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arxiv: 2604.13440 · v1 · submitted 2026-04-15 · 💻 cs.LG · cs.AI

Recognition: unknown

A KL Lens on Quantization: Fast, Forward-Only Sensitivity for Mixed-Precision SSM-Transformer Models

Flavio Ponzina, Jason Kong, Nilesh Prasad Pandey, Tajana Rosing

Pith reviewed 2026-05-10 14:21 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords quantizationmixed precisionstate space modelstransformersKL divergencesensitivity analysisedge deploymentlanguage modeling
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The pith

KL divergence ranks hybrid model components by quantization sensitivity using only forward passes, outperforming MSE and SQNR for mixed-precision decisions.

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

The paper develops a lightweight method to identify which parts of SSM-Transformer hybrid models lose the most performance when quantized to lower bit widths. It relies on the Kullback-Leibler divergence between the output distributions of full-precision and quantized versions, computed in a single forward pass without gradients or large private datasets. This approach matters for edge deployment because it lets designers apply aggressive quantization only to robust components while protecting sensitive ones, cutting memory and latency with little accuracy cost. Experiments confirm that the KL rankings align with measured perplexity increases after quantization and beat common alternatives like mean squared error. Real hardware tests on Intel Lunar Lake further show the resulting mixed-precision models deliver near full-precision quality at sizes and speeds competitive with uniform low-precision baselines.

Core claim

The central claim is that the Kullback-Leibler divergence between full-precision and quantized forward outputs provides a superior surrogate measure of quantization sensitivity for language modeling compared with mean squared error or signal-to-quantization-noise ratio. Applied component-wise in a backpropagation-free surrogate framework, this metric produces rankings that accurately forecast end-to-end performance degradation, enabling targeted mixed-precision configurations that preserve near-FP16 perplexity while reducing model size and increasing inference speed on resource-constrained hardware.

What carries the argument

KL divergence computed on forward passes as a surrogate sensitivity score that ranks individual SSM and transformer components by expected quantization impact.

If this is right

  • KL-guided mixed precision maintains near full-precision perplexity while shrinking model size and raising throughput.
  • The method operates without backpropagation or access to in-domain training data.
  • KL rankings align more closely with observed accuracy drops than MSE or SQNR across SSM and hybrid models.
  • On-device profiling on Intel Lunar Lake hardware shows competitive CPU and GPU performance versus uniform INT4.
  • Ablation studies validate that the framework supports practical deployment with minimal accuracy loss.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The forward-only nature could lower the cost of testing quantization on models where training data remains inaccessible.
  • Similar distribution-shift metrics might extend to other compression methods such as pruning.
  • Integrating hardware cost models directly into the sensitivity step could further optimize bit assignments for specific devices.
  • The same lens could be tested on pure transformer or non-language models to check whether the superiority over MSE generalizes.

Load-bearing premise

The component rankings produced by the forward KL metric will reliably match the actual end-to-end performance loss observed after full quantization.

What would settle it

Quantizing the model according to KL rankings and observing a larger perplexity increase than when using MSE rankings on the same architecture and evaluation set would falsify the claim that KL better captures sensitivity.

Figures

Figures reproduced from arXiv: 2604.13440 by Flavio Ponzina, Jason Kong, Nilesh Prasad Pandey, Tajana Rosing.

Figure 1
Figure 1. Figure 1: Quantization-sensitivity characteristics of Hymba. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Quantization-sensitivity characteristics of Hymba. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: KL-Divergence vs. Perplexity correlation. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Inference latency vs. model size (CPU, Intel Lunar [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Throughput vs. model size (CPU, Intel Lunar Lake). [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: GPU profiling of Mamba2-130M on Intel Lunar Lake. [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
read the original abstract

Deploying Large Language Models (LLMs) on edge devices faces severe computational and memory constraints, limiting real-time processing and on-device intelligence. Hybrid architectures combining Structured State Space Models (SSMs) with transformer-based LLMs offer a balance of efficiency and performance. Aggressive quantization can drastically cut model size and speed up inference, but its uneven effects on different components require careful management. In this work, we propose a lightweight, backpropagation-free, surrogate-based sensitivity analysis framework to identify hybrid SSM-Transformer components most susceptible to quantization-induced degradation. Relying solely on forward-pass metrics, our method avoids expensive gradient computations and retraining, making it suitable for situations where access to in-domain data is limited due to proprietary restrictions or privacy constraints. We also provide a formal analysis showing that the Kullback-Leibler (KL) divergence metric better captures quantization sensitivity for Language modeling tasks than widely adopted alternatives such as mean squared error (MSE) and signal-to-quantization-noise ratio (SQNR). Through extensive experiments on SSM and hybrid architectures, our ablation studies confirm that KL-based rankings align with observed performance drops and outperform alternative metrics. This framework enables the practical deployment of advanced hybrid models on resource-constrained edge devices with minimal accuracy loss. We further validate our approach with real-world on-device profiling on Intel Lunar Lake hardware, demonstrating that KL-guided mixed-precision achieves near-FP16 perplexity with model sizes and throughput competitive with Uniform INT4 on both CPU and GPU execution modes. Code is available at https://github.com/jasonkongie/kl-ssm-quant.

