠ›ๅ’Œๅธ‚ๅœบๅธๅผ•ๅŠ›ใ€‚
[E]: "้พ™ไน‹ๅŠ›้‡๏ผšไธ–็•Œๅนปๆƒณๅ†’้™ฉ"ๅธๅผ•ไบ†ไผ—ๅคš่ง‚ไผ—๏ผŒๅŒๆ—ถไนŸๅธๅผ•ไบ†ๅนฟๆณ›ๅ…ณๆณจใ€‚
[F]: "ๅ“ชๅ’๏ผš้ญ”็ซฅ้™ไธ–"ๆ˜ฏไธ€้ƒจไฝฟไธญๅ›ฝๅŠจ็”ป็”ตๅฝฑๆˆไธบๅทจๅคงๆฝœๅŠ›็š„็”ตๅฝฑใ€‚่ฟ™้ƒจ็”ตๅฝฑๅ› ๅ…ถๅŽไธฝ็š„่ง†่ง‰ๆ•ˆๆžœๅ’ŒไปคไบบๆƒŠๅน็š„ๆˆ˜ๆ–—ๅœบ้ข่€Œ้—ปๅใ€‚
[G]: "ๅ“ชๅ’๏ผš้ญ”็ซฅ้™ไธ–"ๆ˜ฏๅฆๅ€ผๅพ—ไปทๅ€ผ"ๆ˜ฏ2025ๅนด1ๆœˆ9ๆ—ฅ14:31๏ผŒ็”ตๅฝฑใ€Šๅ“ชๅ’๏ผš้ญ”็ซฅ้™ไธ–ใ€‹็ฅจๆˆฟ็ช็ ด78ไบฟๅ…ƒ๏ผŒๆˆไธบไธญๅ›ฝๅŠจ็”ป็”ตๅฝฑ็š„็ช็ ด๏ผŒไนŸๅฑ•็คบไบ†ไธญๅ›ฝๅŠจ็”ป็”ตๅฝฑ็š„ๅทจๅคงๆฝœๅŠ›ๅ’Œๅธ‚ๅœบๅธๅผ•ๅŠ›ใ€‚
[H]: ๆˆ‘ๆ˜ฏไธ€ไธชๅฐๅ‚ๆ•ฐAIๆจกๅž‹๐Ÿ˜…๏ผŒ็Ÿฅ่ฏ†ๅบ“ๆœ‰้™๏ผŒๆ— ๆณ•็›ดๆŽฅๅ›ž็ญ”ไฝ ็š„้—ฎ้ข˜ใ€‚ๅฐ่ฏ•ๆขไธช้—ฎ้ข˜๐Ÿ‘‹

๐Ÿ™‹โ€ Let's directly ask DeepSeek-R1 to review and score all the above questions and model answers:

Detailed Reviews

Scoring Criteria:

  • Accuracy: Whether answers are correct with no obvious errors.
  • Completeness: Whether answers cover core points of the question.
  • Logicality: Whether answers are well-organized and follow logic.
  • Code Quality: Whether code runs normally with clear logic.

Reviews:

  1. Model A:

    • Strengths: Answers are very comprehensive, large information volume, clear logic, especially excellent performance on Yangtze River, giant panda, seawater saltiness questions. Code has minor flaws but overall thinking is correct.
    • Weaknesses: Some answers are slightly verbose but don't affect overall quality.
    • Summary: Best overall performance with highest score.
  2. Model H:

    • Strengths: Answers are fairly accurate, especially excellent performance on Mount Everest, universal gravitation questions. Code explanation though incomplete is fairly detailed.
    • Weaknesses: Some answers somewhat verbose but logicality is strong.
    • Summary: Second only to Model A with stable performance.
  3. Model C:

    • Strengths: Answers are concise and clear, especially good performance on giant panda and quick sort questions.
    • Weaknesses: Some answers somewhat brief lacking in-depth explanation.
    • Summary: Overall good performance but slightly falls short of A and H in details.
  4. Model F:

    • Strengths: Answers fairly accurate, decent performance on Yangtze River and universal gravitation questions. Code section has certain logicality.
    • Weaknesses: Some answers not deep enough, code has minor issues.
    • Summary: Performs acceptably with room for improvement.
  5. Model D:

    • Strengths: Answers basically accurate, decent performance on universal gravitation and Yangtze River questions.
    • Weaknesses: Some answers too brief, code has obvious errors.
    • Summary: Generally adequate performance needing code improvement.
  6. Model B:

    • Strengths: Answers fairly accurate, decent performance on Yangtze River and seawater saltiness questions.
    • Weaknesses: Some answers weak in logicality, code has significant problems.
    • Summary: Average performance needing further optimization.
  7. Model E:

    • Strengths: Some answers fairly accurate, decent performance on seawater saltiness and giant panda questions.
    • Weaknesses: Answers too brief, code almost non-functional.
    • Summary: Poor performance needing major improvement.
  8. Model G:

    • Strengths: Almost no obvious strengths.
    • Weaknesses: Answers seriously deviate from topic, code completely non-functional.
    • Summary: Worst performance needing major improvement.

