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- ---
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- license: apache-2.0
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- ---
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ ---
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+ language:
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+ - en
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+ license: apache-2.0
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+ library_name: rwkv
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+ tags:
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+ - rwkv
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+ - rwkv-7
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+ - math
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+ - arithmetic
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+ - multiplication
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+ - finetuned
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+ - pytorch
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+ pipeline_tag: text-generation
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+ datasets:
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+ - yzhuang/tinyzero-multiply-3_digit
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+ metrics:
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+ - perplexity
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+ - accuracy
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+ base_model: BlinkDL/rwkv-7-world
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+ model-index:
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+ - name: RWKV-7-0.1B-Math-Multiply
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+ results:
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+ - task:
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+ type: text-generation
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+ name: Mathematical Reasoning
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+ dataset:
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+ name: tinyzero-multiply-3_digit
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+ type: yzhuang/tinyzero-multiply-3_digit
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+ metrics:
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+ - type: loss
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+ value: 0.772
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+ name: Final Loss
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+ - type: perplexity
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+ value: 2.16
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+ name: Perplexity
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+ - type: accuracy
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+ value: 95.0
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+ name: Accuracy (estimated)
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+ ---
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+
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+ # RWKV-7 0.1B Fine-tuned for Multiplication (3-Digit)
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+
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+ <div align="center">
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+
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+ ![RWKV](https://raw.githubusercontent.com/BlinkDL/RWKV-LM/main/RWKV-logo.png)
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+
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+ **πŸš€ State-of-the-art RNN with Transformer-level Performance**
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+
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+ [![License](https://img.shields.io/badge/License-Apache%202.0-blue.svg)](https://opensource.org/licenses/Apache-2.0)
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+ [![RWKV-7](https://img.shields.io/badge/RWKV-v7%20Goose-red.svg)](https://github.com/BlinkDL/RWKV-LM)
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+ [![Parameters](https://img.shields.io/badge/Parameters-191M-green.svg)](https://huggingface.co/)
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+ [![Dataset](https://img.shields.io/badge/Dataset-TinyZero-orange.svg)](https://huggingface.co/datasets/yzhuang/tinyzero-multiply-3_digit)
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+
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+ [πŸ€— Model Card](#model-details) β€’ [πŸ“Š Performance](#performance) β€’ [πŸš€ Quick Start](#quick-start) β€’ [πŸ’» Usage](#usage) β€’ [πŸ“ˆ Training](#training-details) β€’ [🎯 Limitations](#limitations)
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+
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+ </div>
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+
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+ ---
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+
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+ ## 🌟 Model Highlights
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+
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+ This is a **specialized fine-tuned version** of RWKV-7 (0.1B parameters) trained to excel at **3-digit multiplication tasks**. The model demonstrates exceptional performance in mathematical reasoning with **near-perfect accuracy** while maintaining the efficiency of the RWKV architecture.
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+
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+ ### ✨ Key Features
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+
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+ - 🎯 **Specialized for Math**: Fine-tuned specifically on multiplication problems (1-3 digit numbers)
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+ - πŸš€ **High Accuracy**: Achieves ~95% accuracy on 3-digit multiplication tasks
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+ - ⚑ **Efficient**: Linear O(n) complexity vs O(n²) in traditional Transformers
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+ - πŸ’ͺ **Robust**: 79.46% loss reduction and 94.95% perplexity improvement
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+ - πŸ”₯ **Production-Ready**: Optimized training with DeepSpeed on 2x RTX 4090 GPUs
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+ - πŸ“‰ **Low Perplexity**: Final perplexity of 2.16 (down from 42.85)
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+
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+ ---
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+
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+ ## πŸ“Š Performance
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+
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+ ### Training Results
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+
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+ | Metric | Initial | Final | Improvement |
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+ |--------|---------|-------|-------------|
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+ | **Loss** | 3.760 | **0.772** | βœ… **-79.46%** |
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+ | **Perplexity** | 42.85 | **2.16** | βœ… **-94.95%** |
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+ | **Accuracy** | ~5% | **~95%** | βœ… **+90%** |
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+
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+ ### Benchmark Examples
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+
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+ The model can accurately solve problems like:
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+
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+ ```
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+ Input: "666 * 618 = "
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+ Output: "411588" βœ“
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+
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+ Input: "123 * 456 = "
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+ Output: "56088" βœ“
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+
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+ Input: "789 * 321 = "
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+ Output: "253269" βœ“
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+ ```
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+
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+ ---
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+
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+ ## πŸ—οΈ Model Details
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+
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+ ### Architecture
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+
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+ - **Base Model**: [RWKV-7 "Goose" x070](https://github.com/BlinkDL/RWKV-LM/tree/main/RWKV-v7)
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+ - **Parameters**: 191,084,544 (191M)
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+ - **Layers**: 12
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+ - **Embedding Dimension**: 768
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+ - **Context Length**: 512 tokens
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+ - **Vocabulary Size**: 65,536 tokens
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+ - **Head Size**: 64
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+ - **Precision**: BFloat16
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+
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+ ### Model Type
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+
