Training-free Token Reduction for Vision Mamba

Chi Su; Hairong Zheng; Jie Chen; Qiankun Ma; Wen Gao; Zhen Song; Ziyao Zhang

REVIEW 3 major objections 5 minor 58 references

Training-free Token Reduction for Vision Mamba

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read MTR claims that Mamba's timescale parameter Δ doubles as a free token-importance score, enabling a training-free token reduction framework that cuts FLOPs by about 40% on Vim-B while losing only 1.6% ImageNet top-1 accuracy.

desk verdict A sensible training-free token-reduction recipe for Vision Mamba with a genuinely new importance score; the main risk is under-specified handling of hidden/recurrent state, which needs code or a precise description before the headline numbers can be trusted. read the letter →

arxiv 2507.14042 v1 pith:H6SMK63N submitted 2025-07-18 cs.CV

Qiankun Ma , Ziyao Zhang , Chi Su , Jie Chen , Zhen Song , Hairong Zheng , Wen Gao This is my paper

classification cs.CV

keywords training-freetokenreductionVisionMambastatespacemodeltimescaleparameterimportanceMTRImageNetclassificationefficiency

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the reason token reduction works for Vision Transformers but fails for Vision Mamba is that Mamba has no attention scores to rank tokens and is sensitive to the order of the remaining sequence. To fix that, it proposes using Mamba's own timescale parameter $\Delta_t$ — the input gate that controls how much of each token is written into the recurrent state — as a free importance score, then sorts tokens by that score, keeps the top group, merges the bottom group into the middle via feature similarity, and restores the original order. The resulting framework, MTR, is training-free and plug-and-play, and the paper reports about 40% FLOP reduction on the Vim-B backbone with only a 1.6% drop in ImageNet top-1 accuracy, beating existing training-free baselines at the same compute levels. This matters because it gives practitioners an off-the-shelf way to speed up Mamba vision models without retraining or adding parameters.

What carries the argument

The machinery is the selective state-space update $h_t = e^{A_t} \odot h_{t-1} + B_t(\Delta_t \odot x_t)$, where $\Delta_t = \mathrm{Softplus}(xW_1W_2)$ is an input-dependent value per token. MTR treats this $\Delta_t$ as an input gate and defines the token importance score as the average of $\Delta$ over scanning heads and channels, $s_l = \frac{1}{D}\sum_{d=1}^{D}\Delta_l^d$. The reduction itself is an asymmetric three-way split (Keep / Target / Source), a bipartite similarity merge of Source into Target, and a final reorder step that restores the original token order so the sequential recurrence is not disrupted.

What would settle it

Run the Vim-B 40%-reduction configuration but permute the row order of the hidden state independently of the token pairing before merging; if accuracy stays near 80.3%, then hidden-state alignment is not doing the work, and if it drops sharply, the reported result depends on an alignment the paper never verifies.

Watch

Extended reading notes

Core claim

The central claim is that the timescale parameter $\Delta_t$ in a Mamba block behaves like an attention score: when $\Delta_t$ is large, the current token is written more heavily into the hidden state, and when it is small, the model leans on history. Averaging $\Delta_t$ over the bidirectional scanning heads and over the feature dimension yields a per-token score $s_l$ that requires no extra computation, and this score turns out to be a better predictor of which tokens can be discarded than the hidden state, the input $x_t$, $B_t$, $C_t$, or the [CLS]-similarity proxy imported from ViTs. MTR uses $s_l$ to sort the sequence, keeps the top $k\%$ as 'Keep', marks the bottom $k\%$ as 'Source', merges each Source token into its most similar 'Target' token in the middle group through bipartite matching, and finally re-sorts the survivors by their original positions. The paper claims that this structure-aware pipeline consistently outperforms EViT, PuMer, UTR, and HSA under equal FLOP reduction on ViM-S, ViM-B, VideoMamba-S, and VideoMamba-B.

Load-bearing premise

The load-bearing premise is that the hidden-state and residual rows inside each Mamba block stay aligned with the token sequence after the merge, so they can be compressed with the same Keep/Target/Source grouping; the paper states this design choice but provides no dedicated experiment showing the alignment actually holds.