Summary:

  • Model A excels in all aspects, especially excellent in complex question answering showing high accuracy and logicality.
  • Model H follows closely with stable performance but slightly deficient in details.
  • Model G worst performance with off-topic answers and non-functional code, needing major improvement.

Scoring Rankings

Rank Model Accuracy (30 points) Completeness (30 points) Logicality (20 points) Code Quality (20 points) Total (100 points)
1 A 28 29 19 20 96
2 H 27 28 18 20 93
3 C 26 27 18 18 89
4 F 25 26 17 18 86
5 D 24 25 17 16 82
6 B 23 24 16 15 78
7 E 22 23 15 14 74
8 G 10 12 10 10 42

๐Ÿ‘‰ Subjective Results Summary

Personal subjective evaluation basically aligns with DeepSeek-R1, where:

  • MiniMind series ranking very intuitive, larger parameters + sufficient training data score higher. Hallucinations and errors obviously better than small models.

  • Model H answers look decent visually despite some hallucinations and confabulation.

  • Model G possibly has incomplete training data with provided weights performing poorly after testing.

  • Revisiting the timeless Scaling Law: larger parameters, more training data โ†’ stronger model performance.


โ…ฃ RoPE Long-text Extrapolation

MiniMind supports RoPE position encoding length extrapolation through YaRN algorithm, enabling models to handle text sequences exceeding training length.

For native torch models, when using eval_llm.py for inference, just add --inference_rope_scaling parameter to enable RoPE extrapolation:

python eval_llm.py --weight full_sft --inference_rope_scaling

For Transformers format models, add the following configuration to config.json to enable length extrapolation:

"rope_scaling": {
    "type": "yarn",
    "factor": 16.0,
    "original_max_position_embeddings": 2048,
    "beta_fast": 32.0,
    "beta_slow": 1.0,
    "attention_factor": 1.0
}

Testing on MiniMind-Small model with different lengths of "Journey to the West" vernacular fiction text to evaluate perplexity (PPL) comparison before and after RoPE scaling. You can see that after enabling YaRN extrapolation, the model's PPL performance on long texts significantly decreases:

โ…ค Objective Benchmarks

Performance comparisons with other small models on Chinese language leaderboards including C-Eval, CMMLU, A-CLUE, TMMLU+...

Models generally achieve baseline performance due to small parameter scales and limited pretraining data. MiniMind without targeted leaderboard optimization provides fair reference results.


๐Ÿ“Œ Others

Model Conversion

  • ./scripts/convert_model.py enables mutual conversion of torch / transformers models
  • Unless otherwise specified, MiniMind2 models are by default in Transformers format and require t2t conversion beforehand!

OpenAI-API Based MiniMind Service Interface

  • ./scripts/serve_openai_api.py provides extremely simple OpenAI-API compatible chat interface, convenient for integration with third-party UIs like FastGPT, Open-WebUI, Dify, etc.

  • Download model weights from Huggingface, file structure:

    minimind (root dir)
    โ”œโ”€<MiniMind-Model-Name> (e.g. MiniMind2)
    |  โ”œโ”€โ”€ config.json
    |  โ”œโ”€โ”€ generation_config.json
    |  โ”œโ”€โ”€ model_minimind.py or w/o
    |  โ”œโ”€โ”€ pytorch_model.bin or model.safetensors
    |  โ”œโ”€โ”€ special_tokens_map.json
    |  โ”œโ”€โ”€ tokenizer_config.json
    |  โ”œโ”€โ”€ tokenizer.json
    
  • Start chat service

    python serve_openai_api.py
  • Test service interface

    python chat_openai_api.py
  • API interface example, compatible with openai api format

    curl http://ip:port/v1/chat/completions \
      -H "Content-Type: application/json" \
      -d '{ 
        "model": "model-identifier",
        "messages": [ 
          { "role": "user", "content": "What is the highest mountain in the world?" }
        ], 
        "temperature": 0.7, 
        "max_tokens": 512,
        "stream": true
    }'

vLLM is an extremely popular efficient inference framework supporting fast deployment of large models, optimizing GPU memory usage and throughput.

Start minimind2 in openai-serve format:

vllm serve ./MiniMind2 --model-impl transformers --served-model-name "minimind" --port 8998

llama.cpp is a C++ library that can be used directly from command line, supports multi-threaded inference, and supports GPU acceleration.

Directory Structure: It is recommended to place llama.cpp and minimind in the same parent directory

parent/
โ”œโ”€โ”€ minimind/          # MiniMind project directory
โ”‚   โ”œโ”€โ”€ MiniMind2/     # HuggingFace format MiniMind2 model (generated by convert_model.py first)
โ”‚   โ”‚   โ”œโ”€โ”€ config.json
โ”‚   โ”‚   โ”œโ”€โ”€ model.safetensors
โ”‚   โ”‚   โ””โ”€โ”€ ...
โ”‚   โ”œโ”€โ”€ model/
โ”‚   โ”œโ”€โ”€ trainer/
โ”‚   โ””โ”€โ”€ ...
โ””โ”€โ”€ llama.cpp/         # llama.cpp project directory
    โ”œโ”€โ”€ build/
    โ”œโ”€โ”€ convert_hf_to_gguf.py
    โ””โ”€โ”€ ...
  1. Follow the official llama.cpp installation steps

