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REVIEW 4 major objections 5 minor 53 references

Parameter Efficient Mamba Tuning via Projector-targeted Diagonal-centric Linear Transformation

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Mamba's transfer learning is carried by its linear projectors, not its state-space core, and a diagonal-centric transform of those frozen projectors tunes the model with under 1% of parameters.

desk verdict The projector-dominance finding is the real contribution; ProDiaL is essentially LoRA on projectors with a diagonal wrapper, and the paper's own ablation contradicts the diagonal-centric narrative. read the letter →

arxiv 2411.15224 v3 pith:OA54K4NA submitted 2024-11-21 cs.LG cs.AI

Seokil Ham , Hee-Seon Kim , Sangmin Woo , Changick Kim This is my paper · ORCID
classification cs.LGcs.AI
keywords Mambaparameter-efficientfine-tuningstate-spacemodelsVisionprojectordiagonal-centrictransformationlow-rankadaptationtransferlearning
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

The paper argues that in Mamba architectures, transfer learning is carried by the two linear projectors—the input and output linear layers that wrap the selective state-space model (SSM)—rather than by the SSM itself. Component-wise fine-tuning experiments on Mamba LLMs and Vision Mamba show that tuning a single projector outperforms tuning the SSM's own parameters. Based on the observation that a fine-tuned projector weight $W'$ can be written as $W T$ with $T$ close to the identity and dominated by its diagonal, the authors propose ProDiaL: freeze $W$ and train $W' = s W D_b + \epsilon$, where $D_b$ is block-diagonal, $s$ is a per-output scaling vector, and $\epsilon$ is low-rank. ProDiaL uses less than 1% of total parameters and reports accuracy higher than or comparable to full fine-tuning, LoRA, and DoRA across language reasoning and image classification benchmarks, at several model sizes.

What carries the argument

The central object is the near-diagonal linear transformation $T$ between pretrained and fine-tuned projector weights, recovered as $T_{\mathrm{det}} = W^{-1}W'$. ProDiaL's update rule $W' = s W D_b + \epsilon$ is a factored stand-in for $W T$: a block-diagonal matrix $D_b$ with block size $r_b$ absorbs the dominant diagonal and block-local rotation, a per-channel scaling vector $s$ adjusts scale, and a low-rank term $\epsilon = B_\epsilon A_\epsilon$ absorbs the residual off-diagonal movement. The learnable parameter count is controlled by $r_b$ and the low-rank value $r_\epsilon$.

What would settle it

Compute $T_{\mathrm{det}} = W^{-1}W'$ for all projector layers on a held-out task and compare the L1 mass of off-diagonal entries with the diagonal; then train ProDiaL with the off-diagonal term removed. If removing $\epsilon$ changes accuracy by more than the method's reported gains, or if a synthetic task with a known rotation $W' = W R$, where $R$ is a 45-degree rotation matrix, causes accuracy to collapse, the diagonal-centric assumption is falsified.

Watch

Extended reading notes

Core claim

On its own terms, the paper reports two findings. First, in a Mamba block the components that dominate downstream-task transfer are the Input-Projector and Output-Projector, the linear layers that expand and compress tokens around the SSM, rather than the SSM parameters themselves, even though those parameters directly control the matrices $B$, $C$, and $\Delta$ in the state-space update. Second, the change from a pretrained projector weight $W$ to a fine-tuned weight $W'$ is well approximated by a linear transformation $W' = W T$ whose matrix $T$ is close to the identity: strong on the diagonal, small off the diagonal, with training gradients concentrated along the diagonal. ProDiaL operationalizes this by freezing $W$ and learning $W' = s W D_b + \epsilon$, where $D_b$ is a block-diagonal matrix, $s$ is a per-output scaling vector, and $\epsilon$ is a low-rank correction for the off-diagonal part. With fewer than 1% of the model's parameters learned, the method reports higher or comparable accuracy than full fine-tuning, LoRA, and DoRA on language reasoning tasks and image classification tasks, across Mamba-130M, Mamba-370M, Mamba-1.4B, Vim-tiny, and Vim-small.

Load-bearing premise

The load-bearing premise is that, across every layer and task, the fine-tuned projector weight is obtained from the pretrained one by a single linear map that is close to the identity matrix; if off-diagonal movement is substantial or the projector is ill-conditioned, the diagonal-centric parameterization cannot represent the needed adaptation.

