Optimal Post-Training Quantization Scales and Where to Find Them

Post-training quantization (PTQ) compresses large language models by mapping weights to low-bit representations. The scaling factor that defines the quantization grid is typically chosen using simple, data-free heuristics. In this work, we present PiSO (Piecewise Scale Optimization), an algorithm that leverages calibration data to compute the optimal channel-wise weight scales exactly and efficiently under round-to-nearest quantization. PiSO partitions the scale search space into finitely many intervals on which the objective admits a closed-form minimizer. We extend PiSO to group-wise quantization via principled heuristics and propose effective strategies for interleaving scale optimization with error correction. Experiments on Llama and Qwen models across multiple model sizes and target weight bit-widths demonstrate consistent improvements in perplexity and downstream zero-shot accuracy, both standalone and combined with error correction. In particular, we observe increased benefits as the target bit-width narrows and quantization becomes more challenging.

dMX: Differentiable Mixed-Precision Assignment for Low-Precision Floating-Point Formats

Quantizing large language models (LLMs) to low-precision floating-point representations is central to efficient deployment, yet applying a single bit-width uniformly across all layers is sub-optimal in terms of both performance and accuracy. This work introduces dMX, a differentiable mixed-precision quantization framework for learnable floating-point bit-width assignment. We study its application for the microscaling floating-point (MXFP) family of data types defined by the Open Compute Project (OCP) standard. The per-layer bit-width assignment is formulated as a continuous optimization problem in which each layer's floating-point format format is parameterized by a scalar parameter, folding the multi-variate design space into a single learnable offset. During training this offset takes continuous values, avoiding sudden oscillations between discrete quantization formats. A temperature-based annealing schedule progressively discretizes the learned offsets, ensuring that the final configuration maps to hardware-compatible MXFP formats without abrupt transitions between training and inference behavior. A target-aware regularization term steers the average bit-width toward a user-specified budget, serving as a coarse-grained proxy for inference cost and balancing model quality against deployment efficiency. We performed experiments on different families of LLM, such as Llama, Qwen3, and SmolLM2, evaluating perplexity on WikiText-2 and accuracy on four zero-shot reasoning benchmarks. Across these settings, dMX consistently yields Pareto-dominating models and improves over Kullback-Leibler (KL) divergence-based layer-selection heuristics, efficiently navigating trade-offs between model quality and average bit-width.

GPU Acceleration of Sparse Fully Homomorphic Encrypted DNNs

Fully homomorphic encryption (FHE) has recently attracted significant attention as both a cryptographic primitive and a systems challenge. Given the latest advances in accelerated computing, FHE presents a promising opportunity for progress, with applications ranging from machine learning to information security. We target the most computationally intensive operation in deep neural networks from a hardware perspective, matrix multiplication (matmul), and adapt it for execution on AMD GPUs. We propose a new optimized method that improves the runtime and complexity of ciphertext matmul by using FIDESlib, a recent open-source FHE library designed specifically for GPUs. By exploiting sparsity in both operands, our sparse matmul implementation outperforms its CPU counterpart by up to $3.0\times$ and reduces the time complexity from cubic to semi-linear, demonstrating an improvement over existing FHE matmul implementations.

MixQuant: Pushing the Limits of Block Rotations in Post-Training Quantization

Recent post-training quantization (PTQ) methods have adopted block rotations to diffuse outliers prior to rounding. While this reduces the overhead of full-vector rotations, the effect of block structure on outlier suppression remains poorly understood. To fill this gap, we present the first systematic, non-asymptotic analysis of outlier suppression for block Hadamard rotations. Our analysis reveals that outlier suppression is fundamentally limited by the geometry of the input vector. In particular, post-rotation outliers are deterministically minimized when the pre-rotation $\ell_1$ norm mass is evenly distributed across blocks. Guided by these insights, we introduce MixQuant, a block rotation-aware PTQ framework that redistributes activation mass via permutations prior to rotation. We propose a greedy mass diffusion algorithm to calibrate permutations by equalizing the expected blockwise $\ell_1$ norms. To avoid adding inference overhead, we identify permutation-equivariant regions in transformer architectures to merge the resulting permutations into model weights before deployment. Experiments show that MixQuant consistently improves accuracy across all block sizes, recovering up to 90% of the full-vector rotation perplexity when quantizing Llama3 1B to INT4 with block size 16, compared to 46% without permutations.

Combining Reinforcement Learning and Behavior Trees for NPCs in Video Games with AMD Schola

While the rapid advancements in the reinforcement learning (RL) research community have been remarkable, the adoption in commercial video games remains slow. In this paper, we outline common challenges the Game AI community faces when using RL-driven NPCs in practice, and highlight the intersection of RL with traditional behavior trees (BTs) as a crucial juncture to be explored further. Although the BT+RL intersection has been suggested in several research papers, its adoption is rare. We demonstrate the viability of this approach using AMD Schola -- a plugin for training RL agents in Unreal Engine -- by creating multi-task NPCs in a complex 3D environment inspired by the commercial video game ``The Last of Us". We provide detailed methodologies for jointly training RL models with BTs while showcasing various skills.