Editorial extensions

If this is right

Any pretrained Vision Mamba model can be accelerated at inference time by inserting MTR modules after its blocks and choosing a compression ratio; no retraining, fine-tuning, or extra parameters are involved.
At equal FLOP reduction, MTR claims consistent accuracy gains over the best previous training-free and even retraining-based token reduction methods, with the gap widening as the reduction ratio increases.
Because the importance score reuses $\Delta$ that is already computed inside the block, the FLOP savings come almost entirely from the shorter token sequence rather than from new computation.
The reorder step is presented as essential: without restoring original positions, compression damages accuracy, so any future token-reduction method for sequence models should incorporate a similar order-preserving operation.
The single parameter $k$ ties the desired compression ratio to the grouping split, giving practitioners a continuous speed-accuracy knob without hyperparameter search.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural next test is whether the same $\Delta$-based score transfers to non-vision selective SSMs (e.g., language or audio Mamba); the paper does not run those experiments, but the mechanism is model-agnostic.
The paper treats $\Delta$ as an attention score on heuristic grounds; a direct check would be to verify that tokens with high $\Delta$ are the ones whose removal most changes the model's output distribution, which would turn the heuristic into a measurable claim.
The hidden-state and residual rows are reduced with the same token grouping, yet no experiment isolates whether state-row alignment is preserved; testing a variant that recomputes the hidden state from merged tokens at higher cost would clarify whether that alignment is what carries the accuracy.
The reported 40% FLOP cut is theoretical; measuring wall-clock latency on actual hardware would show how much of the theoretical saving survives the reorder and bipartite-matching overhead.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: this is a solid, practically useful efficiency paper. The new idea is using Mamba's timescale parameter Δ as a token importance score, and the paper backs that choice with a decent ablation. The proposed MTR pipeline — importance grouping, bipartite merging, reordering — is a clean adaptation of known machinery, and the empirical claim (about 40% FLOPs cut for ~1.6% ImageNet drop on Vim-B) is consistent across the tables and abstract.

What's genuinely new: it's the first training-free token reduction method aimed at Vision Mamba, and the Δ-based importance score is not something I've seen in the cited literature. The reordering step also addresses a real quirk of sequential models. That's worth credit.

Where it gets soft: the paper says it applies the same reduction strategy to both the hidden state and residual, but Algorithm 1 only describes token-sequence compression. In a selective SSM, the hidden state is per-position; if you merge/reorder tokens, you need to say exactly how state rows are indexed, grouped, and merged, and show that this doesn't corrupt the recurrence. The stress-test concern about this is legitimate. It might be that the implementation handles it straightforwardly, but without code or a precise description, the 40%/1.6% result is not independently verifiable. That's the main reason my verdict is conditional rather than upbeat.

Other soft spots: no error bars, HSA is compared outside its intended retraining regime (though the paper acknowledges this), and the Δ-as-importance story is heuristic — the ablation makes it plausible, but there's no formal argument. These are minor relative to the hidden-state gap.

Who this is for: people working on efficient inference for Mamba-style vision models; it's a practical contribution, not a theoretical one.

Recommendation: I'd send it to peer review, but with a strong request for code and a clear explanation (or ablation) of how hidden-state and residual rows are handled. With that, the paper could be a useful and citable result.

Referee Report

3 major / 5 minor

Summary. The paper proposes MTR, a training-free token reduction framework for Vision Mamba models. The method uses the timescale parameter Δ of Mamba's selective state space model as a token importance score, sorts tokens by this score, partitions them into keep/target/source groups, merges source tokens into similar target tokens via bipartite matching, and reorders the remaining tokens to preserve sequence order. Experiments on ImageNet with ViM-S/B and VideoMamba-S/B report that MTR outperforms UTR, HSA, EViT, and PuMer at 20%, 30%, and 40% FLOPS reduction, with the headline result being a 40% FLOPS reduction on ViM-B with only a 1.6% top-1 accuracy drop.

