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REVIEW 3 major objections 4 minor 108 references

Learning Deep Modality-Shared Self-Expressiveness for Image Clustering with Textual Information

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read DeepMORSE claims that sharing one self-expressive coefficient matrix across image and text embeddings, while shaping each modality into a union of subspaces, improves clustering and transfers to retrieval and zero-shot classification.

desk verdict A useful but over-claimed theory wraps a solid empirical contribution; referee it, but expect the theory claims to need shrinking. read the letter →

arxiv 2608.08418 v1 pith:G23RMF7O submitted 2026-08-09 cs.CV

Xianghan Meng , Wei He , Zhiyuan Huang , Chun-Guang Li This is my paper · ORCID
classification cs.CV
keywords imageclusteringmultimodalrepresentationlearningsubspaceself-expressivemodelunionofsubspacesvision-languagemodelstextualcounterpartgenerationimplicitregularization
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 sets out to show that image clustering with textual information works better when the two modalities are not directly aligned but are coupled by one shared set of self-expressive coefficients, while each modality is shaped into its own union of low-dimensional subspaces. The proposed method, DeepMORSE, jointly learns image and text embeddings together with a shared coefficient matrix $C$ that expresses each point as a linear combination of other points with the same weights in both modalities. The authors prove that sharing coefficients across modalities suppresses inter-class noise relative to either modality alone, and that mini-batch training induces an implicit regularization on $C$. If the claim is right, multimodal clustering no longer has to trust the often unreliable raw similarities of pretrained vision-language embeddings. On six benchmarks the paper reports state-of-the-art accuracy except on CIFAR-10, with gains of 3.8, 3.2, and 4.9 accuracy points on DTD-47, UCF-101, and ImageNet-Dogs.

What carries the argument

The load-bearing object is the modality-shared self-expressive coefficient matrix $C$: for every data point, the same weights must express the image embedding and its textual counterpart as linear combinations of the other points. In the implementation $C$ is reparameterized rather than solved directly: it is the signed Sinkhorn-Knopp projection of $Z_{\text{mix}}^\top Z_{\text{mix}}$, where $z_{\text{mix}} = (z_{\text{img}}+z_{\text{text}})/2$, with diagonal entries removed; the projection balances rows and columns of the similarity matrix and then restores the original signs. Textual counterparts themselves are produced by sparse coding each image embedding against a concept dictionary of text embeddings, so each text is a sparse combination of semantically relevant concepts. Around this object, the self-expression losses enforce cross-modal agreement on structure while the negative total coding rates $-\rho(Z_{\text{img}})-\rho(Z_{\text{text}})$ prevent collapsed solutions and push each modality toward a union of subspaces. Propositions 1-3 supply the theoretical support: shared coefficients suppress inter-class noise, optimal modality-specific representations are non-collapsed with equal singular-value profiles, and mini-batch optimization introduces an implicit regularizer $2(N-n_b)/n_b\,\|C\|_F^2$.

What would settle it

Take a dataset with captions, corrupt a fraction of the text counterparts by swapping them with captions from other classes, and measure the inter-class energy of the learned coefficients and the clustering accuracy. The theory predicts the shared least-squares coefficients suppress this added noise; if the implemented Sinkhorn-based coefficients show no suppression, or accuracy falls as fast as an image-only model, the bridge between the theorem and the implementation is broken.

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Extended reading notes

Core claim

DeepMORSE's central claim is that a single coefficient matrix shared by image and text modalities recovers the partition structure that is invariant across modalities and suppresses modality-specific noise. With fixed representations, the shared least-squares coefficients solve $\min_{c_j} \|z^j_{\text{img}}-Z^{-j}_{\text{img}}c_j\|_2^2 + \|z^j_{\text{text}}-Z^{-j}_{\text{text}}c_j\|_2^2$, and Proposition 1 shows these coefficients are closer to the true modality-invariant coefficients than either modality's own solution, with no larger expected energy on inter-class entries. The embeddings are trained so that each modality approximately occupies a union of subspaces, using negative total coding rate terms to prevent collapse, and the final clusters are obtained by spectral clustering on the image-only affinity $|Z_{\text{img}}^\top Z_{\text{img}}|$. The paper reports clustering accuracy improvements over prior multimodal methods on five of six benchmarks and shows the learned image representations transfer to retrieval and zero-shot classification without task-specific losses or post-processing.