Editorial extensions

If this is right

  • PEFT in Mamba should target projectors rather than SSMs; applying existing LoRA and DoRA to projectors outperforms applying the same methods to SSM parameters.
  • ProDiaL matches or exceeds full fine-tuning and current PEFT baselines on HellaSwag, Winogrande, ARC-E, ARC-C, StanfordCars, Caltech, and Flowers while training less than 1% of the model's parameters.
  • The method transfers across Mamba 1 and Mamba 2 architectures, across model sizes from 130M to 1.4B parameters, and works when tuning only the input projector or only the output projector.
  • After training, the transformation can be merged into the frozen projector weights, so no additional parameters need to be stored at inference time.
  • Ablations show each component contributes: the block-diagonal term alone captures most of the gain, while the off-diagonal low-rank term and the scaling vector add further accuracy.

Reading between the lines

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

  • Extension not in the paper: if the near-diagonal transfer phenomenon holds for large pretrained linear layers generally, a similar diagonal-centric transform could cheapen adaptation of Transformer FFN and MLP blocks; the paper only probes non-attention modules with a single ViT experiment.
  • Extension: the near-diagonal evidence is visualized for one input projector at one layer on one dataset, so measuring the off-diagonal mass of $T_{\mathrm{det}}$ across every layer, both projectors, and several tasks would establish how general the mechanism is.
  • Extension: because $r_b$ and $r_\epsilon$ form a continuous parameter-accuracy knob, a scheduler that adds off-diagonal capacity only for hard layers or hard datasets could improve cases like Flowers, where the paper reports that more parameters help.
  • Extension: since only block-diagonal, scaling, and low-rank factors are trained, ProDiaL could be combined with quantized Mamba weights without needing full precision for the frozen projectors, analogous to quantized low-rank recipes for Transformers.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper studies parameter-efficient fine-tuning (PEFT) for Mamba architectures. It makes two claims: (1) the linear Projectors in Mamba blocks, not the SSM modules, are the main contributors to transfer learning; (2) based on an observed near-diagonal linear relation W' ≈ W T between pretrained and fine-tuned projector weights, the paper proposes ProDiaL, which freezes W and trains a block-diagonal matrix Db, a low-rank off-diagonal term ε, and a scaling vector s, giving W' = s W Db + ε. The method is evaluated on Mamba-130M/370M/1.4B for language reasoning tasks and Vim-tiny/small for vision classification tasks, with comparisons to full fine-tuning, BitFit, Strong, LoRA, and DoRA. The paper reports that ProDiaL outperforms baselines while using a small fraction of the model parameters.

Significance. The finding that Projectors, rather than SSMs, are the primary drivers of downstream adaptation in Mamba is a useful empirical insight and is broadly supported by the component-level comparisons in Tables 1 and 2. If the ProDiaL parameterization were shown to be the source of the reported gains, the method would be a valuable addition to PEFT for Mamba. The paper also provides a breadth of experiments across vision and language models and model scales, and it includes ablation studies. However, as written, two load-bearing claims are not supported by the paper's own numbers: the 'less than 1%' parameter claim is factually contradicted by Tables 3 and 4, and the ablation in Table 7 indicates that the off-diagonal LoRA term, not the diagonal-centric block, drives most of ProDiaL's improvement over the projector-only baseline. These issues require substantial revision before the central methodological claims can be accepted.