Provable Post-Training Quantization: Theoretical Analysis of OPTQ and Qronos

Post-training quantization (PTQ) has become a crucial tool for reducing the memory and compute costs of modern deep neural networks, including large language models (LLMs). Among PTQ algorithms, the OPTQ framework-also known as GPTQ-has emerged as a leading method due to its computational efficiency and strong empirical performance. Despite its widespread adoption, however, OPTQ lacks rigorous quantitative theoretical guarantees. This paper presents the first quantitative error bounds for both deterministic and stochastic variants of OPTQ, as well as for Qronos, a recent related state-of-the-art PTQ algorithm. We analyze how OPTQ's iterative procedure induces quantization error and derive non-asymptotic 2-norm error bounds that depend explicitly on the calibration data and a regularization parameter that OPTQ uses. Our analysis provides theoretical justification for several practical design choices, including the widely used heuristic of ordering features by decreasing norm, as well as guidance for selecting the regularization parameter. For the stochastic variant, we establish stronger infinity-norm error bounds, which enable control over the required quantization alphabet and are particularly useful for downstream layers and nonlinearities. Finally, we extend our analysis to Qronos, providing new theoretical bounds, for both its deterministic and stochastic variants, that help explain its empirical advantages.

Qronos: Correcting the Past by Shaping the Future... in Post-Training Quantization

We introduce Qronos -- a new state-of-the-art post-training quantization algorithm that sequentially rounds and updates neural network weights. Qronos not only explicitly corrects errors due to both weight and activation quantization, but also errors resulting from quantizing previous layers. Our iterative algorithm is based on an interpretable and disciplined optimization framework that subsumes and surpasses existing data-driven approaches. At each step, Qronos alternates between error correction and diffusion via optimal update rules. Importantly, we prove that Qronos admits an efficient implementation that uses the Cholesky decomposition for solving least-squares problems. We also demonstrate that Qronos is compatible with existing transformation techniques such as Hadamard-based incoherence processing and weight-activation scaling equalization, among others. We evaluate Qronos using recent autoregressive language generation models in the Llama3 family; Qronos consistently outperforms previous state-of-the-art adaptive rounding methods when quantizing the weights, activations, and/or KV caches.

Exploiting Unstructured Sparsity in Fully Homomorphic Encrypted DNNs

The deployment of deep neural networks (DNNs) in privacy-sensitive environments is constrained by computational overheads in fully homomorphic encryption (FHE). This paper explores unstructured sparsity in FHE matrix multiplication schemes as a means of reducing this burden while maintaining model accuracy requirements. We demonstrate that sparsity can be exploited in arbitrary matrix multiplication, providing runtime benefits compared to a baseline naive algorithm at all sparsity levels. This is a notable departure from the plaintext domain, where there is a trade-off between sparsity and the overhead of the sparse multiplication algorithm. In addition, we propose three sparse multiplication schemes in FHE based on common plaintext sparse encodings. We demonstrate the performance gain is scheme-invariant; however, some sparse schemes vastly reduce the memory storage requirements of the encrypted matrix at high sparsity values. Our proposed sparse schemes yield an average performance gain of 2.5x at 50% unstructured sparsity, with our multi-threading scheme providing a 32.5x performance increase over the equivalent single-threaded sparse computation when utilizing 64 cores.

Accumulator-Aware Post-Training Quantization

Several recent studies have investigated low-precision accumulation, reporting improvements in throughput, power, and area across various platforms. However, the accompanying proposals have only considered the quantization-aware training (QAT) paradigm, in which models are fine-tuned or trained from scratch with quantization in the loop. As models continue to grow in size, QAT techniques become increasingly more expensive, which has motivated the recent surge in post-training quantization (PTQ) research. To the best of our knowledge, ours marks the first formal study of accumulator-aware quantization in the PTQ setting. To bridge this gap, we introduce AXE, a practical framework of accumulator-aware extensions designed to endow overflow avoidance guarantees to existing layer-wise PTQ algorithms. We theoretically motivate AXE and demonstrate its flexibility by implementing it on top of two state-of-the-art PTQ algorithms: GPFQ and OPTQ. We further generalize AXE to support multi-stage accumulation for the first time, opening the door for full datapath optimization and scaling to large language models (LLMs). We evaluate AXE across image classification and language generation models, and observe significant improvements in the trade-off between accumulator bit width and model accuracy over baseline methods.

A2Q+: Improving Accumulator-Aware Weight Quantization

Quantization techniques commonly reduce the inference costs of neural networks by restricting the precision of weights and activations. Recent studies show that also reducing the precision of the accumulator can further improve hardware efficiency at the risk of numerical overflow, which introduces arithmetic errors that can degrade model accuracy. To avoid numerical overflow while maintaining accuracy, recent work proposed accumulator-aware quantization (A2Q), a quantization-aware training method that constrains model weights during training to safely use a target accumulator bit width during inference. Although this shows promise, we demonstrate that A2Q relies on an overly restrictive constraint and a sub-optimal weight initialization strategy that each introduce superfluous quantization error. To address these shortcomings, we introduce: (1) an improved bound that alleviates accumulator constraints without compromising overflow avoidance; and (2) a new strategy for initializing quantized weights from pre-trained floating-point checkpoints. We combine these contributions with weight normalization to introduce A2Q+. We support our analysis with experiments that show A2Q+ significantly improves the trade-off between accumulator bit width and model accuracy and characterize new trade-offs that arise as a consequence of accumulator constraints.