Cooldown & QAT Fusion Approach

• Cooldown and QAT fusion combines the gradual reduction of learning rates with quantization-aware updates to refine model performance and efficiency.
• The approach employs unified loss scaling laws and tokens-per-parameter-byte metrics to optimally allocate training resources between full-precision and quantized phases.
• Fusion of these phases reduces redundant compute, lowers final loss, and enhances adaptability in models ranging from vision transformers to RNN-Ts.

Cooldown and QAT Fusion Approach encompasses methodologies that unify the learning rate decay (“cooldown”) phase of neural network training with quantization-aware adaptation phases (QAT) to maximize model efficiency and accuracy under quantized, resource-constrained, or hybrid analog-digital regimes. Cooldown refers to the gradual reduction in learning rate at the final phase of training (“decay”), which is critical for refining model parameters in a smooth loss landscape. QAT is the process by which model weights and activations are optimized in the presence of simulated quantization, enabling subsequent deployment at low bit-widths. Fusion of these phases—rather than performing them sequentially or redundantly—has emerged as an optimal strategy, yielding significant reductions in wasted computation and improved adaptability to hardware constraints. The concept is relevant across diverse domains including LLMs, vision transformers, RNN-Ts, 3D perception models, and PIM-based accelerators.

1. Theoretical Foundations and Loss Scaling Laws

A cornerstone of the cooldown and QAT fusion paradigm is the use of unified loss scaling laws to predict optimal allocation of training compute between full-precision (FP) and QAT phases. As described in "Compute-Optimal Quantization-Aware Training" (Dremov et al., 26 Sep 2025), the final validation loss $L$ can be expressed in terms of model parameters ($N$), quantization bit-width ($B$), and training tokens ($D_\text{total}$):

$$L(N, D_\text{qat}, D_\text{fp}, B) = \Theta + \Delta_Y \beta + \zeta N^n + \Phi(N, D_\text{qat}, D_\text{fp}, B)$$

where $\Phi$ is a QAT penalty term. Central to this framework is the tokens-per-parameter-byte statistic:

$S_\text{total} = D_\text{total} / (N \cdot B)$

Optimal QAT fraction $f^*$ is thus determined by minimizing $L$ with respect to $D_\text{qat}$ (QAT tokens) under the constraint $D_\text{fp} + D_\text{qat} = D_\text{total}$. Experiments show $f^*$ rises with $S_\text{total}$, particularly for longer training runs or higher bit-widths. This analytic approach guides not only the compute allocation but also selection of quantization bit-width under hardware or memory constraints.

2. Fusion of Cooldown and Quantization-Aware Training

Traditional practice isolates the cooldown phase (final learning rate decay in FP training) from QAT. This sequence is suboptimal since low-magnitude FP updates during cooldown are typically overwritten by quantization initialization. The fusion approach, as formalized in (Dremov et al., 26 Sep 2025), begins QAT immediately after the constant learning rate phase, merging the learning rate decay with quantization adaptation. This “recycles” FP cooldown updates in the quantized regime, saves redundant compute, and preserves accuracy:

• Eliminates unnecessary FP update steps that have negligible post-quantization effect.
• Reduces “wasted tokens,” i.e. training steps that could be reallocated more optimally.
• Decreases final loss and perplexity compared to two-phase strategies.

Empirical data show that, for 4- or 6-bit QAT allocations, the fused strategy consistently outperforms the classic scheme and yields measurable savings in token usage (e.g., up to 1.72% for 10.5B tokens trained across various model sizes).

3. Methodological Innovations in Hybrid Strategies

Beyond the global fusion of cooldown and QAT, several parameter-efficient algorithms leverage selective adaptation for practical scalability:

• EfQAT (Ashkboos et al., 17 Nov 2024): Starting from a PTQ-quantized model, only the most critical parameter blocks (channels or layers, as measured by average absolute weight magnitude) are updated during a short fine-tuning (cooldown) phase. Others are frozen, resulting in a backward pass acceleration of 1.44–1.64× with near full-QAT accuracy.
• PTQAT (Wang et al., 14 Aug 2025): Differentiates layers by their output discrepancies (MSE between quantized and FP outputs), fine-tuning only those with deceptively low errors. This compensates for error propagation, allowing nearly 50% of quantizable layers to be fixed for efficiency, yet achieving superior NDS ($+0.2$–$0.9\%$) and mAP gains ($+0.3$–$1.0\%$) in 3D perception tasks.
• DL-QAT (Ke et al., 12 Apr 2025): Uses LoRA low-rank matrices for local weight updates (less than 1% of parameters) and introduces learnable group-specific quantization magnitudes. The two-stage schedule consists of quantization parameter warmup followed by simultaneous LoRA and magnitude adaptation, stabilized by a cooldown phase in which freezing quantization parameters expedites convergence.

These approaches demonstrate that fusion—strategic selection and joint adaptation of parameters during cooldown—can enable rapid, compute-efficient QAT without a major accuracy penalty.