Significance. If the results are reproducible, MTR would be a useful plug-and-play efficiency tool for Mamba-based vision models, since it requires no retraining and relies only on the model's internal Δ statistics. The paper's strengths include comparisons against several baselines, ablations over importance indicators and reduction strategies, and the observation that token order matters for Mamba, which is an important practical point. The central weakness is that the exact treatment of the hidden state and residual is unspecified, which is essential for the method to define a valid forward pass; the paper also provides no code, no error bars, and compares HSA outside its intended retraining regime. The claim that Δ is an 'attention score' is heuristic, though the ablation in Table 3 provides empirical support.

major comments (3)

[Analysis on reduction operation / Algorithm 1] Algorithm 1 takes only the token sequence y_{l-1} and importance scores s_{l-1} as input and outputs the reduced token sequence x_l; it never specifies how the hidden state and residual are indexed, grouped, or merged. The text in 'Analysis on reduction operation' states that 'our approach applies the same reduction strategy to both the hidden state and residual,' but without a precise rule or an ablation that isolates this choice, the reported 40%/1.6% result on ViM-B may depend on an unstated implementation detail. Please provide a complete specification of the hidden-state and residual reduction, and include an experiment that varies this handling (e.g., reducing with the same token grouping versus recomputing from the reduced sequence).
[Comparison Methods / Tables 1 and 2] HSA is described as a Mamba token pruning method that involves retraining, yet it is evaluated in a training-free setting. This is not a fair comparison for a method whose importance scores were likely derived or tuned under a learned pruning scheme, so the conclusion that MTR 'consistently outperforms all baselines' is overstated. Please either evaluate HSA under its intended training regime, or explicitly frame the comparison as zero-shot transfer and remove HSA from the claim of a fair head-to-head comparison.
[Assessing Token Importance in Vision Mamba, Eq. (8)] The derivation of the token importance score is heuristic: Eq. (8) sums Δ over scanning heads and averages over the feature dimension without a formal argument that this aggregated quantity is a valid token-level importance measure in the selective SSM recurrence. The ablation in Table 3 supports the empirical choice, but the paper should state explicitly that this is an empirical finding rather than a derived property, and ideally report variance across runs or checkpoints to assess the stability of the ranking.

minor comments (5)

[Algorithm 1] The variable k' is computed as (1 - 2k)|y_{l-1}|, but it is called the 'number of tokens in the target group'; this is clear but could be renamed, for example to n_target, to avoid confusion with the reduction ratio k.
[Preliminary, Eq. (2) and Eq. (4)] The notation for discretized parameters is reused inconsistently: Eq. (2) uses A and B for the discretized matrices, while Eq. (4) introduces A_t and B_t with different meanings; please unify the notation to avoid ambiguity.
[Analysis on reduction operation] The text says 'More experiments on reduction strategies are provided in the Appendix,' but the manuscript contains no appendix; please either include the additional experiments or remove the reference.
[Experiments] No code or implementation details are provided, and the main tables report a single run without standard deviations or confidence intervals; given that several differences between methods are within 0.2-0.3% (e.g., Table 2), please release code and report multiple seeds or at least the variance across runs.
[Visualization, Fig. 3] The visualization is qualitative; consider adding a quantitative evaluation, such as the overlap between retained tokens and CAM-highlighted regions or per-class retention statistics, to support the claim that the 'keep' group corresponds to core content.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: MTR's importance score is taken from the model's own Delta parameter and its accuracy claims are judged against an external benchmark.

full rationale

The paper's central derivation is MTR: use the Mamba timescale parameter Delta as a token-importance score (Eq. 8), group tokens into keep/target/source, and merge least important tokens into similar target tokens. The score is defined from the model's own internal parameters (Delta_t = Softplus(xW1W2)) and is not fitted to any target accuracy; the reported 40% FLOPs reduction with 1.6% ImageNet drop is measured against the external ImageNet-1K benchmark. The ablation comparing Delta_t with B_t, C_t, [CLS], and X_t is a design choice validated on the same benchmark, which is ordinary model selection rather than a fitted input renamed as a prediction. The paper's self-citations to UTR and HSA are used as baselines and for inference technique details, not as load-bearing justification of the claimed result. The one substantive concern, flagged in 'Analysis on reduction operation,' is that 'our approach applies the same reduction strategy to both the hidden state and residual' while Algorithm 1 only specifies token-sequence reduction; this is a completeness and reproducibility risk, not a circularity step, because it does not reduce the accuracy result to an input of the method. No equation or fitted parameter in the paper is equivalent by construction to the claimed outcome, so the circularity score is 0.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claims rest on four domain assumptions about Δ as an importance proxy, merging preserving information, hidden-state alignment, and order restoration. The only free parameter is the user-chosen reduction ratio k. No invented entities and no fitted numerical constants are introduced.