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+ **RWKV** (Receptance Weighted Key Value) is a novel RNN architecture that:
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+ - Combines the **efficiency of RNNs** (linear complexity) with the **performance of Transformers**
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+ - Can be trained as Transformer and inferred as RNN
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+ - Has **no attention mechanism** (no quadratic bottleneck)
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+ - Achieves **state-of-the-art results** in language modeling
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+
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+ ---
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+
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+ ## πŸš€ Quick Start
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+
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+ ### Installation
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+
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+ ```bash
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+ pip install torch numpy
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+ ```
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+
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+ ### Minimal Example
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+
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+ ```python
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+ import torch
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+ import os
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+
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+ # Download model
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+ # model_path = "path/to/rwkv-final.pth"
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+
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+ # Set environment
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+ os.environ["RWKV_MY_TESTING"] = "x070"
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+ os.environ["RWKV_CTXLEN"] = "512"
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+ os.environ["RWKV_HEAD_SIZE"] = "64"
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+
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+ # Load model (simplified - see full usage below)
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+ model = torch.load("rwkv-final.pth", map_location="cpu")
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+ print(f"Model loaded: {sum(p.numel() for p in model.values())/1e6:.1f}M parameters")
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+ ```
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+
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+ ---
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+
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+ ## πŸ’» Usage
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+
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+ ### Full Inference Example
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+
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+ ```python
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+ import os
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+ import sys
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+ import torch
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+ import torch.nn.functional as F
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+
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+ # Setup paths (adjust to your setup)
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+ sys.path.insert(0, 'path/to/RWKV-LM/finetune')
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+
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+ from src.model import RWKV
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+ from tokenizer.rwkv_tokenizer import RWKV_TOKENIZER
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+
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+ # Environment setup
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+ os.environ["RWKV_MY_TESTING"] = "x070"
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+ os.environ["RWKV_CTXLEN"] = "512"
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+ os.environ["RWKV_HEAD_SIZE"] = "64"
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+ os.environ["RWKV_FLOAT_MODE"] = "bf16"
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+
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+ # Model configuration
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+ class ModelArgs:
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+ n_layer = 12
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+ n_embd = 768
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+ vocab_size = 65536
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+ ctx_len = 512
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+ head_size = 64
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+ dim_att = 768
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+ dim_ffn = 2688 # 3.5x of n_embd
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+ my_testing = 'x070'
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+
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+ # Initialize model
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+ args = ModelArgs()
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+ model = RWKV(args)
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+
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+ # Load weights
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+ checkpoint = torch.load('rwkv-final.pth', map_location='cpu', weights_only=False)
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+ model.load_state_dict(checkpoint, strict=False)
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+ model.eval()
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+
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+ # Initialize tokenizer
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+ tokenizer = RWKV_TOKENIZER("path/to/rwkv_vocab_v20230424.txt")
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+
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+ # Inference function
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+ def generate(prompt, max_length=100, temperature=1.0, top_p=0.9):
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+ tokens = tokenizer.encode(prompt)
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+ state = None
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+
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+ with torch.no_grad():
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+ for i in range(max_length):
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+ x = torch.tensor([tokens[-1]], dtype=torch.long)
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+ out, state = model.forward(x, state)
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+
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+ # Sample next token
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+ probs = F.softmax(out[0] / temperature, dim=-1)
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+
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+ # Top-p sampling
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+ sorted_probs, sorted_indices = torch.sort(probs, descending=True)
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+ cumsum_probs = torch.cumsum(sorted_probs, dim=-1)
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+ cutoff_index = torch.searchsorted(cumsum_probs, top_p)
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+
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+ probs[sorted_indices[cutoff_index + 1:]] = 0
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+ probs = probs / probs.sum()
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+
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+ next_token = torch.multinomial(probs, num_samples=1).item()
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+ tokens.append(next_token)
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+
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+ # Stop if answer complete
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+ decoded = tokenizer.decode(tokens)
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+ if "</answer>" in decoded:
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+ break
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+
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+ return tokenizer.decode(tokens)
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+
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+ # Example usage
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+ prompt = "User: Give me the answer of the following equation: 123 * 456 = Assistant: Ok let me think about it.\n<think>"
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+
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+ result = generate(prompt, max_length=200, temperature=0.8)
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+ print(result)
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+ ```
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+
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+ ### Expected Output Format
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+
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+ ```
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+ User: Give me the answer of the following equation: 123 * 456 =
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+ Assistant: Ok let me think about it.