major comments (4)
  1. [Abstract and Section 7] The claim that ProDiaL fine-tunes 'less than 1% of the total parameters' is contradicted by the parameter counts in Tables 3 and 4. For Mamba-130M, the Both-Proj ProDiaL configuration uses 2.42M parameters, which is 1.86% of 130M; for Vim-tiny, 0.67M parameters is about 9.6% of the 7M-parameter model; for Mamba-370M and Mamba-1.4B, the reported values are about 1.55% and 3.6%, respectively. The efficiency claim should be corrected to state the actual fractions, or the experimental configurations should be changed so that the stated bound holds.
  2. [Table 7 and Section 5.5] The ablation study does not support the paper's central claim that the diagonal-centric transformation is the key component. On Caltech, Proj-Db alone reaches 95.24 with 0.57M parameters, adding ε raises accuracy to 96.16, and adding s gives 96.24. Thus ε contributes +0.92 points once Db is present, whereas the entire diagonal-centric machinery (Db plus s) contributes only +0.08 points once ε is included. Moreover, ordinary LoRA on the same projectors reaches 96.01 with 0.63M parameters, which is already above the Db-only result and within 0.23 points of full ProDiaL. These numbers suggest that ProDiaL behaves essentially as 'LoRA on projectors' and that the diagonal-centric component is not the source of the reported gains. The authors need to either provide evidence that the diagonal structure is genuinely load-bearing or reframe the method's contribution accordingly.
  3. [Section 4.2.1, Eq. (5), and Fig. 2] The evidence that the projector transformation T is near-diagonal is weak and partly circular. Since Tdet = W⁺W' = I + W⁺(W' - W), any fine-tuned W' that is close to W will produce a Tdet close to the identity, regardless of whether diagonal or off-diagonal structure is important for the task. The visualization in Fig. 2 shows only a single input projector at layer 4 on the Caltech dataset, and the supplementary text confirms this choice, so the claim that the pattern is 'consistently observed across both Projectors, all layers, and both Mamba LLM and Vision models' is not supported by the reported evidence. The paper should report a quantitative diagonal-energy measure across layers, projectors, and datasets, and ideally compare against a random or permutation baseline.
  4. [Tables S6–S9 and Table S1] The hyperparameters rb1, rb2, and rε are selected per dataset, and Table S1 shows that the best configuration varies with the dataset and appears to be chosen with reference to test accuracy. Combined with the fact that the main tables report single runs (only Table S4 gives three-seed results), the reported differences between ProDiaL and the LoRA/DoRA baselines are not shown to be statistically reliable. For example, the Caltech gap between ProDiaL (96.24) and LoRA (96.01) is 0.23 points, which is smaller than the seed variation reported for similar settings in Table S4. The authors should fix hyperparameters on a validation split or report error bars across multiple seeds for all headline comparisons.
minor comments (5)
  1. [Abstract] The sentence 'While state-space models (SSMs) have been regarded as the cornerstone of Mamba architecture, then expected to play a primary role in transfer learning' contains a grammatical error ('then expected' should likely be 'and are expected').
  2. [Eq. (7) and Algorithm 1] The notation for the scaling vector s is ambiguous: s is defined as a vector in R^{d_out}, but it is used in the product s W Db without specifying whether it is a diagonal matrix, a row-wise scaling, or an outer product. Please define the broadcasting or use an explicit diagonal operator.
  3. [Section 5.3 and Table 4] In Table 4, the parameter counts for the larger models are rounded to values such as 0.06B and 0.05B, which makes it difficult to verify the claimed parameter-efficiency ratios. Reporting exact parameter counts would allow readers to check the efficiency claims.
  4. [Appendix B, Table S1] The Flower results in Table S1 are inconsistent with the main text: Table S1 reports 86.96 for the (192,384,16) configuration and 89.12 for the (8,32,8) configuration, while Table 3 reports 88.00 for ProDiaL on Flowers and Table S8 lists (8,32,8). Please clarify which hyperparameter configuration corresponds to the results in Table 3.
  5. [Algorithm 1] The algorithm constructs Da = diag(x1, ..., xrb), while Eq. (7) uses Da = diag(x1, ..., xn). The notation n and rb should be unified.

Circularity Check

1 steps flagged · score 3.0 of 10

The near-identity T observation is largely a definitional restatement of small fine-tuning updates; the core projector-dominance and benchmark results remain independent.

  1. renaming known result [Section 4.2.1, Eq. (5), Fig. 2a]
    "Given the fine-tuned and pretrained Projector weights, we can deterministically calculate Tdet using the pseudo-inverse of W as follows: Tdet = W^{-1}W'. As shown in Fig. 2a, the matrix Tdet closely resembles an identity matrix, with high values (close to 1) along the diagonal and near-zero values elsewhere."

    By construction, Tdet is the exact linear map sending W to W', so W' = W Tdet holds identically for the computed matrix. Whenever fine-tuning changes W by a small relative amount, Tdet = I + W^{-1}(W'-W) is automatically close to the identity, regardless of layer type or task. The 'near-identity with strong diagonal values' observation therefore largely restates the smallness of the weight change rather than demonstrating that diagonal entries are the distinctive locus of transfer. This definitionally near-identity T is then used in Sec. 4.2.2 to justify training only a diagonal-centric Db, so the motivating 'insight' is, in its near-diagonal part, an artifact of the definition rather than an independent empirical discovery about Projectors.

full rationale

The central empirical claims of the paper—that Projectors, not SSMs, dominate transfer in Mamba models, and that ProDiaL achieves competitive accuracy with under 1% of parameters—are supported by direct experiments (Tabs. 1–4) and are not circularly forced by the method definition. The one load-bearing analytical step that reduces by construction is the Tdet observation: because Tdet = W^{-1}W' by definition, its near-identity form is guaranteed whenever the fine-tuned weights remain close to the pretrained weights, and the paper overinterprets this as evidence that diagonal entries are the special locus of adaptation. Separately, Tab. 7 shows that the LoRA off-diagonal term ε contributes +0.92 accuracy over Db alone while the scaling factor s adds only +0.08, which weakens the stated diagonal-centric mechanism; this is a substantive strength/correctness concern but not itself a circularity. The use of Caltech for the motivation analysis and for hyperparameter selection (Tab. S1) is a benchmark-leakage risk, not a circular derivation. Overall, the score reflects one partial circularity in the motivation chain while the main results retain independent empirical content.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central design choices of ProDiaL rest on an empirical observation about the shape of the transformation between pretrained and fine-tuned Projector weights, which is only demonstrated on limited data. The per-dataset hyperparameters are free parameters selected on the test sets. There are no invented entities: the block-diagonal matrix and low-rank residual are standard PEFT building blocks.

