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REVIEW 3 major objections 6 minor 68 references

GG-SSMs: Graph-Generating State Space Models

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read GG-SSMs replace fixed scanning paths with a dynamically built minimum spanning tree and claim state-of-the-art results across vision and time-series tasks in linear time.

desk verdict A novel MST-based scan idea undermined by a forward pass that doesn't match its own equation, a bogus O(L) claim, and misleading bolded results — needs major revision, not a desk reject. read the letter →

arxiv 2412.12423 v2 pith:WU6DHNZT submitted 2024-12-17 cs.LG

Nikola Zubić , Davide Scaramuzza This is my paper · ORCID
classification cs.LG
keywords statespacemodelsminimumspanningtreeChazelle'salgorithmdynamicgraphconstructionvisualtimeseriesforecastingopticalflowevent-basedeyetracking
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 introduces Graph-Generating State Space Models (GG-SSMs), which replace the fixed one-dimensional scanning paths used by models like Mamba and VMamba with a graph whose edges are chosen dynamically from the input features. For each layer, the model builds a minimum spanning tree over the feature embeddings using Chazelle's near-linear-time MST algorithm, then propagates state updates along the edges of that tree. This lets the model adapt its information flow to the data's intrinsic structure instead of forcing a handcrafted raster order. The authors report state-of-the-art results on all 11 datasets tested: 84.9% top-1 ImageNet accuracy, 2.77% Fl-all error on KITTI-15 optical flow after finetuning, improved pupil-detection rates on event-based eye tracking, and better forecasting error on six time-series benchmarks, all in linear O(L) time.

What carries the argument

The central object is the minimum spanning tree (MST) built over feature embeddings, with edge weights defined by cosine dissimilarity. Because an MST has exactly one path between any two nodes, it fixes a unique propagation route for each pair; the hidden state at node $i$ is the sum over all $j$ of the ordered product of transition matrices along that path, applied to the projected input. The paper uses Chazelle's MST algorithm to obtain the tree in near-linear time (with an inverse-Ackermann factor), and claims that leaf-to-root forward and root-to-leaf backward traversals implement this aggregation in $O(L)$.

What would settle it

Take a small tree (for example, $L=4$ nodes) with fixed transition matrices, implement both the explicit sum in Eq. (4) and the described leaf-to-root/root-to-leaf traversal, and compare the hidden states; if they differ at any node, the implementation does not match the definition, and the reported results cannot be attributed to the stated model. A controlled reimplementation of the ImageNet experiment with the same hyperparameters would check whether the 84.9% top-1 accuracy reproduces.

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Extended reading notes

Core claim

The central claim is that dynamic, data-dependent graph generation is a better scanning strategy than any fixed path. Given a set of L feature embeddings (pixels, tokens, or variates), GG-SSM treats them as vertices of a complete graph with edge weights given by cosine dissimilarity, computes the minimum spanning tree, and defines the hidden state at each node as a sum over all nodes of the product of state-transition matrices along the unique tree path, times the projected input. The tree's L−1 edges and unique paths make the propagation sparse and, the paper argues, computable in linear time; each layer builds a fresh tree, so the structure adapts per layer and per input. On the strength of this design, the paper reports state-of-the-art numbers across eleven datasets spanning image classification, optical flow, event-based eye tracking, and multivariate time-series forecasting.

Load-bearing premise

The claimed linear-time results depend on the assumption that a single leaf-to-root forward pass and root-to-leaf backward pass computes the all-pairs path-product aggregation defined in Eq. (4); the paper provides no explicit algorithm or experiment showing that these two computations coincide.

Editorial extensions

If this is right

  • If the reported numbers hold, GG-SSM would be the first single architecture to beat both transformer-based and prior SSM baselines across image classification, optical flow, and time-series forecasting.
  • The dynamic MST construction means the model's receptive field is decided by feature similarity rather than grid geometry, so it should transfer to irregular data such as event streams without task-specific scanning heuristics.
  • The claimed O(L) complexity with exactly L−1 edges makes the approach scalable to high-resolution inputs, with the ablation showing Chazelle's MST gives near-identical accuracy to Kruskal's or Prim's but lower runtime.
  • On optical flow, the reported 2.77% KITTI-15 Fl-all after finetuning would be a substantial improvement over the previous best multi-frame method (3.65%).

