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arxiv: 2606.26650 · v1 · pith:QYE6VEL3new · submitted 2026-06-25 · 💻 cs.CL · cs.AI

CAT-Q: Cost-efficient and Accurate Ternary Quantization for LLMs

Shigeng Wang , Chao Li , Yangyuxuan Kang , Jiawei Fan , Anbang Yao This is my paper

Pith reviewed 2026-06-26 05:18 UTC · model grok-4.3

classification 💻 cs.CL cs.AI
keywords ternary quantizationpost-training quantizationlarge language modelsmodel compressionLLM accelerationcalibration data
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The pith

CAT-Q quantizes pre-trained LLMs to ternary using 512 calibration samples while outperforming BitNet models trained on 100 billion tokens.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces CAT-Q as a post-training quantization method for converting pre-trained large language models into ternary-weight versions. It relies on two coupled components: learnable modulation that adjusts the distribution of high-precision weights and the ternary threshold, and a softened ternarization function that provides a differentiable path for optimization. These elements allow the method to work with only 512 calibration samples across model sizes from 1.7B to 235B parameters. The resulting ternary models show better accuracy than the BitNet 1.58-bit families, which were trained from scratch on 100 billion tokens, corresponding to a claimed 100,000X reduction in required training data.

Core claim

CAT-Q is a post-training ternary quantization scheme that couples learnable modulation factors, which modulate the distribution of pre-trained weights and the ternary threshold, with a differentiable softened transition function to guide stable convergence, enabling accurate ternary models for LLMs ranging from 1.7B to 235B parameters using only 512 calibration samples and achieving superior performance to BitNet 1.58-bit v1 and v2 models trained on 100B tokens.

What carries the argument

Learnable modulation (LM) and softened ternarization (ST) coupled from an optimization perspective, where LM uses learnable factors to modulate weight distributions and thresholds while ST supplies a differentiable transition function.

Load-bearing premise

Optimizing the learnable modulation factors and softened transition function on 512 calibration samples produces a ternary model whose accuracy holds on the full evaluation distribution across different model sizes and architectures.

What would settle it

Run the CAT-Q ternary models on a large held-out evaluation set never seen during the 512-sample calibration and compare accuracy directly against the BitNet baselines under matched conditions.

Figures

Figures reproduced from arXiv: 2606.26650 by Anbang Yao, Chao Li, Jiawei Fan, Shigeng Wang, Yangyuxuan Kang.

Figure 1
Figure 1. Figure 1: Overview of the CAT-Q’s learning flow for ternarizing the weights of a linear layer in any pre-trained LLM and its hardware￾friendly weight reconstruction for ternary model deployment. Please see [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of weight reconstruction errors with the scaling factor α and the threshold ∆ determined by static approxi￾mation (blue dots), direct learning (orange dots) and our learnable modulation (green dots). Under the same settings, we use the 4 th layer of Qwen3-4B for an illustration. In the Appendix, we provide additional comparisons on different layers across multiple LLMs. and ∆ = 0.7 n Pn i=1 |Wi … view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of the softened ternarization (ST) process. For a linear layer, taking its pre-trained weights W as the initialization point (t = 0), ST employs a learnable two-stage relay of differentiable ternarization and hard ternarization to ensure stable convergence. In the first stage, ST produces an asymptotic ternary output by performing continuous quantization based on the transformed weights Wˆ . I… view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces CAT-Q, a post-training ternary quantization method for pre-trained LLMs. It relies on two coupled components—learnable modulation (LM) of weight distributions and ternary thresholds via learnable factors, plus a softened differentiable transition function (ST)—optimized jointly on a 512-sample calibration set. The central claim is that this yields ternary models (1.7B–8B parameters) outperforming BitNet 1.58-bit v1/v2 models (1.3B–7B) trained from scratch on 100B tokens, for a claimed ~100,000X token reduction, while also scaling to 14B–235B models in 8–60 hours on 8 A100 GPUs.