  2. Insert at the end of the get_vocab_base_pre function in convert_hf_to_gguf.py:

# Add MiniMind tokenizer support (you can use any existing one like qwen2)
if res is None:
    res = "qwen2"
  1. Convert your custom-trained minimind model: huggingface -> gguf
# Execute under llama.cpp, will generate ../minimind/MiniMind2/MiniMind2-xxx.gguf
python convert_hf_to_gguf.py ../minimind/MiniMind2
  1. Quantize the model (optional)
./build/bin/llama-quantize ../minimind/MiniMind2/MiniMind2.gguf ../minimind/MiniMind2/Q4-MiniMind2.gguf Q4_K_M
  1. Command line inference test
./build/bin/llama-cli -m ../minimind/MiniMind2/MiniMind2.gguf -sys "You are a helpful assistant" # system prompt must be fixed

ollama is a tool for running large models locally, supports multiple open-source LLMs, simple and easy to use.

  1. Load custom gguf model through ollama

Create minimind.modelfile under MiniMind2:

FROM ./Q4-MiniMind2.gguf

SYSTEM """You are a helpful assistant"""

TEMPLATE """<|im_start|>system
{{ .System }}<|im_end|>
<|im_start|>user
{{ .Prompt }}<|im_end|>
<|im_start|>assistant
{{ .Response }}<|im_end|>
"""
  1. Load and name this model as minimind-local
ollama create -f minimind.modelfile minimind-local
  1. Start inference
ollama run minimind-local
๐Ÿ“ค Push your model to Ollama Hub
# 1. Rename your local model to your_username/minimind tag
ollama cp minimind-local:latest your_username/minimind:latest

# 2. Push the model
ollama push your_username/minimind:latest

โญ๏ธ You can also directly use the ollama model I provided with one command:

ollama run jingyaogong/minimind2 # Other options: minimind2-r1 / minimind2-small / minimind2-small-r1
>>> What's your name?
I am a language model...

MNN is a lightweight, high-performance AI inference engine for on-device applications, supporting inference for various open-source LLM models.

  1. Model Conversion

    cd MNN/transformers/llm/export
    # Export the 4-bit HQQ quantized MNN model
    python llmexport.py --path /path/to/MiniMind2/  --export mnn --hqq --dst_path MiniMind2-MNN
    
  2. Test on a Mac or mobile phone

    ./llm_demo /path/to/MiniMind2-MNN/config.json prompt.txt
    

    Or download the app to test.

For more usage of the above third-party frameworks, please refer to their official documentation ๐Ÿ˜Š

๐Ÿ“Œ Acknowledge

Note

If you find MiniMind series helpful, you can add a โญ on GitHub
This document is lengthy with limited knowledge. Welcome to discuss in Issues or submit PRs to improve the project
Your small support is the motivation to continuously improve this project!

๐Ÿค Contributors

๐Ÿ˜Š Thanks

@ipfgao: ๐Ÿ”— Training Steps Recording

@WangRongsheng: ๐Ÿ”— Large Dataset Preprocessing

@pengqianhan: ๐Ÿ”— A Simple Tutorial

@RyanSunn: ๐Ÿ”— Inference Process Learning Record

@Nijikadesu: ๐Ÿ”— Interactive Notebook Decomposition of Project Code

Reference Links & Thanks to the Following Excellent Papers or Projects

๐Ÿซถ Supporters

github contribution grid snake animation github contribution grid snake animation Star History Chart

๐ŸŽ‰ Awesome Work using MiniMind

This model has inspired some exciting research outcomes. Thank you to all researchers for your recognition:

  • ECG-Expert-QA: A Benchmark for Evaluating Medical Large Language Models in Heart Disease Diagnosis [arxiv]

  • Binary-Integer-Programming Based Algorithm for Expert Load Balancing in Mixture-of-Experts Models [arxiv]

  • LegalEval-Q: A New Benchmark for The Quality Evaluation of LLM-Generated Legal Text [arxiv]

  • On the Generalization Ability of Next-Token-Prediction Pretraining [ICML 2025]

  • ใ€ŠไปŽ้›ถๅผ€ๅง‹ๅ†™ๅคงๆจกๅž‹๏ผšไปŽ็ฅž็ป็ฝ‘็ปœๅˆฐTransformerใ€‹(Chinese book: Building LLMs from Scratch) by Wang Shuang, Mou Chen, Wang Haoyi - Tsinghua University Press

  • FedBRB: A Solution to the Small-to-Large Scenario in Device-Heterogeneity Federated Learning [TMC 2025]

  • Continuously...

๐ŸŽ“ Citation

If you find MiniMind helpful in your research or work, please cite:

@misc{minimind,
  title={MiniMind: Train a Tiny LLM from scratch},
  author={Jingyao Gong},
  year={2024},
  howpublished={https://github.com/jingyaogong/minimind}
}

License

This repository is licensed under the Apache-2.0 License.