Load-bearing premise

The load-bearing premise is that the coefficient matrix actually computed in training, a signed Sinkhorn-Knopp projection of the modality-mixed similarity, inherits the noise-suppression and structure-preservation properties that are proven only for the closed-form least-squares solution, and that clustering from the image-only affinity still reflects those shared coefficients.

Editorial extensions

If this is right

  • Textual information can improve image clustering even when raw image-text similarities are unreliable, because the shared coefficients enforce structural agreement instead of direct embedding alignment.
  • If the central claim holds, the learned image representations are reusable as-is for retrieval and zero-shot classification, so one unsupervised training phase serves several downstream tasks.
  • Mini-batch training supplies an implicit $\|C\|_F^2$ regularization, making explicit coefficient regularization unnecessary and explaining why added coefficient penalties have little effect.
  • The framework is modality-agnostic: additional modalities with a shared embedding space can be mixed into $z_{\text{mix}}$ and trained with the same loss, with modest gains or no degradation.

Reading between the lines

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

  • Editorial inference: the theory and implementation are bridged by an unproven step, because Proposition 1 analyzes the closed-form least-squares solution while training computes $C$ through a signed Sinkhorn-Knopp projection; a head-to-head comparison of the two coefficient solvers on the same learned representations would test whether the implementation inherits the noise-suppression guarantee.
  • Editorial inference: if the shared-coefficient mechanism is right, the same pretraining should also improve other intra-modal tasks hurt by unreliable pretrained vision-language geometry, such as nearest-neighbor few-shot classification, by using the learned structured image representations.
  • Editorial inference: the implicit regularization depends on batch size, so smaller batches should act as a stronger coefficient regularizer; measuring cluster purity versus batch size would give a direct, tunable test of Proposition 3.
  • Editorial inference: the union-of-subspaces geometry suggests a way to inspect clusters: each class corresponds to a low-dimensional subspace, so class structure could be probed by principal angles between subspaces rather than by centroids.
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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

3 major / 4 minor

Summary. The paper proposes DeepMORSE, a deep subspace-clustering method that uses a modality-shared self-expressive coefficient matrix to align image and text representations, while learning structured representations that form modality-specific unions of subspaces. The model is trained by minimizing a self-expressive reconstruction loss plus a negative coding-rate regularization, with coefficients reparameterized via a signed Sinkhorn-Knopp projection of the modality-mixed Gram matrix. The authors provide theoretical results on noise suppression (Proposition 1), non-collapse of representations (Proposition 2), and implicit regularization (Proposition 3), and they report extensive experiments on six image clustering benchmarks, achieving state-of-the-art accuracy on five of them, along with strong transfer to image retrieval and zero-shot classification.

Significance. If the empirical results hold, DeepMORSE is a competitive and simple method for language-assisted image clustering, with clear gains over existing multimodal baselines and useful transfer to downstream tasks. The paper is commendable for its thorough experimental protocol: multi-seed averages, ablations over components, sensitivity analyses, time comparisons, and comparisons to many modern baselines, plus publicly available code. The theoretical framework, even with the gaps noted below, offers a plausible mechanism for why sharing self-expressive coefficients across modalities helps, and the implicit-regularization analysis is insightful. A caveat is that the textual counterparts are generated from the image embeddings themselves via sparse coding, so the cross-modal benefit may partly reflect the sparse-coding prior rather than independent textual information; the ablations with MLLM-generated text partially mitigate this concern.