Significance. If the empirical superiority and generalization claims are substantiated with full metrics and ablations, the result would be significant: it would demonstrate that post-training ternary quantization can match or exceed the accuracy of models trained from scratch with orders-of-magnitude less data, lowering the barrier to deploying efficient 1.58-bit LLMs across model scales.

major comments (3)
  1. [Abstract] Abstract and §4 (presumed evaluation): the headline claim of superior performance to BitNet v1/v2 with only 512 calibration samples is load-bearing yet unsupported by any reported quantitative metrics, error bars, dataset names, or per-task scores in the provided abstract; without these, the 100,000X token-reduction assertion cannot be assessed.
  2. [§3, §4] §3 (method) and §4: the optimization of the learnable modulation factors and softened-transition parameters on a fixed 512-sample set is presented without any ablation on calibration-set size, domain coverage, or held-out validation split; this directly undermines the weakest assumption that the resulting ternary weights generalize to the full evaluation distribution across model sizes.
  3. [§3] No equations or derivations are supplied that define how the LM factors rescale weights/thresholds or how the ST function is parameterized and differentiated; without these, it is impossible to verify that the reported gains are not simply the result of per-model fitting rather than a generalizable procedure.
minor comments (2)
  1. [Abstract] The abstract states results for 1.7B–8B and 14B–235B models but does not specify the exact model families or architectures used in the comparisons.
  2. [Abstract] Code link is provided, but no statement on whether the 512-sample calibration sets or optimization hyperparameters are released for reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and will revise the manuscript accordingly to strengthen clarity and substantiation of claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract and §4 (presumed evaluation): the headline claim of superior performance to BitNet v1/v2 with only 512 calibration samples is load-bearing yet unsupported by any reported quantitative metrics, error bars, dataset names, or per-task scores in the provided abstract; without these, the 100,000X token-reduction assertion cannot be assessed.

    Authors: We agree that the abstract should include concrete quantitative support. In the revised version, we will update the abstract to report key metrics such as average accuracy on benchmarks (e.g., MMLU, Hellaswag), specific per-task scores where space allows, dataset names, and variance indicators from our experiments. This will directly substantiate the performance superiority and token-reduction claims. revision: yes

  2. Referee: [§3, §4] §3 (method) and §4: the optimization of the learnable modulation factors and softened-transition parameters on a fixed 512-sample set is presented without any ablation on calibration-set size, domain coverage, or held-out validation split; this directly undermines the weakest assumption that the resulting ternary weights generalize to the full evaluation distribution across model sizes.

    Authors: We acknowledge the need for such ablations to demonstrate robustness. We will add an ablation study in §4 evaluating performance across calibration set sizes (128, 256, 512, 1024 samples) on representative models. We will also expand the discussion in §3 and §4 on how the 512-sample calibration set was selected for domain diversity and include any available held-out validation results or limitations. revision: yes

  3. Referee: [§3] No equations or derivations are supplied that define how the LM factors rescale weights/thresholds or how the ST function is parameterized and differentiated; without these, it is impossible to verify that the reported gains are not simply the result of per-model fitting rather than a generalizable procedure.

    Authors: We will revise §3 to include explicit mathematical definitions and derivations for the learnable modulation (LM) factors (showing how they rescale weight distributions and ternary thresholds) and the softened ternarization (ST) function (including its parameterization and gradient computation for differentiability). This will clarify the generalizable optimization procedure. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical PTQ method with independent calibration-based optimization

full rationale

The paper describes a post-training quantization procedure (learnable modulation factors and softened transition function optimized on 512 calibration samples) whose performance claims rest on direct empirical comparison against BitNet models trained from scratch on 100B tokens. No equations, derivations, or self-citations are presented that reduce the reported accuracy to quantities defined by the fitted parameters themselves or that rename a known result as a new prediction. The central result is therefore an empirical observation rather than a self-referential derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only review; the method introduces learnable factors whose values are determined during the quantization step on calibration data.

free parameters (1)
  • learnable modulation factors
    Composition of learnable factors used to modulate weight distribution and ternary threshold; fitted during the post-training procedure.
axioms (1)
  • domain assumption Learnable modulation makes pre-trained weights less sensitive to ternarization when optimized on a small calibration set.
    Central design premise stated in the abstract for the LM component.

pith-pipeline@v0.9.1-grok · 5826 in / 1229 out tokens · 21063 ms · 2026-06-26T05:18:53.890886+00:00 · methodology

discussion (0)

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Reference graph

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