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arxiv: 2605.11563 · v1 · submitted 2026-05-12 · 💻 cs.CV · cs.AI

Recognition: 2 theorem links

· Lean Theorem

TCP-SSM: Efficient Vision State Space Models with Token-Conditioned Poles

Hun-Seok Kim, Morteza Tavakoli Taba, Sara Shoouri

Pith reviewed 2026-05-13 01:46 UTC · model grok-4.3

classification 💻 cs.CV cs.AI
keywords state space modelsvision mambatoken-conditioned polesefficient SSMrecurrent dynamicsimage classificationsemantic segmentationobject detection
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The pith

By conditioning poles on visual tokens, TCP-SSM cuts computation in state space models by up to 44% while matching or exceeding baseline accuracy.

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

The paper introduces Token-Conditioned Poles SSM to turn the recurrence dynamics of state space models for vision into something explicit and controllable. It constructs each scan step from real poles that handle decay and complex-conjugate poles that handle oscillation, then modulates these shared base poles per token using bounded changes in radius and angle. This token-specific adaptation lets the model adjust its memory behavior to the current visual input without losing stability. The design adds grouped pole sharing and a low-rank input path to keep the overall scan linear in time and cheaper to run. A reader would care because it addresses the hard-to-control memory horizon in compact vision backbones that use long scans, offering a direct way to trade compute for expressivity.

Core claim

TCP-SSM builds each scan operator with real poles that model monotone or sign-alternating decay and complex-conjugate poles that capture damped oscillatory responses. Using bounded radius and angle modulation, it converts shared base poles into token-dependent poles so that each scan step adapts its memory behavior to the current visual token while preserving pole stability. Grouped pole sharing combined with a lightweight low-rank input pathway yields an efficient scan operator that keeps linear-time complexity. Across image classification, semantic segmentation, and object detection, this produces up to 44% reduction in SSM computation in Vision Mamba-style models while maintaining or surp

What carries the argument

Token-Conditioned Poles: shared base poles turned into per-token poles by bounded radius and angle modulation, so the scan operator adapts its decay or oscillation behavior to each visual token while staying stable.

If this is right

  • SSM computation complexity drops by up to 44% in Vision Mamba-style models.
  • Accuracy stays the same or improves on image classification, semantic segmentation, and object detection.
  • Recurrence dynamics become explicit and interpretable through the choice of real versus complex poles.
  • Linear-time scan complexity is preserved via grouped pole sharing and low-rank input pathways.
  • Each scan step can adapt its memory horizon to the specific content of the current token.

Where Pith is reading between the lines

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

  • The explicit pole control could let designers tune memory length separately for different visual regions instead of using a fixed scan length.
  • Because poles are stable by construction, the method may support longer effective context in compact models without the instability that appears in some selective SSM variants.
  • The same token-conditioning idea might transfer to non-vision sequential tasks where input-dependent memory decay would be useful.
  • A direct test would be to measure whether pole angle modulation improves performance on images with strong periodic patterns compared with decay-only poles.

Load-bearing premise

That modulating shared base poles with bounded radius and angle per token preserves both stability and enough expressivity without adding overhead that cancels the claimed efficiency gains.

What would settle it

A controlled experiment on ImageNet classification showing that the token-modulated version either drops below the unmodulated baseline accuracy or fails to deliver net compute savings after including the modulation cost.

Figures

Figures reproduced from arXiv: 2605.11563 by Hun-Seok Kim, Morteza Tavakoli Taba, Sara Shoouri.

Figure 1
Figure 1. Figure 1: Illustration of the dominant pole-derived memory horizon at layers 13, 20, and 22 (of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of TCP-SSM Model. Left: TCP-SSM is inserted into the Vision Mamba [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Accuracy-computation trade-off on EVM-B. [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
read the original abstract

State Space Models (SSMs) have emerged as a compelling alternative to attention models for long-range vision tasks, offering input-dependent recurrence with linear complexity. However, most efficient SSM variants reduce computation cost by modifying scan routes, resolutions, or traversal patterns, while largely leaving the recurrent dynamics implicit. Consequently, the model's state-dependent memory behavior is difficult to control, particularly in compact backbones where long scan paths can exceed the effective memory horizon. We propose Token-Conditioned Poles SSM (TCP-SSM), a structured selective SSM framework that improves efficiency while making recurrence dynamics explicit and interpretable through stable poles. TCP-SSM builds each scan operator with 1) real poles that model monotone or sign-alternating decay, and 2) complex-conjugate poles that capture damped oscillatory responses. Using bounded radius and angle modulation, TCP-SSM converts shared base poles into token-dependent poles, allowing each scan step to adapt its memory behavior to the current visual token while preserving pole stability. For practical scalability, we integrate grouped pole sharing with a lightweight low-rank input pathway, yielding an efficient scan operator that preserves linear-time scan complexity. Across image classification, semantic segmentation, and object detection, TCP-SSM reduces SSM computation complexity up to 44% in Vision Mamba-style models while maintaining or surpassing baseline accuracy.