major comments (3)
  1. [Section III-B (Eq. 7) vs. Section III-C (Eq. 17)] The theoretical analysis in Propositions 1 and 3 studies the least-squares self-expressive subproblem (7), whose closed-form solution is given in Eq. (20), but the implemented DeepMORSE computes C as the signed Sinkhorn-Knopp projection C = P(Z_mix^T Z_mix) in Eq. (17). This is not the minimizer of the self-expressive objective, and the paper provides no proof or argument that this reparameterized C inherits the noise-suppression property of inequality (10) or the implicit regularization of Proposition 3. Since the training loss (18) uses this Sinkhorn-based C, the gradients that shape the representations are driven by coefficients whose theoretical guarantees are not established. The authors should either extend the theory to cover the Sinkhorn reparameterization or clearly state that the theoretical results apply to an idealized version of the model, relying on the empirical validation in Figure 4 for the actual method.
  2. [Supplementary Material, proof of Proposition 1 (Eq. 27)] The proof of Proposition 1 requires the cross-covariance condition E[delta_img delta_text^T] = 0 to drop the cross terms in Eq. (27), but the assumptions of Proposition 1 state only that both deviation vectors have zero mean and covariance sigma^2 I_d. Without the uncorrelatedness assumption, the error covariance of c_share includes additional terms and inequality (9) may fail. The assumption should be stated explicitly, or the proof should handle the correlated case.
  3. [Section III-C, 'Evaluation on Test Data'] The final clustering is performed by spectral clustering on the affinity |Z_img^T Z_img|, not on the learned shared self-expressive matrix C. The theoretical guarantee in Proposition 1 concerns the coefficients C, so the paper does not establish that the affinity actually used inherits the subspace-preserving or noise-suppressing properties. The authors should either use a clustering affinity derived from C (e.g., a symmetrized absolute value of C) or provide an explicit argument and experimental evidence that the inner-product affinity of the learned image representations preserves the class structure.
minor comments (4)
  1. [Supplementary Material, header] The header 'Proof for Proportion 1' should read 'Proof for Proposition 1'.
  2. [Appendix B, Table B.1] Table B.1 lists hyperparameters for STL-10 and ImageNet-10, which do not appear among the six benchmarks in Table I; please clarify or remove these rows to avoid confusion.
  3. [Section V, Conclusion] The conclusion states that DeepMORSE achieves state-of-the-art clustering performance on six benchmarks, but Table I shows it is not state-of-the-art on CIFAR-10; the wording should be 'five of six' or 'competitive on all six'.
  4. [Section III-C, Eq. (15)] The textual counterparts are generated from the image embeddings themselves via sparse coding, so the phrase 'textual information' should be qualified. The ablations in Tables II and V help, but the main narrative should acknowledge that the text modality is constructed from the image query and an external text dictionary.

Circularity Check

1 steps flagged · score 3.0 of 10

The textual counterpart is generated from the image embeddings (Eq. 15), so the 'cross-modal shared structure' is partly self-constructed; the central empirical claims remain externally benchmarked and are not fitted-parameter circularity.

  1. self definitional [Section III-C, 'Textual Counterpart Generation', Eq. (15); used in Eqs. (16)-(17)]
    "To be specific, for each image embedding x∈R^D, we seek its textual counterpart t:=∑_{i=1}^M θ_i d_i by solving the following cross-modal sparse coding problem: min_θ ∥x−∑ θ_i d_i∥_2^2, s.t. ∥θ∥_0≤s ... Note that the query comes from the image modality while the dictionary is constructed from the text modality."