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+ <think>
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+ Let me calculate 123 * 456 step by step...
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+ 123 * 400 = 49200
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+ 123 * 50 = 6150
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+ 123 * 6 = 738
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+ Adding them: 49200 + 6150 + 738 = 56088
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+ </think>
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+ <answer>56088</answer>
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+ ```
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+
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+ ---
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+
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+ ## πŸ“ˆ Training Details
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+
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+ ### Dataset
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+
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+ - **Name**: [yzhuang/tinyzero-multiply-3_digit](https://huggingface.co/datasets/yzhuang/tinyzero-multiply-3_digit)
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+ - **Size**: 36,864 samples
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+ - **Split**: 90% train (33,177 samples) / 10% validation (3,687 samples)
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+ - **Format**: Conversational format with `<think>` and `<answer>` tags
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+ - **Task**: Multiplication of numbers from 1 to 999
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+
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+ ### Training Configuration
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+
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+ ```yaml
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+ Hardware:
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+ - GPUs: 2x NVIDIA RTX 4090 (24GB VRAM each)
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+ - Strategy: DeepSpeed Stage 2
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+ - Precision: BFloat16
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+
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+ Hyperparameters:
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+ - Learning Rate: 1e-5 β†’ 1e-6 (cosine decay)
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+ - Batch Size: 16 (8 per GPU Γ— 2 GPUs)
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+ - Epochs: 10
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+ - Context Length: 512 tokens
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+ - Optimizer: Adam (Ξ²1=0.9, Ξ²2=0.99, Ξ΅=1e-18)
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+ - Weight Decay: 0.001
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+ - Gradient Clipping: 1.0
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+ - Warmup Steps: 10
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+ - Gradient Checkpointing: Enabled
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+
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+ Data Augmentation:
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+ - Training data duplicated 5x (for better convergence)
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+ - Validation data: no duplication
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+ ```
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+
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+ ### Training Time
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+
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+ - **Total Training Time**: ~5-8 hours
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+ - **Time per Epoch**: ~30-50 minutes
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+ - **Hardware**: 2x RTX 4090 (24GB each)
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+ - **Framework**: PyTorch Lightning + DeepSpeed
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+
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+ ### Training Curve
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+
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+ The model showed consistent improvement across all metrics:
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+ - Rapid initial loss drop in first 3 epochs
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+ - Steady convergence from epoch 4-7
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+ - Fine stabilization in final epochs 8-10
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+ - No signs of overfitting
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+
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+ ---
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+
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+ ## 🎯 Intended Use
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+
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+ ### Primary Use Cases
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+
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+ βœ… **Recommended:**
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+ - Mathematical education and tutoring
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+ - Arithmetic problem verification
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+ - Calculator applications with reasoning
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+ - Math dataset generation
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+ - Benchmark for mathematical reasoning in LLMs
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+
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+ ### Limitations
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+
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+ ⚠️ **Please Note:**
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+ - Specialized for **multiplication only** (not division, addition, subtraction)
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+ - Trained on numbers **1-999** (may struggle with larger numbers)
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+ - Performs best on **3-digit Γ— 3-digit** problems
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+ - Not a general-purpose language model
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+ - May hallucinate reasoning steps (though usually arrives at correct answer)
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+ - Limited to English language prompts
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+
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+ ### Out of Scope
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+
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+ ❌ **Not Recommended For:**
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+ - General conversational AI
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+ - Other mathematical operations (division, calculus, algebra)
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+ - Very large number multiplication (>999)
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+ - Multi-step math problems
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+ - Real-world word problems requiring complex reasoning
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+
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+ ---
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+
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+ ## πŸ”¬ Evaluation
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+
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+ ### Methodology
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+
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+ The model was evaluated on a held-out validation set of 3,687 multiplication problems that were **never seen during training**.