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 proposes Token-Conditioned Poles SSM (TCP-SSM), a selective state-space model for vision that makes recurrence dynamics explicit by constructing scan operators from real poles (monotone/sign-alternating decay) and complex-conjugate poles (damped oscillations). Shared base poles are converted to token-dependent poles via bounded radius and angle modulation; grouped pole sharing plus a lightweight low-rank input pathway is used to preserve linear-time scan complexity. The central empirical claim is that this yields up to 44% reduction in SSM computation complexity relative to Vision Mamba-style baselines while maintaining or improving accuracy on image classification, semantic segmentation, and object detection.

Significance. If the net efficiency gain survives quantitative overhead accounting, the approach supplies an interpretable, stability-preserving mechanism for controlling memory horizons in compact SSM backbones—an explicit alternative to purely implicit selective SSMs. The combination of pole modulation with grouped sharing could influence design of efficient long-range vision models, provided the claimed reductions are shown to be robust across resolutions and tasks.

major comments (3)
  1. [Abstract] Abstract: the headline claim of 'up to 44% reduction in SSM computation complexity' is presented without a breakdown of measured quantity (FLOPs vs. wall-clock), the precise baseline architecture, or an ablation isolating the cost of the low-rank input pathway and per-token pole modulation. Without these, it is impossible to verify that the added operations do not erode or reverse the reported net saving.
  2. [Method] Method (pole-modulation and low-rank pathway description): the stability argument relies on bounded radius/angle adjustments, yet no explicit complexity analysis or operation count is supplied showing that the per-token modulation (even when grouped) remains negligible relative to the base selective SSM scan for typical vision token counts (thousands of patches). This directly affects the central efficiency claim.
  3. [Experiments] Experiments: the accuracy-maintenance claim is stated at a high level; the manuscript must report per-task tables with error bars, exact model sizes, and direct comparisons against the unmodified Vision Mamba baseline under identical training protocols to substantiate that no hidden accuracy–efficiency trade-off occurs.
minor comments (2)
  1. [Method] Notation for real versus complex poles and the exact form of the bounded modulation functions should be introduced with a small illustrative equation or diagram early in the method section for readability.
  2. [Abstract] The abstract lists three vision tasks but does not name the concrete datasets or resolutions used; these should be stated explicitly.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment point by point below, providing clarifications and committing to revisions that strengthen the manuscript without altering its core contributions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline claim of 'up to 44% reduction in SSM computation complexity' is presented without a breakdown of measured quantity (FLOPs vs. wall-clock), the precise baseline architecture, or an ablation isolating the cost of the low-rank input pathway and per-token pole modulation. Without these, it is impossible to verify that the added operations do not erode or reverse the reported net saving.

    Authors: We agree that the abstract requires greater specificity to support the efficiency claim. In the revised manuscript we have updated the abstract to state that the 44% figure measures FLOPs in the SSM scan operator relative to the unmodified Vision Mamba baseline. We have also added a new subsection (Section 4.4) that reports both theoretical FLOPs and measured wall-clock times on A100 GPUs, together with an ablation isolating the overhead of the low-rank pathway and grouped pole modulation. These additions show a net saving of 39% after overhead, confirming the claim holds. revision: yes

  2. Referee: [Method] Method (pole-modulation and low-rank pathway description): the stability argument relies on bounded radius/angle adjustments, yet no explicit complexity analysis or operation count is supplied showing that the per-token modulation (even when grouped) remains negligible relative to the base selective SSM scan for typical vision token counts (thousands of patches). This directly affects the central efficiency claim.

    Authors: We acknowledge the absence of an explicit operation-count analysis. The revised Method section now contains a dedicated complexity paragraph (Section 3.3) that derives the added cost of bounded radius/angle modulation under grouped sharing (group size 4) and low-rank projection (rank 16). For typical patch counts (196–1024), the incremental cost is shown to be O(N·r) with r ≪ d, amounting to <3% of the base scan. Empirical timing measurements are included to corroborate that the overhead remains negligible. revision: yes

  3. Referee: [Experiments] Experiments: the accuracy-maintenance claim is stated at a high level; the manuscript must report per-task tables with error bars, exact model sizes, and direct comparisons against the unmodified Vision Mamba baseline under identical training protocols to substantiate that no hidden accuracy–efficiency trade-off occurs.

    Authors: We agree that more granular reporting is required. The revised Experiments section now provides full per-task tables for ImageNet classification, ADE20K segmentation, and COCO detection. Each table lists mean performance and standard deviation over three independent runs, exact parameter counts and FLOPs for every model variant, and side-by-side results against the unmodified Vision Mamba trained with identical protocols, schedules, and data augmentations. The updated results confirm that accuracy is maintained or improved while the efficiency gains persist. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation introduces independent architectural mechanisms

full rationale

The paper proposes TCP-SSM as a new structured selective SSM variant that explicitly defines token-conditioned poles via bounded radius/angle modulation, real/complex pole types, grouped sharing, and a low-rank input pathway. These are presented as design choices that yield an efficient scan operator, with the 44% complexity reduction and accuracy claims framed as empirical results from the architecture rather than quantities derived by construction from the same hyperparameters or prior self-citations. No load-bearing step reduces to self-definition, fitted-input renaming, or an unverified self-citation chain; the central efficiency and stability arguments rest on the introduced mechanisms and external benchmarks, making the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the pole stability and bounded modulation are presented as design choices whose justification is not detailed.

pith-pipeline@v0.9.0 · 5540 in / 1206 out tokens · 23203 ms · 2026-05-13T01:46:12.677624+00:00 · methodology

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