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

2 major / 1 minor

Summary. The manuscript presents a backpropagation-free, forward-pass-only framework for analyzing quantization sensitivity in hybrid SSM-Transformer models using KL divergence as a surrogate metric. It includes formal analysis arguing for KL's advantages over MSE and SQNR in language modeling, ablation studies verifying that the resulting rankings predict performance degradation, and practical validation via mixed-precision quantization on edge hardware achieving near full-precision perplexity.

Significance. Should the results hold, particularly the predictive accuracy of the KL metric without gradients and under data constraints, the work offers substantial practical value for deploying large hybrid models on edge devices. It addresses key challenges in quantization management for efficiency gains while respecting privacy limitations on data access, with added credibility from real-world hardware profiling.

major comments (2)
  1. [Abstract] Abstract: The claim that KL-based rankings align with observed performance drops (and outperform MSE/SQNR) is load-bearing, yet the validation appears to rely on full in-domain calibration sets. This does not establish reliability under the paper's stated operating constraints of limited or out-of-domain data due to privacy/proprietary restrictions; explicit experiments with restricted calibration data are required to support the surrogate's predictive power.
  2. [Abstract] Abstract: Potential circularity exists if the same forward-pass outputs used to compute KL rankings are also used to measure the perplexity drops in the ablations; an independent held-out evaluation or external benchmark is needed to confirm that the metric genuinely predicts end-to-end degradation rather than reflecting internal consistency.
minor comments (1)
  1. The abstract references extensive experiments and ablations but provides no quantitative details (e.g., correlation values or specific component rankings); the full manuscript should include these to allow assessment of effect sizes.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and detailed comments. We address each major comment below and indicate the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that KL-based rankings align with observed performance drops (and outperform MSE/SQNR) is load-bearing, yet the validation appears to rely on full in-domain calibration sets. This does not establish reliability under the paper's stated operating constraints of limited or out-of-domain data due to privacy/proprietary restrictions; explicit experiments with restricted calibration data are required to support the surrogate's predictive power.

    Authors: We agree that explicit validation under limited-data and out-of-domain conditions is necessary to fully substantiate the framework's utility in the privacy-constrained regimes highlighted in the paper. Although the current ablations use full calibration sets, the method itself requires only forward passes and is therefore directly applicable to smaller or shifted datasets. In the revised manuscript we will add new ablation results that subsample the calibration set to 5% and 10% of its original size as well as results using out-of-domain calibration data drawn from a different corpus; these experiments will report both ranking stability and the correlation between KL rankings and measured perplexity degradation. revision: yes

  2. Referee: [Abstract] Abstract: Potential circularity exists if the same forward-pass outputs used to compute KL rankings are also used to measure the perplexity drops in the ablations; an independent held-out evaluation or external benchmark is needed to confirm that the metric genuinely predicts end-to-end degradation rather than reflecting internal consistency.

    Authors: The KL rankings are derived from forward passes on a designated calibration split, while end-to-end perplexity is evaluated after quantization on the standard held-out test splits of the respective benchmarks (distinct from the calibration data). This separation already exists in the experimental protocol. To eliminate any ambiguity we will revise the relevant sections to explicitly document the data splits and, space permitting, add a small additional experiment on an external benchmark to further demonstrate that the predictive relationship holds outside the calibration distribution. revision: partial

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper's core contribution is a forward-only KL surrogate for sensitivity ranking in SSM-Transformer quantization, supported by a separate formal comparison of KL versus MSE/SQNR and by empirical ablations that measure end-to-end perplexity degradation after actual quantization. These steps rely on distinct computations (KL on unquantized forward passes for ranking; full quantized inference for validation) and do not reduce to each other by definition or by fitting the same quantities. No load-bearing self-citations, ansatz smuggling, or uniqueness theorems imported from prior author work are evident in the provided abstract or description. The framework is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, ad-hoc axioms, or invented entities; the method appears to rest on standard assumptions of quantization noise models and language-model output distributions.

pith-pipeline@v0.9.0 · 5599 in / 1187 out tokens · 45129 ms · 2026-05-10T14:21:16.522813+00:00 · methodology

discussion (0)

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