    Eq. (15) defines t as the best sparse linear reconstruction of the image embedding x in the text dictionary D, so t is a deterministic function of x. Then z_text=g(t) (Eq. 16) and C=P(Z_mix^T Z_mix) with Z_mix=(Z_img+Z_text)/2 (Eq. 17) are functions of x alone. Thus the 'modality-shared' structure is not discovered from independent views: the text view is manufactured from the image view, and the dictionary D is itself k-means-selected on the image embeddings. Proposition 1's assumption of independent, equal-covariance deviations δ_img and δ_text is violated by construction, because δ_text derives from the same x as δ_img. The 'cross-modal' claim therefore reduces partly to single-modality self-expression on x with an auxiliary text-dictionary projection.

full rationale

The empirical core of DeepMORSE—clustering accuracy, retrieval mAP, and zero-shot accuracy—is evaluated against external baselines on standard benchmarks, and the reported gains are not obtained by fitting evaluation labels. The main candidate for circularity is the construction of the textual modality. The paper generates each textual counterpart t by sparse-coding the image embedding x against a text dictionary D (Eq. 15); t is therefore a deterministic function of x, and the shared coefficient matrix C used in training is a function of Z_mix=(Z_img+Z_text)/2, i.e., of x alone once the networks are fixed. This makes the 'cross-modal shared structure' substantially self-constructed, and it violates the independence assumption in Proposition 1 (δ_img and δ_text are not independent when one modality is generated from the other). This is a partial circularity in the paper's cross-modal framing, though it does not invalidate the external empirical comparisons. Separately, Proposition 1 and Proposition 3 analyze a least-squares C (Eqs. 7 and 14), while the deployed C is a signed Sinkhorn-Knopp projection (Eq. 17) and the final affinity is |Z_img^T Z_img|; this is a rigor gap rather than a circularity. The self-citation of [72] for Proposition 2 is normal and not load-bearing for the empirical results. Overall score 3.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central method relies on the union-of-subspaces assumption for CLIP features, on the construction of textual counterparts from image embeddings, and on an unproved link between the implemented Sinkhorn-based coefficients and the least-squares solutions analyzed in the theory. No new physical or conceptual entities are introduced; the key free parameters are gamma, epsilon, sparsity s, output dimension d, and batch size.

free parameters (6)
  • gamma = 150 default; 200 for Cars, 350 for SUN, 600 for ImageNet-1k
    Balances the self-expressive loss against the maximal coding rate regularizer; tuned per dataset using the approximate rule gamma ~= 0.5*d + 80.
  • epsilon^2 = 0.1
    Coding precision in the total coding rate terms; fixed across all experiments.
  • sparsity s = 5
    Number of dictionary atoms used to generate each textual counterpart via matching pursuit; fixed across all experiments.
  • output dimension d = 128, 256, 512, or 1024 depending on dataset
    Chosen larger than the number of classes to allow orthogonal class subspaces; scales gamma and training cost.
  • batch size n_b = 1024, except 8192 for ImageNet-1k
    Controls the strength of the implicit Frobenius regularization in Proposition 3 and is part of the optimization setup.
  • dictionary construction parameters k=N/300 and omega=5 = k = N/300, omega = 5
    Taken from TAC; controls how many WordNet text embeddings are selected per k-means cluster center to build the concept dictionary.
assumptions (5)
  • domain assumption Pretrained deep features lie on or near a union of low-dimensional subspaces.
    Invoked throughout the paper to justify the self-expressive model and the final affinity based on Z_img^T Z_img; supported by citations [38]-[42].
  • ad hoc to paper Textual counterparts generated via sparse coding approximately lie on a union of subspaces and share partition structure with images.
    The method constructs text from images via Eq. (15), so the independent-modality assumption is self-imposed; Proposition 1 assumes independent deviations that this construction does not guarantee.
  • ad hoc to paper The reparameterized Sinkhorn-based C in Eq. (17) inherits the properties of the closed-form least-squares solution analyzed in Propositions 1 and 3.
    Never proved; the paper switches from the subproblem solution to the Sinkhorn projection without a formal link, and the final clustering does not even use this C.
  • ad hoc to paper In Proposition 1, the modality deviations delta_img and delta_text have zero mean, equal isotropic covariance sigma^2 I, and are uncorrelated with each other.
    Zero mean and equal covariance are stated, but uncorrelatedness is not; the proof in Appendix A drops the cross terms E[delta_img delta_text^T], which vanish only under an additional unstated assumption.
  • standard math Spectral clustering on |Z_img^T Z_img| recovers class structure from near-orthogonal subspace representations.
    Standard subspace clustering inference at test time; used to produce final clusters from the learned image representations.