Reading between the lines

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

  • The tree propagates information along a single path per pair, so the effective receptive field is the tree diameter; one could test whether shallower trees (e.g., low-diameter spanning trees or adding a few short-cut edges) change the accuracy-efficiency trade-off.
  • If the leaf-to-root/root-to-leaf traversal does not exactly compute Eq. (4), the reported results may reflect a different, weaker aggregation; a direct check would be to compare the forward pass against the explicit all-pairs sum on small L.
  • The same graph-generation idea could be applied to other architectures that rely on a fixed ordering, such as recurrent networks or linear-attention variants, suggesting the principle is not specific to SSMs.
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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 / 6 minor

Summary. This paper proposes GG-SSM, a state space model that replaces fixed 1D scanning with a dynamically generated minimum spanning tree (MST) computed over token/pixel feature embeddings. The hidden state at a node is defined via path products of transition matrices over the tree, and the authors claim an O(L) forward/backward pass using Chazelle's MST algorithm. Experiments cover event-based eye tracking, ImageNet classification, optical flow, and six time-series datasets, reporting state-of-the-art numbers (84.9% ImageNet top-1, 2.77% KITTI-15 Fl-all, and superior forecasting results). The paper also includes an ablation of MST construction algorithms.

Significance. If the method and complexity analysis were correct, the work would offer a novel way to inject adaptive, data-dependent scanning into SSMs, backed by a broad benchmark evaluation. The main strengths are the wide experimental coverage and the MST-algorithm ablation. However, the manuscript currently lacks a precise algorithm for the state propagation, contradicts its own complexity model by starting from a fully connected graph, and contains internally inconsistent table formatting that overstates the forecasting results. These issues must be resolved before the SOTA claims can be assessed.

major comments (3)
  1. [Sec. 3.2.2 (Eq. (4)) and Sec. 3.3] Equation (4) defines h_i as a sum over all nodes v_j of path products S_ji Bbar_j x_j. The forward pass described in Section 3.3 is only a leaf-to-root aggregation, in which each node aggregates states from child nodes and updates its hidden state. In a rooted tree, such a pass provides node i with contributions only from its own subtree; contributions from ancestors and from sibling subtrees are not included unless a subsequent root-to-leaf state pass is performed. The paper mentions a root-to-leaf traversal only for the backward pass ('gradients are propagated from the root back down to the leaves'), not for hidden states. No derivation, pseudocode, or experiment shows that the described leaf-to-root pass computes Eq. (4) for all L nodes in O(L) time. Consequently, the relation between the model definition and the implemented forward pass is unresolved, and the reported SOTA numbers cannot be tied to the stated model.
  2. [Sec. 3.2.1 and Sec. 3.3] The paper defines a fully connected undirected graph G=(V,E) with edge weights computed for every pair (Eq. (2)), so E = O(L^2). It then invokes Chazelle's MST algorithm, whose complexity is O(E alpha(E,V)), to obtain the MST. The claim in Section 3.3 that 'MST construction itself runs in O(L) for sparse graphs where E = O(L)' does not apply to the described construction, because the input graph is dense, not sparse. No approximate-MST or sparsification procedure is described, and no runtime scaling experiment is given to support the overall O(L) claim. Since the advertised efficiency advantage over transformers depends on the O(L) claim, this is a load-bearing inconsistency.
  3. [Table 4] Several cells are bolded as 'best' even though a competitor has a strictly lower error. For instance, on Exchange horizon 96, GG-SSM's MSE 0.0878 and MAE 0.2073 are bolded while S-Mamba and iTransformer report 0.0860 and 0.2070; on horizon 192, GG-SSM's MSE 0.1813 is bolded while S-Mamba (0.1770) and PatchTST (0.1760) are better. This contradicts the caption and the text's assertion that GG-SSM 'consistently achieves the best accuracy.' The table and any claim based on it must be corrected before the forecasting results can be interpreted.
minor comments (6)
  1. [Table 1] The row for GG-SSM reads '89.3389.8999.50' without separators; it should read '89.33, 98.89, 99.50.'
  2. [Tables 5 and 7] Both tables state that the best results are bold and the second-best are underlined, but no underlined entries appear; either add the underlining or revise the captions.
  3. [Supplementary Section 8.1] The description of Chazelle's algorithm says 'with high probability, only a small fraction of edges require re-checking'; Chazelle's MST algorithm is deterministic, so this probabilistic language should be corrected.
  4. [Section 4.4] The optical-flow metrics are written inconsistently as 'Fl-epe' and 'Fl-all'; please standardize the notation (e.g., 'F1-epe' and 'F1-all').
  5. [Section 4.1] The dataset name appears as both 'INI-30' and 'Ini-30' in the text and tables; please use one consistent spelling.
  6. [Section 3.2.1] Equation (2) defines edge weights as exp(-cosine similarity), which is not 'cosine dissimilarity' in the usual sense; please state the intended dissimilarity measure explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: GG-SSMs are validated against external benchmarks and their design choices are not derived from the reported results.

