Boosting Entropy with Bell Box Quantization

Quantization-Aware Pre-Training (QAPT) can increase the inference efficiency of DNNs, but a problematic behaviour known as rounding boundary weight oscillation can introduce detrimental noise into the training process and significantly reduce convergence speed. While existing methods can reduce this detrimental noise, they either introduce additional hyperparameters or memory overhead, or cannot consistently improve model accuracy. In this work, we propose optimization with $\textbf{C}$onstrained $\textbf{E}$mpirical $\textbf{W}$eight dis$\textbf{T}$ribution (CEWT), the first hyperparameter-free memory-overhead-free oscillation suppression method that consistently improves QAPT performance: an optimizer post-update step that projects weights to the nearest point in weight space whose empirical distribution (histogram) matches a zero-mean Gaussian. Our key insight is many quantizers are designed with the implicit assumption that the to-be-quantized data are permutations of samples from a zero-mean Gaussian, and this assumption is not true during QAPT. By enforcing the zero-mean Gaussian prior as a hard constraint, CEWT can suppress this detrimental noise. Empirical results on various combinations of SOTA quantizers and hypersphere optimizers suggest, that with a geomean increase of 4% in training time, CEWT can consistently reduce the pre-training perplexity (by an average of 2.5 and up to 21 points) of low-precision (down to 1-bit activations and weights and up to 610M parameters) LLaMA/GPT models without introducing any hyperparameters or storage overhead. Code is available at https://github.com/1733116199/cewt

Post-training quantization (PTQ) compresses deep neural networks for deployment under limited memory and computational budgets. However, low-bit (i.e., 2-bit or 4-bit) PTQ often suffers from substantial performance degradation. Most existing PTQ methods operate on an unconstrained full-precision (FP) model and primarily address quantization errors through post-hoc reconstruction. We argue that low-bit PTQ accuracy is limited not only by post-quantization error minimization, but also by the quantization-error tolerance of a FP model itself. In this paper, we propose Efficient Tuning Before Quantization (ETBQ), a pre-conditioning tuning stage for Stochastic Gradient Descent (SGD)-optimized models before PTQ. During tuning, the FP model is optimized under perturbations sampled from the error distributions of weight and activation quantization, guiding the model toward a loss-landscape region that is less sensitive to the subsequent PTQ. Unlike QAT, ETBQ does not train a fake-quantized deployment model, which is computationally and memory intensive. Instead, ETBQ outputs a FP model that can be used by any PTQ backend. Experiments on CIFAR-100, Tiny-ImageNet, ImageNet, and Cityscapes provide consistent evidence that ETBQ improves low-bit PTQ across diverse tasks. Under W2A4 settings, e.g., ETBQ improves over naive PTQ by 2.14% top-1 accuracy on Tiny-ImageNet and by 5.80% mIoU on Cityscapes. Code is available at https://github.com/xpxpxp2001xpxpxp/ETBQ.

We introduce ApexQuant, a calibration-free quantization method that recursively re-quantizes the residual error, serving as a refinement layer on top of existing quantizers. We establish that a fresh random rotation returns each residual to the uniform distribution on the hypersphere, which characterizes the rate of progressive error decay across successive passes. This result lets us determine, before any weight is read, how many passes a layer needs for a target weight-space error. Every prefix is itself a valid lower-rate model, so one artifact serves several precisions. We instantiate ApexQuant with three interchangeable stages, scalar, $E_8$ and trellis, and validate it on four open-weight LLMs and on Earth-observation and medical domains where in-distribution data is often unattainable as imagery arrives under restrictive licences or due to patient material under privacy constraints. Progressive re-isotropization comes within a few percent of full precision at four bits and gives the best two-bit arm we measure, in a completely data-free setting.