arxiv: 2604.20606 · v1 · submitted 2026-04-22 · 💻 cs.CV · cs.AI

Recognition: unknown

Beyond ZOH: Advanced Discretization Strategies for Vision Mamba

Fady Ibrahim , Guangjun Liu , Guanghui Wang

Authors on Pith no claims yet

Pith reviewed 2026-05-10 00:06 UTC · model grok-4.3

classification 💻 cs.CV cs.AI

keywords Vision Mambastate space modelsdiscretization methodsbilinear transformimage classificationsemantic segmentationobject detection

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The pith

Replacing zero-order hold with bilinear discretization in Vision Mamba delivers consistent accuracy gains across vision tasks at modest extra cost.

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

Vision Mamba processes images through state space models that require turning continuous dynamics into discrete steps. The standard zero-order hold treats each input as fixed between samples, which reduces how accurately the model tracks changing visual content. This work inserts and tests five other discretization rules inside the identical Vision Mamba architecture and measures them on classification, segmentation, and detection benchmarks. Polynomial interpolation and higher-order hold produce the largest accuracy lifts, yet the bilinear transform supplies reliable improvement over the default while adding only light training overhead. A reader who accepts these results would treat bilinear as the stronger practical baseline for state-space vision models.

Core claim

Vision Mamba currently employs zero-order hold discretization, which assumes input signals remain constant between sampling instants and thereby degrades temporal fidelity in dynamic visual environments. A controlled comparison of zero-order hold, first-order hold, bilinear transform, polynomial interpolation, higher-order hold, and fourth-order Runge-Kutta within the Vision Mamba framework shows that polynomial interpolation and higher-order hold produce the largest accuracy increases on image classification, semantic segmentation, and object detection, albeit with greater training-time computation. The bilinear transform, however, supplies steady improvements over zero-order hold while添加只有

What carries the argument

The discretization scheme that converts the continuous state-space equations into a discrete recurrence inside Vision Mamba; it determines how the input signal is approximated between sampling instants and therefore controls the model's temporal resolution.

If this is right

Future Vision Mamba models could adopt the bilinear transform as the default discretization to raise baseline accuracy without large training-time penalties.
When maximum accuracy is required and extra compute is available, polynomial interpolation or higher-order hold should be selected instead.
The performance gap between discretization choices demonstrates that the discretization step itself is a first-order design decision for state-space vision architectures.
Empirical results supply a concrete justification for replacing zero-order hold in subsequent SSM-based vision papers and libraries.

Where Pith is reading between the lines

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

The same discretization comparisons could be repeated on video or temporal action datasets where motion is continuous rather than static images.
Other state-space models outside vision, such as those used for audio or time-series, might exhibit similar accuracy-compute trade-offs when their discretization is upgraded.
Hardware-aware implementations could reduce the training overhead of polynomial or Runge-Kutta methods, potentially making them competitive with bilinear in practice.

Load-bearing premise

The six discretization schemes were coded correctly and applied under identical conditions inside the Vision Mamba code base, and the chosen image benchmarks adequately reflect the temporal changes that matter in real dynamic scenes.

What would settle it

An independent re-implementation of the bilinear transform on a new high-motion video benchmark that shows no accuracy gain over zero-order hold would falsify the reported trade-off advantage.

Figures

Figures reproduced from arXiv: 2604.20606 by Fady Ibrahim, Guanghui Wang, Guangjun Liu.

**Figure 3.** Figure 3: POL fits a polynomial through sampled points of the input, allowing the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: HOH uses multiple samples to construct a higher-order polynomial ap [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: RK4 is a fourth-order iterative method that approximates the value at [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: Statistical scatter plot - performance vs. efficiency. Mean [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

read the original abstract

Vision Mamba, as a state space model (SSM), employs a zero-order hold (ZOH) discretization, which assumes that input signals remain constant between sampling instants. This assumption degrades temporal fidelity in dynamic visual environments and constrains the attainable accuracy of modern SSM-based vision models. In this paper, we present a systematic and controlled comparison of six discretization schemes instantiated within the Vision Mamba framework: ZOH, first-order hold (FOH), bilinear/Tustin transform (BIL), polynomial interpolation (POL), higher-order hold (HOH), and the fourth-order Runge-Kutta method (RK4). We evaluate each method on standard visual benchmarks to quantify its influence in image classification, semantic segmentation, and object detection. Our results demonstrate that POL and HOH yield the largest gains in accuracy at the cost of higher training-time computation. In contrast, the BIL provides consistent improvements over ZOH with modest additional overhead, offering the most favorable trade-off between precision and efficiency. These findings elucidate the pivotal role of discretization in SSM-based vision architectures and furnish empirically grounded justification for adopting BIL as the default discretization baseline for state-of-the-art SSM models.

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.