full rationale

The paper's central claims are empirical benchmark outcomes (ImageNet top-1 accuracy, KITTI-15 Fl-all error, time-series MSE) obtained by training on public datasets; none of these targets is used to define the model or to fit the reported constants. The graph construction in Eq. (2) uses input features, but that is the model's mechanism rather than a reduction of the output to the input. Chazelle's MST algorithm is cited from an external J. ACM source, and the ablation in Table 8 shows that the choice among MST algorithms has almost no effect on accuracy, so the algorithmic claim is not enforced by a self-citation. The paper does cite prior work by the authors (refs. [45], [67], [68], [69]), but only as background on SSMs, event-based representations, and sequence modeling; none of these citations is load-bearing for the GG-SSM derivation or the reported state-of-the-art results. The most substantive concern is a potential mismatch between the all-pairs path-product hidden state in Eq. (4) and the described leaf-to-root forward pass in Section 3.3; however, that is a correctness/completeness issue about whether the implementation matches the stated definition, not a circularity in which a prediction is equivalent to its inputs by construction. Accordingly, no circular step can be exhibited, and the score is 0.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The central claim relies on the unverified equivalence between the defining all-pairs path-sum equation and the described single-pass implementation, plus an incorrect complexity claim for dense graphs. These are structural assumptions the paper does not justify.

free parameters (1)
  • Root node of the MST
    The direction of state propagation in Section 3.3 depends on a chosen root, but the paper does not specify how the root is selected. The hidden state definitions in Eq. (4) are root-independent, while the described leaf-to-root pass is not.
assumptions (3)
  • ad hoc to paper The leaf-to-root state aggregation in Section 3.3 exactly computes the all-pairs path-sum hidden state defined in Eq. (4).
    No derivation or algorithm is supplied showing equivalence; the two descriptions use different information flow.
  • domain assumption A minimum spanning tree can be constructed from the fully connected feature graph in O(L) time.
    Section 3.3 claims O(L) because Chazelle's MST is near-linear, ignoring that E equals O(L squared) for a complete graph; reading the edges is already quadratic.
  • domain assumption Chazelle's MST algorithm is implemented correctly in CUDA and returns the true MST.
    The algorithm is theoretically complex and no implementation details or correctness tests are provided.

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Cite this review

Pith. "Pith review of GG-SSMs: Graph-Generating State Space Models." pith.science (2026). https://pith.science/paper/WU6DHNZT

@misc{pith2026241212423,
  author       = {Pith},
  title        = {Pith review of: GG-SSMs: Graph-Generating State Space Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WU6DHNZT}},
  note         = {Machine review of arXiv:2412.12423}
}
read the original abstract

State Space Models (SSMs) are powerful tools for modeling sequential data in computer vision and time series analysis domains. However, traditional SSMs are limited by fixed, one-dimensional sequential processing, which restricts their ability to model non-local interactions in high-dimensional data. While methods like Mamba and VMamba introduce selective and flexible scanning strategies, they rely on predetermined paths, which fails to efficiently capture complex dependencies. We introduce Graph-Generating State Space Models (GG-SSMs), a novel framework that overcomes these limitations by dynamically constructing graphs based on feature relationships. Using Chazelle's Minimum Spanning Tree algorithm, GG-SSMs adapt to the inherent data structure, enabling robust feature propagation across dynamically generated graphs and efficiently modeling complex dependencies. We validate GG-SSMs on 11 diverse datasets, including event-based eye-tracking, ImageNet classification, optical flow estimation, and six time series datasets. GG-SSMs achieve state-of-the-art performance across all tasks, surpassing existing methods by significant margins. Specifically, GG-SSM attains a top-1 accuracy of 84.9% on ImageNet, outperforming prior SSMs by 1%, reducing the KITTI-15 error rate to 2.77%, and improving eye-tracking detection rates by up to 0.33% with fewer parameters. These results demonstrate that dynamic scanning based on feature relationships significantly improves SSMs' representational power and efficiency, offering a versatile tool for various applications in computer vision and beyond.

Figures

Figures reproduced from arXiv: 2412.12423 by the authors.

Figure 1
Figure 1. Illustration of the Graph-Generating State Space Model (GG-SSM). Given an input feature set {xi} L i=1, we con￾struct a graph based on feature dissimilarities and apply an effi￾cient algorithm to generate a minimum spanning tree T . SSM state propagation is then performed along this tree to obtain im￾proved feature representations. dependencies is crucial for understanding intricate struc￾tures and relationships wit… view at source ↗
Figure 2
Figure 2. Chazelle’s MST Overview. Soft heaps allow near￾linear sorting of edges. MST edges (in blue) form a spanning structure with no cycles, connecting all vertices using the small￾est weights w. 8.1. Core Idea and Time Complexity Chazelle’s MST algorithm belongs to the family of soft heap approaches. Its most prominent feature is achieving a runtime of O(E α(E, V )), where • V is the number of vertices in the graph, • E i… view at source ↗

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.