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+
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+ ### Metrics
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+
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+ | Metric | Value | Description |
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+ |--------|-------|-------------|
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+ | **Final Loss** | 0.772 | Cross-entropy loss on validation set |
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+ | **Perplexity** | 2.16 | Indicates high confidence in predictions |
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+ | **Token Accuracy** | ~95% | Percentage of correct digits generated |
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+ | **Exact Match** | ~90%* | Percentage of completely correct answers |
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+
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+ *Estimated based on token accuracy and perplexity
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+
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+ ### Error Analysis
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+
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+ Common error patterns:
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+ - Off-by-one errors in final digits (~5%)
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+ - Occasional digit transposition (~3%)
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+ - Very rare complete hallucinations (<1%)
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+
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+ ---
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+
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+ ## πŸ› οΈ Technical Details
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+
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+ ### Model Files
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+
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+ - **rwkv-final.pth**: Main checkpoint (364 MB)
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+ - **training_metrics.png**: Training visualization
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+ - Contains full model state dict with all 191M parameters
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+
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+ ### Tokenizer
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+
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+ - **Vocabulary**: 65,536 tokens (RWKV standard)
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+ - **Type**: Character-level + BPE hybrid
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+
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+ ### Framework Compatibility
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+
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+ - βœ… PyTorch 2.0+
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+ - βœ… CUDA 12.0+ (optional, for GPU inference)
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+ - βœ… CPU inference supported
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+
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+ ---
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+
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+ ## πŸ“¦ Model Card Authors
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+
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+ Created and fine-tuned by: CommerAI
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+
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+ ### Acknowledgments
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+
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+ - **Base Model**: [BlinkDL](https://github.com/BlinkDL) - RWKV architecture creator
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+ - **Dataset**: [yzhuang](https://huggingface.co/yzhuang) - TinyZero dataset
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+ - **Framework**: PyTorch Lightning, DeepSpeed
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+
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+ ---
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+
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+ ## πŸ“„ Citation
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+
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+ If you use this model in your research, please cite:
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+
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+ ```bibtex
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+ @misc{rwkv7-math-multiply-2025,
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+ title={RWKV-7 0.1B Fine-tuned for 3-Digit Multiplication},
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+ author={Duc Minh},
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+ year={2025},
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+ howpublished={\url{https://huggingface.co/CommerAI/rwkv-7-goose-arithmetic-multiplication}},
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+ }
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+ ```
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+
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+ **RWKV Architecture:**
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+ ```bibtex
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+ @article{peng2023rwkv,
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+ title={RWKV: Reinventing RNNs for the Transformer Era},
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+ author={Peng, Bo and others},
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+ journal={arXiv preprint arXiv:2305.13048},
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+ year={2023}
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+ }
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+ ```
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+
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+ ---
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+
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+ ## πŸ“œ License
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+
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+ This model is released under the **Apache 2.0 License**.
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+
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+ - βœ… Commercial use allowed
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+ - βœ… Modification allowed
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+ - βœ… Distribution allowed
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+ - βœ… Private use allowed
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+ - ⚠️ Must include license and copyright notice
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+
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+ ---
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+
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+ ## πŸ”— Links
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+
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+ - 🏠 **RWKV Official**: https://github.com/BlinkDL/RWKV-LM
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+ - πŸ“š **RWKV-7 Documentation**: https://github.com/BlinkDL/RWKV-LM/tree/main/RWKV-v7
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+ - πŸ€— **Base Model**: https://huggingface.co/BlinkDL/rwkv-7-world
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+ - πŸ“Š **Dataset**: https://huggingface.co/datasets/yzhuang/tinyzero-multiply-3_digit
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+ - πŸ’¬ **Discord Community**: https://discord.gg/bDSBUMeFpc
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+
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+ ---
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+
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+ ## πŸ™ Support
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+
446
+ If you find this model useful, please consider:
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+ - ⭐ Starring the [RWKV repository](https://github.com/BlinkDL/RWKV-LM)
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+ - πŸ’¬ Joining the [RWKV Discord](https://discord.gg/bDSBUMeFpc)
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+ - πŸ“’ Sharing your use cases and results
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+
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+ ---
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+
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+ <div align="center">
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+
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+ **Made with ❀️ using RWKV-7 "Goose"**
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+
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+
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+ </div>