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BackSlash: Rate Constrained Optimized Training of Large Language Models
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Proposes BackSlash, a rate-distortion-optimized training method that adds a generalized-Gaussian rate penalty to the loss so LLM weights become compressible with exp-Golomb coding during training.
Problem
Model compression of LLMs is usually applied after training; the paper targets compressing parameters during training to trade off accuracy and model size for edge deployment.
Approach
Adds a discretized generalized-Gaussian rate term (sum of |theta|^nu with a dynamically estimated shape nu and soft gradient clipping) to the training loss, and entropy-codes the resulting parameter indices with exp-Golomb (k=0) codes after value mapping.
Key results
- On BERT sentiment analysis, BackSlash with EG coding reduces average code length from 7.31 to 2.64 bits (74% compression) with accuracy 92.59% vs 93.63% for normal training.
- Across BERT, GPT-2, Llama-3 and Gemma-2 on sentiment analysis, BackSlash yields 74%-89% EG compression with accuracy changes within about 1 point.
- Pruning experiments on BERT report the BackSlash model maintaining accuracy at 80% pruning rate, while normal training degrades at 50-60%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply rate-constrained BackSlash training | BERT · Sentiment analysis | EG code length: 7.31 -> 2.64 | Helped |
| Apply rate-constrained BackSlash training | GPT-2 · Sentiment analysis | accuracy: 85.92% -> 88.73% | Helped |
| Apply rate-constrained BackSlash training | Llama-3 · Sentiment analysis | accuracy: 86.09% -> 86.93% | Helped |
| Apply rate-constrained BackSlash training | Gemma-2 · Sentiment analysis | accuracy: 86.95% -> 85.86% | Hurt |
| Apply rate-constrained BackSlash training | BERT · SQuAD | next token accuracy: 99.97% -> 99.97% | No clear effect |
| Apply rate-constrained BackSlash training | BERT · WMT-19 | next token accuracy: 99.96% -> 99.95% | Hurt |
| Replace adaptive DGGR with L0.5 regularization (ablation) | BackSlash · BERT sentiment analysis | EG code length: 1.37 -> 2.90 | Hurt |
| Replace adaptive DGGR with L0.5 regularization (ablation) | BackSlash · BERT sentiment analysis | accuracy: 91.18% -> 91.88% | Helped |
| Replace adaptive DGGR with L1 regularization (ablation) | BackSlash · BERT sentiment analysis | accuracy: 91.18% -> 90.65% | Hurt |
| Replace adaptive DGGR with L2 regularization (ablation) | BackSlash · BERT sentiment analysis | accuracy: 91.18% -> 88.29% | Hurt |
| Replace adaptive DGGR with L2 regularization (ablation) | BackSlash · BERT sentiment analysis | EG code length: 1.37 -> 1.16 | Helped |
Surprising findings
- Accuracy was reported as non-monotonic in the Lagrange multiplier, suggesting an optimal intermediate value.
- Huffman coding gives only minimal gains over exp-Golomb codes on BackSlash-trained models.
Limitations
- The Lagrange multiplier is chosen by trial and error with no principled selection rule.
- Experiments are mostly classification on BERT; generation results are limited to next-token accuracy on DeepSeek with little detail.
- Hardware, training budget, and inference speed are not reported, so edge-deployment benefits are not measured.
Experimental setup
Datasets: IMDB Enron-Spam 20 Newsgroups SQuAD WMT-19
Benchmarks: IMDB Enron-Spam 20 Newsgroups SQuAD WMT-19
Metrics: accuracy average code length (bits) compression rate vs fixed-length coding next token accuracy
Baselines: unconstrained training with EG coding unconstrained training with Huffman coding DGGR vs L0.5 regularization L1 regularization L2 regularization
Builds on: rate-distortion optimization exp-Golomb codes Huffman coding
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