free parameters (3)
  • Block sizes rb1 and rb2 = e.g., (192,384) for Caltech; (16,16) for Flowers
    Chosen per dataset to maximize test accuracy (Tables S6-S8).
  • Low-rank value r_epsilon = 8 or 16 depending on dataset
    Selected per dataset; affects parameter count and performance.
  • Learning rates = varies by method and dataset (e.g., 1e-4 for HellaSwag, 5e-6 for Winogrande)
    Searched for each method (Table S5) to ensure fair comparison; the selected values are part of the reported results.
assumptions (4)
  • domain assumption The relationship between pretrained and fine-tuned Projector weights can be written as W' = W T (Eq. 4).
    This linear transform representation is assumed for all layers; it is verified only indirectly via Fig. 2 on one layer.
  • standard math The pseudo-inverse W^{-1} in Eq. 5 is numerically stable and meaningful.
    The paper computes T_det via pseudo-inverse; if W is ill-conditioned, T_det may be dominated by noise.
  • domain assumption Fine-tuning other Mamba components (SSM, embeddings, convolution) is unnecessary or harmful for downstream tasks.
    The ablations in Tables 1-2 support this but use specific datasets and no statistical tests.
  • domain assumption The Mamba block structure, with two projectors, an SSM, and a convolution, is correctly identified and isolated.
    The paper assumes the standard Mamba block decomposition; any implementation differences could affect the projector/SSM attribution.

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Cite this review

Pith. "Pith review of Parameter Efficient Mamba Tuning via Projector-targeted Diagonal-centric Linear Transformation." pith.science (2026). https://pith.science/paper/OA54K4NA

@misc{pith2026241115224,
  author       = {Pith},
  title        = {Pith review of: Parameter Efficient Mamba Tuning via Projector-targeted Diagonal-centric Linear Transformation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OA54K4NA}},
  note         = {Machine review of arXiv:2411.15224}
}
read the original abstract

Despite the growing interest in Mamba architecture as a potential replacement for Transformer architecture, parameter-efficient fine-tuning (PEFT) approaches for Mamba remain largely unexplored. In our study, we introduce two key insights-driven strategies for PEFT in Mamba architecture: (1) While state-space models (SSMs) have been regarded as the cornerstone of Mamba architecture, then expected to play a primary role in transfer learning, our findings reveal that Projectors -- not SSMs -- are the predominant contributors to transfer learning. (2) Based on our observation, we propose a novel PEFT method specialized to Mamba architecture: Projector-targeted Diagonal-centric Linear Transformation (ProDiaL). ProDiaL focuses on optimizing only the pretrained Projectors for new tasks through diagonal-centric linear transformation matrices, without directly fine-tuning the Projector weights. This targeted approach allows efficient task adaptation, utilizing less than 1% of the total parameters, and exhibits strong performance across both vision and language Mamba models, highlighting its versatility and effectiveness.

Figures

Figures reproduced from arXiv: 2411.15224 by the authors.

Figure 1
Figure 1. Overview of Mamba Architecture and Perfor￾mance Comparison. (a) The Mamba block structure, illustrating key components including the Input-Projector (In-Proj), Output￾Projector (Out-Proj), and State-Space Model (SSM). (b) Perfor￾mance analysis in Fine-Tuning for Vision Mamba and Mamba LLM, showing that projectors are essential for effective down￾stream task performance. (c) The radar chart illustrates the rela￾tive … view at source ↗
Figure 2
Figure 2. Analysis of a linear transformation matrix T. (a) The matrix closely resembles an identity matrix, with strong diagonal values and minimal off-diagonal values. (b) The accumulated gra￾dient is concentrated along the diagonal, emphasizing the impor￾tance of training these elements for effective adaptation. than the SSM—are crucial for learning downstream tasks in Mamba architecture. However, Projectors in Mamba repre… view at source ↗
Figure 3
Figure 3. Overview of ProDiaL Architecture for Efficient Parameter Tuning in Mamba Models: A detailed structure of ProDiaL’s approach to fine-tuning Mamba architecture by focusing on Projector transformations. ProDiaL selectively updates the diagonal(Db) and non-diagonal(ϵ) matrices in Projectors, enabling efficient learning with minimal parameters. In addition, we measure the L1 norm of the difference between the identity ma… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Performance comparison across four T configura￾tions in Mamba model. The diagonal-centric approach achieves near-optimal performance with a significantly reduced parameter number (0.57M), supporting the validity of our ProDiaL. results emphasize the adaptability and ef…

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.