SSR: Sparse Segment Reduction for Ternary GEMM Acceleration

Large language models (LLMs) exhibit exceptional general language processing capabilities, but their memory and compute costs hinder deployment. Ternarization has emerged as a promising compression technique, offering significant reductions in model size and inference complexity. However, existing methods struggle with heavy-tailed activation distributions and therefore keep activations in high precision, fundamentally limiting end-to-end inference acceleration. To overcome this limitation, we propose TWLA, a post-training quantization (PTQ) framework that achieves 1.58-bit weight compression and 4-bit activation quantization while maintaining high accuracy. TWLA comprises three components: (1) Euclidean-to-Manifold Asymmetric Ternary Quantizer (E2M-ATQ) minimizes layer-output error under weight ternarization via a two-stage optimization from Euclidean initialization to manifold relocation; (2) Kronecker Orthogonal Tri-Modal Shaping (KOTMS) applies a Kronecker-structured orthogonal rotation to reshape weights into ternary-friendly tri-modal distributions, while the shared rotation statistically suppresses activation outliers; and (3) Inter-Layer Aware Activation Mixed Precision (ILA-AMP) explicitly introduces adjacent-layer second-order interaction costs in bit allocation and jointly optimizes for the layer-wise disparity of activation quantization gains induced by the shared orthogonal transform, preventing cascades triggered by a few weak layers. Extensive experiments demonstrate that TWLA maintains high accuracy under W1.58A4, while delivering significant inference acceleration. The code is available at https://github.com/Kishon-zzx/TWLA.

Ternary Large Language Models (LLM) store every weight as one of three symbols $\{-1,0,+1\}$, so the cost of a ternary model is conventionally referenced to the information-theoretic $\log_2 3 \approx 1.585$ bits per weight. The prevailing deployment format packs five ternary weights into one byte (five-trit packing), and due to the power-of-two group sizes used in practice this rounds up to $1.625$ bits per weight. This effective storage bit-width treats the three symbols $\{-1,0,+1\}$ as equiprobable. We measure the actual symbol distribution of 29 ternary LLM models and find that zeros account for up to $51.5\%$ of all weights. Motivated by this finding, we introduce BITCOS, a simple distribution-adaptive layout comprised of a dense presence bitmap plus a compacted sign vector, and costs $2 - z$ bits per weight element given a zero density $z$ in the model's weights. BITCOS stores weights more compactly than the five-trit packing in 26 of the 29 tested models, and reaches $1.485$ bits per weight on the sparsest of them. BITCOS is amenable to efficient unpacking on modern processors and GPUs, and we present optimized unpacking sequences for AVX-512, AVX2 and Intel Xe2 GPUs. Measured against production state-of-the-art ternary matrix-vector multiplication kernels, at the zero densities real-world ternary models exhibit, the realized gain with our proposed layout is up to $1.28\times$. Finally, we illustrate end-to-end LLM inference results on 5 different platforms (client and server CPUs, integrated and discrete Xe2 GPUs) where decode throughput improves by up to $1.18\times$ on CPUs and $1.27\times$ on GPUs.

In this paper, we present CAT-Q, Cost-efficient and Accurate Ternary Quantization, 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 100,000X 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.