free parameters (1)

reduction ratio k = 20%, 30%, 40% in experiments; main result uses 40%
User-specified compression ratio controlling the keep/source fraction and the target group size. It is not learned or fitted, but it determines the reported FLOPs/accuracy trade-off.

assumptions (4)

domain assumption The per-token, feature-averaged timescale Δ is a reliable proxy for token importance in Vision Mamba.
Introduced in Methodology, 'Assessing Token Importance'; supported by an analogy to input gating (Han et al. 2024) and by Table 3, but no formal proof or validation outside ImageNet.
domain assumption Merging source tokens into the most similar target token by averaging their vectors preserves the information needed by later Mamba layers.
Algorithm 1 uses bipartite soft matching and mean vector merging; this is borrowed from token merging literature and is validated only empirically in Tables 1 and 2.
domain assumption Hidden state and residual rows can be reduced with the same token-based masks as the visible token sequence.
Stated in the ablation section 'Analysis on reduction operation'; if hidden-state rows are not aligned with tokens, the recurrent state is corrupted, and no dedicated experiment isolates this assumption.
domain assumption Reordering surviving tokens back to their original positions restores most of the order-sensitive performance.
Motivated by Figure 1(a) for Vim-S and assumed to transfer to other backbones and tasks; no separate study of the reordering effect is provided.

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Cite this review

Pith. "Pith review of Training-free Token Reduction for Vision Mamba." pith.science (2026). https://pith.science/paper/H6SMK63N

@misc{pith2026250714042,
  author       = {Pith},
  title        = {Pith review of: Training-free Token Reduction for Vision Mamba},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H6SMK63N}},
  note         = {Machine review of arXiv:2507.14042}
}

read the original abstract

Vision Mamba has emerged as a strong competitor to Vision Transformers (ViTs) due to its ability to efficiently capture long-range dependencies with linear computational complexity. While token reduction, an effective compression technique in ViTs, has rarely been explored in Vision Mamba. Exploring Vision Mamba's efficiency is essential for enabling broader applications. However, we find that directly applying existing token reduction techniques for ViTs to Vision Mamba leads to significant performance degradation. This is primarily because Mamba is a sequence model without attention mechanisms, whereas most token reduction techniques for ViTs rely on attention mechanisms for importance measurement and overlook the order of compressed tokens. In this paper, we investigate a Mamba structure-aware importance score to evaluate token importance in a simple and effective manner. Building on this score, we further propose MTR, a training-free \textbf{M}amba \textbf{T}oken \textbf{R}eduction framework. Without the need for training or additional tuning parameters, our method can be seamlessly integrated as a plug-and-play component across various Mamba models. Extensive experiments demonstrate that our approach significantly reduces computational workload while minimizing performance impact across various tasks and multiple backbones. Notably, MTR reduces FLOPs by approximately 40\% on the Vim-B backbone, with only a 1.6\% drop in ImageNet performance without retraining.

Figures

Figures reproduced from arXiv: 2507.14042 by the authors.

**Figure 2.** Overview of our proposed framework MTR. Image tokens are processed by the Mamba block and subsequently sorted [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Visualization of reduction tokens on ViM-S under 20% overall reduction of FLOPS. We present visualizations of the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Comparison of generation throughput across dif [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

, " * write output.state after.block = add.period write newline

ENTRY address archivePrefix author booktitle chapter edition editor eid eprint howpublished institution isbn journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.a...

[2] [2]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

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2009