Desk Editor's Note private letter to a colleague

Bilinear discretization gives the best practical trade-off for Vision Mamba on the tested tasks, but the static-image benchmarks leave the temporal-fidelity motivation unproven.

read the letter

The main thing to know is that this paper finds bilinear discretization gives the best accuracy-efficiency balance for Vision Mamba compared to the default zero-order hold, while polynomial and higher-order holds deliver larger accuracy improvements at the expense of more training time. They take the existing Vision Mamba setup and plug in six different discretization approaches: ZOH, FOH, BIL, POL, HOH, and RK4. Then they run them on ImageNet for classification, ADE20K for segmentation, and COCO for detection. The results point to BIL as the sweet spot for most users. This kind of side-by-side test is straightforward but still valuable. It gives practitioners a clear, empirically backed default to try instead of sticking with ZOH. The biggest limitation is that every benchmark is a static image task. The paper's introduction stresses the need for better temporal fidelity in dynamic scenes, but there are no video datasets or time-series vision experiments here. The observed gains could come from other factors like altered gradient flow or receptive field effects rather than true improvements in modeling continuous-time signals. The abstract also skips the actual performance numbers and any mention of variance or statistical significance. Without those, it's difficult to gauge how meaningful the differences are or whether they hold across random seeds. Readers already deep into state space models for vision will find this useful as a practical tuning guide. It doesn't change the core architecture or add new capabilities, so it stays within that subfield. I would recommend sending this to peer review. The comparison is honest and the trade-off analysis is the kind of thing that helps the community move forward, even if the dynamic motivation needs stronger evidence from future work on video tasks.

Referee Report

1 major / 1 minor

Summary. The paper conducts a controlled comparison of six discretization schemes (ZOH, FOH, BIL, POL, HOH, RK4) inside the Vision Mamba SSM framework. It evaluates them on ImageNet classification, ADE20K segmentation, and COCO detection, reporting that POL and HOH deliver the largest accuracy gains at higher training cost while BIL provides consistent improvements over ZOH with modest overhead and is recommended as the new default.

Significance. If the reported accuracy gains are reproducible and attributable to discretization rather than confounding factors, the work supplies practical guidance for SSM-based vision models and could influence default choices in future architectures. The systematic, side-by-side evaluation is a clear strength. However, because all benchmarks are static-image tasks, the significance for the paper's stated motivation around temporal fidelity in dynamic environments remains limited.

major comments (1)

[Introduction] Introduction and Abstract: The motivation centers on ZOH degrading 'temporal fidelity in dynamic visual environments,' yet every reported experiment uses static-image datasets (ImageNet, ADE20K, COCO) that contain no continuous-time dynamics. Observed gains could therefore arise from altered receptive fields or optimization behavior rather than superior discretization of time-varying signals, directly undermining the link between the empirical conclusions and the central thesis.

minor comments (1)

[Abstract] Abstract: Performance rankings are stated without any numerical deltas, standard deviations, or statistical tests, which reduces the reader's ability to gauge the practical magnitude of the claimed improvements.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and for identifying the gap between our stated motivation and the experimental setup. We address this point directly below and outline the revisions we will make.

read point-by-point responses

Referee: [Introduction] Introduction and Abstract: The motivation centers on ZOH degrading 'temporal fidelity in dynamic visual environments,' yet every reported experiment uses static-image datasets (ImageNet, ADE20K, COCO) that contain no continuous-time dynamics. Observed gains could therefore arise from altered receptive fields or optimization behavior rather than superior discretization of time-varying signals, directly undermining the link between the empirical conclusions and the central thesis.

Authors: We agree that the experiments are conducted exclusively on static-image benchmarks and therefore do not directly demonstrate improved handling of continuous-time dynamics. The performance gains we report could indeed result from changes in effective receptive field, state evolution across patch sequences, or optimization landscape rather than from superior approximation of time-varying signals. To correct the misalignment, we will revise both the Abstract and Introduction to (1) explicitly note that the present study quantifies discretization effects on standard static vision tasks, (2) frame the dynamic-environment motivation as the broader context that originally motivated the work rather than a claim supported by the current results, and (3) add a short discussion paragraph acknowledging alternative explanations for the observed gains and outlining future experiments on video and other temporally dynamic data. These textual changes will ensure the manuscript's claims are commensurate with the evidence provided. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical comparisons rest on direct benchmarks, not self-referential derivations

full rationale

The paper conducts a controlled empirical evaluation of six discretization methods (ZOH, FOH, BIL, POL, HOH, RK4) inside the Vision Mamba architecture, reporting accuracy and efficiency on ImageNet, ADE20K, and COCO. No equations, predictions, or first-principles claims are present that reduce by construction to author-defined inputs, fitted parameters, or self-citations. The central results are benchmark deltas; the motivation regarding temporal fidelity is interpretive but does not create a load-bearing circular step because the reported gains are measured quantities, not quantities defined by the discretization choice itself. This is a standard self-contained empirical study.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the empirical performance of standard discretization methods applied to an existing model architecture; no new free parameters, axioms, or invented entities are introduced beyond the choice of which known methods to test.

axioms (1)

domain assumption Standard numerical discretization schemes (ZOH, FOH, BIL, POL, HOH, RK4) can be directly substituted into the Vision Mamba state-space update equations without altering the model's learned parameters.
Invoked when the authors state they 'instantiated' each scheme inside the Vision Mamba framework.

pith-pipeline@v0.9.0 · 5503 in / 1360 out tokens · 26810 ms · 2026-05-10T00:06:20.815629+00:00 · methodology

discussion (0)

Reference graph

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