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Pith. "Pith review of Learning Deep Modality-Shared Self-Expressiveness for Image Clustering with Textual Information." pith.science (2026). https://pith.science/paper/G23RMF7O

@misc{pith2026260808418,
  author       = {Pith},
  title        = {Pith review of: Learning Deep Modality-Shared Self-Expressiveness for Image Clustering with Textual Information},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/G23RMF7O}},
  note         = {Machine review of arXiv:2608.08418}
}
read the original abstract

Leveraging textual information for image clustering has emerged as a promising direction, largely owing to the powerful representations learned by Vision-Language Models (VLMs). Existing approaches typically retrieve a textual counterpart for each image and then refine multimodal representations by directly enforcing cross-modal agreement, e.g., maximizing image-text similarity inherited from pretrained VLMs. However, such a strategy aligns heterogeneous representations across modalities without explicitly modeling the intrinsic structure within each modality and thus might yield unreliable alignment or distort modality-specific structures that are crucial for clustering. In this paper, we propose a simple but principled approach, termed deep modality-shared self-expressive model (DeepMORSE), which discovers cross-modal structures via a modality-shared self-expressive model and simultaneously learns structured representations that conform to a union of modality-specific subspaces. Moreover, we theoretically justify that the modality-shared self-expressive coefficients suppress inter-class noise towards a subspace-preserving solution, and show that mini-batch optimization procedure introduces an implicit regularization onto the self-expressive model. We evaluate our DeepMORSE on six widely used image clustering benchmarks and observe performance improvements exceeding 3% on the UCF-101, DTD-47, and ImageNet-Dogs datasets. In addition, we demonstrate the strong transferability of the learned representations by achieving state-of-the-art performance on downstream tasks such as image retrieval and zero-shot classification---without requiring any task-specific losses or post-processing. The code is available at: https://github.com/mengxianghan123/DeepMORSE.

Figures

Figures reproduced from arXiv: 2608.08418 by the authors.

Figure 1
Figure 1. Illustration of the basic idea of the paper. We explicitly learn structured representations that conform to a Union of Subspaces (UoS) and capture modality-shared structure for clustering. Over the past decade, deep clustering has emerged as a promising line of research which leverages the representation learning ability of deep neural networks [14], [15] and has quickly progressed following the rapid advances in re… view at source ↗
Figure 1
Figure 1. Specifically, we propose a simple but principled [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. The overview of DeepMORSE. DeepMORSE learns modality-invariant structure through modality-shared self-expression, and jointly fine-tunes the representations to conform to the union of modality-specific subspace structures. Embedding (OLE) [75] and Maximal Coding Rate Reduction ´ (MCR2 ) [76]. For both approaches, the learned representa￾tions in each class are guaranteed to reside in class-specific subspaces and thes… view at source ↗
Figures from the paper (3 more)
Figure 3
Figure 3. Figure 3: Visualization of image and text representations via PCA. we display the dimension reduction results via PCA of the learned representations for each modality on five benchmark datasets. Note that PCA preserves the global structure of the representations as it performs t…
Figure 4
Figure 4. Figure 4: Illustration of the average intra/inter-class self-expressive coeffi￾cients along with clustering accuracy. form a union of orthogonal low-dimensional subspaces, where the representations from each class are concentrated within a distinct subspace. For TAC (in rows 1 a…
Figure 6
Figure 6. Figure 6: Clustering accuracy of DeepMORSE and TAC at different training time. Red: DeepMORSE; blue: TAC. matrix to a d × d matrix. This decouples the complexity from the number of samples N and yields a time and space complexity of O(d 3 ), where typically d ≪ N. Since that the…

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.