Quantization-Aware Training (QAT) enables the deployment of quantized models with minimal accuracy degradation. However, in practical scenarios, training labels are often unavailable due to privacy, copyright, or cost constraints. Knowledge Distillation (KD) is a common approach to address this challenge, but we observe that prior work combining QAT with KD suffers from a fundamental limitation: during distillation, the range mismatch between the teacher and the quantized student model induces an unattainable residual, resulting in an irreducible lower bound on the distillation loss. Motivated by this observation, we propose SQuaT (Student-Aware Quantized Teacher Features), a label-free QAT framework with KD that theoretically eliminates this lower bound by applying the student's quantization parameters to quantize the teacher's features during distillation. Through comprehensive experiments across diverse settings, we demonstrate that SQuaT consistently outperforms strong baselines, with particularly pronounced gains in extreme low-bit (e.g., 1- and 2-bit) settings. Furthermore, extensive evaluations across various model design choices show that our approach does not rely on specific architectural assumptions, making it broadly applicable across diverse architectures and quantization settings. The source code is available at https://github.com/lcdbsa522/SQuaT.
Quantization-aware training (QAT) is widely deployed but typically relies on the Straight-Through Estimator (STE), which passes gradients through non-differentiable quantizers by fiat. This often makes training brittle near bin boundaries and weakly aligned with the actual behavior of the low-precision model. We introduce JacQuant, a QAT framework that learns a lightweight surrogate of the model's local sensitivity to parameter changes and uses it to stabilize and accelerate training within standard variance-reduced optimizers. The surrogate is inexpensive (diagonal or block-diagonal), data-driven, and compatible with common weight and activation quantizers. On code-preserving training phases, we prove convergence for non-convex objectives and obtain linear rates under a PL condition, and we relate the learned sensitivity to end-to-end output fidelity via a simple calibration argument. Across LLM benchmarks at ≤2 bits, JacQuant consistently reaches higher accuracy than STE-based QAT, and the runtime analyses on various models show that the added cost remains negligible under practical group sizes. The method is drop-in and requires no changes to the forward quantizers; our empirical claims are scoped to ultra-low-bit LLM QAT.
The rapid development of LLMs incurs prohibitive memory footprints and intensive computational demands. Quantization-Aware Training (QAT) techniques have emerged as a promising solution to address these challenges by explicitly simulating quantization effects during model training, yielding low-bit models that achieve accuracy comparable to their full-precision counterparts. In this work, we provide a target-centric survey of QAT, aimed at clarifying both its theoretical foundations and its evolving implementation landscape. We systematically review existing QAT methods through a target-centric taxonomy and synthesize cross-target differences in error characteristics, numerical formats, and strategy transferability. We further summarize QAT evaluation paradigms and discuss challenges in optimization and deployment, outlining potential directions for future research.
Quantization-aware distillation (QAD) restores much of the short-form question-answering performance lost to sub-3-bit quantization, yet leaves mathematical and code reasoning substantially impaired. Long generations often degenerate into repetitive loops, exhausting the decoding budget without completing a solution. We trace this gap to quantization-amplified exposure bias: QAD trains on fixed corpus prefixes, while quantization-induced deviations compound along the model's own autoregressive trajectories. To address this mismatch, we introduce an on-policy distillation (OPD) stage that places teacher supervision where the quantized model actually goes. Starting from a QAD checkpoint, the student generates through the quantized forward path used at deployment and receives feedback from a frozen full-precision teacher on its own prefixes, combining dense token-level guidance with task-verifier rewards. Across four models at 2.79 and 1.88 effective bits, OPD raises average BF16 performance retention from 35% to 70% on MATH-500 and from 66% to 91% on HumanEval while preserving short-form performance, with reasoning gains substantially exceeding those of continued teacher-forced QAD in matched-budget comparisons. By coupling QAD's stable low-bit initialization with OPD's on-policy reasoning recovery, our framework provides a comprehensive sub-3-bit solution that preserves broad capabilities while restoring long-form reasoning.