4. Application-Specific Adaptations

Cooldown and QAT fusion strategies have been adapted across several model classes:

• Vision Transformers (ViTs): GPLQ (Liang et al., 13 Jun 2025) employs an “activation-first, weights-later” schedule. Only activations are quantized/optimized during a one-epoch Act-QAT stage (using a feature mimicking loss to maintain the original optimization basin), followed by rapid PTQ for weights. This sequential schedule achieves 100× speedup versus standard QAT and maintains downstream generalization.
• Instruction-Tuned LLMs: UPQ (Lee et al., 10 Jun 2025) proposes progressive INT4 PTQ (block-wise), then DISTILL-QAT to INT2. The QAT phase minimizes Jensen-Shannon divergence between teacher and INT2 student, preserving instruction-following abilities without proprietary data.
• RNN-T Speech Models: Aggressive INT4 quantization of weights and activations (Fasoli et al., 2022), paired with locally-tailored QAT, allows real-time factor reductions (RTF as low as 0.06) with minimal WER loss. Layer-specific quantizers (FIX, MAX, SAWB, PACT) are selected based on distributional properties; QAT is scheduled with reduced epochs and learning rates to control adaptation cost.

The adaptability of fusion strategies to complex domains highlights its generality.

5. Cooldown Phase Dynamics and Optimizer Interactions

The quality of the cooldown phase—its duration, shape, and interaction with optimizers—is critical. "Training Dynamics of the Cooldown Stage in Warmup-Stable-Decay Learning Rate Scheduler" (Dremov et al., 2 Aug 2025) analyzes how different cooldown shapes (cosine, squared, sqrt, lowered linear, mirror cosine) impact the bias–variance trade-off:

• Shapes that balance exploration (low bias, higher learning rate early in cooldown) and exploitation (low variance, steeper decay) outperform others.
• Optimal configurations occupy minima in the loss/bias–variance plot (e.g., sqrt, lowered linear with parameter 0.7).
• AdamW hyperparameter tuning (notably higher $\beta_2$ during cooldown) can improve final perplexity as much as the choice of cooldown profile.
• The “river valley” loss landscape emerges during cooldown, suggesting the model makes a broad descent before settling into the final basin.

These findings suggest that fusion schemes benefit from precise management of learning rate decay and optimizer behavior, facilitating more robust post-quantization adaptation.

6. Extensions to Hardware-Aware and Meta-Learning Quantization

Fusion methods have also been extended to hardware-specific and meta-learning-driven QAT protocols:

• PIM-QAT (Jin et al., 2022): In neuromorphic PIM systems, extra analog-digital quantization steps and nonideal effects necessitate explicit forward and backward rescaling, batch normalization calibration, and adjusted precision training (effectively a cooldown). The fusion of these corrections alongside standard QAT enables accuracy comparable to digital hardware models, even in the presence of stochastic noise and imperfect ADC linearity.
• Adaptive Bitwidth QAT with Meta-Learning (MEBQAT) (Youn et al., 2022): Models are trained to be robust across bitwidths via meta-task construction involving bitwidth tuples. A “cooldown” task with full-precision parameters is always included, enabling retention of FP performance knowledge and smooth transition to aggressive quantization regimes. Knowledge distillation further fuses FP and quantized domains.

These innovations reflect expanding mainstream applicability of cooldown & QAT fusion concepts in diverse hardware and adaptive problem scenarios.

7. Practical Guidelines and Implications

Cooldown & QAT fusion approaches yield several actionable recommendations:

• Begin QAT immediately from the constant learning rate phase, joint with learning rate decay, to maximize compute utilization.
• Utilize unified loss scaling laws and the tokens-per-parameter-byte statistic to select the optimal proportion of QAT training for a given model size, epoch count, and bit-width (Dremov et al., 26 Sep 2025).
• Consider hybrid algorithms that freeze less susceptible layers, adapt critical components, or utilize low-rank local updates during cooldown (Ashkboos et al., 17 Nov 2024, Ke et al., 12 Apr 2025, Wang et al., 14 Aug 2025).
• In transformer architectures, select cooldown shapes (e.g., sqrt, lowered linear) that minimize bias–variance and tune optimizer EMA decays for best results during final annealing (Dremov et al., 2 Aug 2025).
• In meta-learning scenarios, always preserve a full-precision reference task during quantization adaptation (Youn et al., 2022).
• For vision transformers and 3D perception, first quantize activations while maintaining feature consistency, then rapidly quantize weights via PTQ (Liang et al., 13 Jun 2025, Wang et al., 14 Aug 2025).

The approach offers a unified scheme for efficiently training high-quality quantized models, with verified gains in accuracy, generalization, and real-world deployment cost.

Summary Table: Core Strategies and Outcomes in Cooldown & QAT Fusion

Approach (Editor’s term)	Key Mechanism	Typical Gains
Cooldown–QAT Fusion (Dremov et al., 26 Sep 2025)	Joint LR decay in QAT phase	↑ accuracy, ↓ compute
EfQAT (Ashkboos et al., 17 Nov 2024)	Selective parameter updates	~1.6× speedup, ↑ accuracy
PTQAT (Wang et al., 14 Aug 2025)	Fine-tune “cold” layers only	↑ mAP/NDS/mIoU, ↓ fine-tuning cost
DL-QAT (Ke et al., 12 Apr 2025)	LoRA + group magnitude, 2-stage	↑ MMLU, <1% parameters updated
GPLQ (Liang et al., 13 Jun 2025)	Activation-prioritized QAT, mimic loss	100× speed, ↑ generalization
MEBQAT (Youn et al., 2022)	Meta-task, FP preservation	High accuracy, low cost
PIM-QAT (Jin et al., 2022)	Hardware-specific rescaling, BN calibration	Comparable to digital hardware

Cooldown and QAT fusion synthesizes the learning rate schedule, adaptive quantization training, and targeted parameter refinement to yield compute-optimal, robust, deployment-ready models across modalities and platforms.