In this paper, we present CAT-Q, **C**ost-efficient and **A**ccurate **T**ernary **Q**uantization, for compressing and accelerating LLMs. Unlike existing state-of-the-art ternary quantization methods that rely on data-intensive and costly quantization-aware training to mitigate severe performance degradation, CAT-Q is a simple yet effective post-training quantization scheme that is readily applicable to LLMs with diverse architectures and model sizes. It has two key components, learnable modulation (LM) and softened ternarization (ST), which are coupled from an optimization perspective. LM leverages a composition of learnable factors to modulate the distribution of pre-trained high-precision weights and the ternary threshold, making them less sensitive to ternarization. ST further introduces a differentiable transition function to guide the ternarization process toward stable convergence. We show that, for pre-trained LLMs with 1.7B to 8B parameters, CAT-Q can efficiently quantize them into ternary models using only 512 calibration samples, while achieving superior performance than the seminal BitNet 1.58-bit v1 and v2 families (with 1.3B to 7B parameters) trained with 100B tokens, yielding about a 100,000$\times$ reduction in training tokens. Moreover, we show for the first time that CAT-Q can quantize much larger pre-trained LLMs having 14B to 235B parameters into leading ternary models within just 8 to 60 hours on 8 A100-80GB GPUs. Code is available at https://github.com/IntelChina-AI/BitTern.

Efficient and stable training of large language models (LLMs) remains a core challenge in modern machine learning systems. To address this challenge, Reparameterized Orthogonal Equivalence Training (POET), a spectrum-preserving framework that optimizes each weight matrix through orthogonal equivalence transformation, has been proposed. Although POET provides strong training stability, its original implementation incurs high memory consumption and computational overhead due to intensive matrix multiplications. To overcome these limitations, we introduce POET-X, a scalable and memory-efficient variant that performs orthogonal equivalence transformations with significantly reduced computational cost. POET-X maintains the generalization and stability benefits of POET while achieving substantial improvements in throughput and memory efficiency. In our experiments, POET-X enables the pretraining of billion-parameter LLMs on a single Nvidia H100 GPU, and in contrast, standard optimizers such as AdamW run out of memory under the same settings.

Large Reasoning Models (LRMs) achieve strong problem-solving through long chain-of-thought, but their deployment is constrained by the high cost of full-precision inference and growing KV cache footprints. Microscaled FP4 formats enable efficient FP4 deployment; however, fully quantizing weights, activations, and KV caches (W4A4KV4) causes severe reasoning degradation that existing PTQ and QAT fail to recover. We identify that FP4 failures concentrate on low-entropy tokens—precise symbolic commitments such as digits and operators—where quantization noise inflates sampling errors that cascade through reasoning traces. Based on this insight, we propose ReQAT, a reasoning-centric FP4 training framework with three components: (i) Trace-Aligned QAT (TAQ), which revisits identical reasoning traces to focus updates on critical low-entropy decisions; (ii) Selective Entropy Minimization (SEM), which reinforces confidence at low-entropy positions; and (iii) Q-FIT, a quantization-friendly initialization that jointly calibrates RoPE-consistent KV cache transformations to stabilize QAT. Under the same training budget, ReQAT not only recovers but surpasses BF16 fine-tuning accuracy, while delivering up to $3.9\times$ throughput speedup on NVIDIA DGX Spark and $3.1\times$ on B200. The project repository is available at https://github.com/aiha-lab/ReQAT.

Large language models (LLMs) perform inference by following a fixed depth and order, non-recurrent execution of all layers. We reveal the wide existence of training-free, flexible, dynamic program-of-layers (PoLar), where pretrained layers can be packed as modules and then skipped or looped to form a customized program for each input. For most inputs, substantially shorter program executions can achieve the same or better accuracy, while incorrect predictions of the original LLM can be corrected by alternative programs with fewer layers. These observations indicate that inference admits multiple valid latent computations beyond the standard forward pass. To efficiently achieve PoLar in practice, we propose a lightweight PoLar prediction network, which learns to generate execution programs that dynamically skip or repeat pretrained layers for each input. Experiments on mathematical reasoning benchmarks demonstrate that PoLar consistently improves accuracy over standard inference and prior dynamic-depth methods, often while executing fewer layers, and that these gains persist under out-of-distribution evaluation. Our results suggest that fixed-depth execution captures only a narrow subset of an LLM’s latent reasoning capacity.