QUASAR: Lowering the Loss Floor of Quantization-Aware Training with Loss-Aware Reconstruction

• URL: http://arxiv.org/abs/2608.13966v1
• Date: Fri, 14 Aug 2026 05:29:58 GMT
• Title: QUASAR: Lowering the Loss Floor of Quantization-Aware Training with Loss-Aware Reconstruction
• Abstract summary: QUASAR continuously performs loss-aware reconstruction in the training loop to lower the loss floor and improve the resulting low-bit model.<n>It achieves the lowest held-out KL divergence among competitive QAT methods at 2, 3, and 4 bits.<n>It improves average accuracy across eight tasks by 3.5-4.3 percentage points over strong QAT and PTQ baselines.
• Score: 29.200349824129102
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: As large language model inference shifts toward lower precision, post-training quantization (PTQ) becomes increasingly brittle, making quantization-aware training (QAT) essential for preserving model quality. However, QAT computes the loss and surrogate gradients using a lossy reconstruction of latent full-precision weights, while applying updates to the latent weights themselves. This mismatch can lead to suboptimal training trajectories and a higher loss floor. Second-order PTQ methods mitigate a similar gap by minimizing loss-aware reconstruction error, but doing it once for a frozen model can take hours; repeating this process throughout QAT as the weights evolve is impractical. We introduce QUASAR, a QAT method that continuously performs lightweight, loss-aware reconstruction in the training loop to lower the loss floor and improve the resulting low-bit model. At each training step, QUASAR uses the exponential moving average of squared gradients as online saliency estimates, searches over a small set of clipping ranges, and fits affine dequantizers via saliency-weighted least squares. Our analysis shows that the loss-aware reconstruction error is the only reconstruction-dependent term in the QAT convergence bound and controls the loss of the final quantized model, establishing QUASAR's objective as a principled optimization target. QUASAR modifies only the training procedure and supports standard deployment formats, including integer quantization and NVFP4, with no inference-time changes or overhead. Across Qwen3 and Llama-3.1, QUASAR achieves the lowest held-out KL divergence among competitive QAT methods at 2, 3, and 4 bits, reducing KL by at least 10% at 3 and 4 bits and by 29% at 2 bits. At 2 bits, it improves average accuracy across eight tasks by 3.5-4.3 percentage points over strong QAT and PTQ baselines.

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