HESTIA: A Hessian-Guided Differentiable Quantization-Aware Training Framework for Extremely Low-Bit LLMs

As large language models (LLMs) continue to scale, deployment is increasingly bottlenecked by the memory wall, motivating a shift toward extremely low-bit quantization. However, most quantization-aware training (QAT) methods apply hard rounding and the straight-through estimator (STE) from the beginning of the training, which prematurely discretizes the optimization landscape and induces persistent gradient mismatch between latent weights and quantized weights, hindering effective optimization of quantized models. To address this, we propose Hestia, a Hessian-guided differentiable QAT framework for extremely low-bit LLMs, which replaces the rigid step function with a temperature-controlled softmax relaxation to maintain gradient flow early in training while progressively hardening quantization. Furthermore, Hestia leverages a tensor-wise Hessian trace metric as a lightweight curvature signal to drive fine-grained temperature annealing, enabling sensitivity-aware discretization across the model. Evaluations on Llama-3.2 show that Hestia consistently outperforms existing ternary QAT baselines, yielding average zero-shot improvements of 5.39% and 4.34% for the 1B and 3B models. These results indicate that Hessian-guided relaxation effectively recovers representational capacity, establishing a more robust training path for 1.58-bit LLMs. The code is available at https://github.com/hestia2026/Hestia.

LLM-Sketch: Enhancing Network Sketches with LLM

Network stream mining is fundamental to many network operations. Sketches, as compact data structures that offer low memory overhead with bounded accuracy, have emerged as a promising solution for network stream mining. Recent studies attempt to optimize sketches using machine learning; however, these approaches face the challenges of lacking adaptivity to dynamic networks and incurring high training costs. In this paper, we propose LLM-Sketch, based on the insight that fields beyond the flow IDs in packet headers can also help infer flow sizes. By using a two-tier data structure and separately recording large and small flows, LLM-Sketch improves accuracy while minimizing memory usage. Furthermore, it leverages fine-tuned large language models (LLMs) to reliably estimate flow sizes. We evaluate LLM-Sketch on three representative tasks, and the results demonstrate that LLM-Sketch outperforms state-of-the-art methods by achieving a $7.5\times$ accuracy improvement.