Application of Quantized Algorithms for Language Model Adaptation in the Task of Verifying the Solution Process of Quadratic Equations
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Abstract
This paper investigates quantized approaches to language model adaptation for the task of automatic step-by-step verification of the correctness of quadratic equation solutions. The study examines the effectiveness of Parameter-Efficient Fine-Tuning (PEFT) methods when adapting the DeepSeek-R1-Distill-Qwen-1.5B and InternLM2-Math-Plus-1.8B language models to build a mathematical verifier (Process-supervised Reward Model, PRM). Experiments were conducted on a synthetic dataset of quadratic equations augmented with negative sampling to simulate learner errors. A comparative evaluation of standard (LoRA, DoRA, rsLoRA) and quantized (QLoRA, QDoRA, LoftQ) fine-tuning algorithms was performed. Zero-shot transfer generalization was additionally assessed on a structurally distinct dataset of linear equations. Results show that quantization resolves numerical stability issues for non-standard architectures (InternLM2) while achieving quality comparable to standard methods. For the DeepSeek-R1 model, QLoRA, LoftQ, and QDoRA reached accuracies of 97.77%, 98%, and 98% respectively, only marginally below the standard LoRA (98.67%). Similarly, for the non-standard InternLM2 architecture, QLoRA achieved 92.67% accuracy (vs. 93% for baseline LoRA). However, full-precision algorithms (LoRA) tend to preserve richer representations of learned patterns, providing better knowledge transfer for Reasoning-class models (DeepSeek-R1 accuracy 66.8% vs. 61.4% for QLoRA on unseen data).
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References
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