REVIEW 3 major objections 3 minor 104 references
RPN 2: On Interdependence Function Learning Towards Unifying and Advancing CNN, RNN, GNN, and Transformer
T0 review · 3 major / 3 minor · reviewed 2026-08-12 · deepseek-v4-flash
Pith's one-line read The paper claims that CNN, RNN, GNN, and Transformer architectures differ only in their interdependence functions within one shared RPN 2 model.
desk verdict A real framework paper with a public toolkit, but the Transformer-unification claim is asserted rather than proven, and the empirical summary overreaches; worth refereeing with the equivalence proofs demanded. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The carrying object is the interdependence matrix: a typically sparse matrix $\mathbf{A}$ computed from the input batch and optional structure, applied to the data before or after transformation as $\mathbf{X}\mathbf{A}_{\xi_a}$ and $\mathbf{A}_{\xi_i}^{\top}(\cdot)$. The paper defines a library of interdependence functions—constant and identity, statistical and numerical kernels, parameterized bilinear forms, geometric grid patches (cuboid, cylinder, sphere) with packing schemes, chain-based unidirectional, bidirectional, and multi-hop functions, graph adjacency and PageRank functions, and hybrid fusions—and claims that these functions supply the locality, sequential, structural, and attention mechanisms that distinguish existing backbones. Everything else in the architecture, including data expansion and compression, parameter reconciliation, remainder, and fusion, is shared across families.
What would settle it
Take a standard transformer block with softmax attention, layer normalization, and a residual connection, and transcribe its forward pass using only functions in the paper's catalogue. If any operation requires a function outside that catalogue, or if the residual-plus-normalization interaction cannot be represented through the interdependence matrices, then the claimed unification is approximate rather than exact.
Extended reading notes
Core claim
RPN 2 retains the original RPN decomposition $g(\mathbf{x}|w) = \langle \kappa_\xi(\mathbf{x}), \psi(w)\rangle + \pi(\mathbf{x})$, but replaces the plain data expansion with a data interdependent transformation $\kappa_\xi(\mathbf{X}) = \mathbf{A}_{\xi_i}^{\top}\kappa(\mathbf{X}\mathbf{A}_{\xi_a})$, where $\mathbf{A}_{\xi_a}$ and $\mathbf{A}_{\xi_i}$ are attribute and instance interdependence matrices returned by new interdependence functions. The paper's discovery claim is that every major backbone can be written in this form, and that the distinctions among CNN, RNN, GNN, and Transformer are explained by which interdependence function is used rather than by any deeper architectural difference. It substantiates this with explicit reconstruction recipes in Section 8 for each family, a catalogue of interdependence functions including grid patches, chains with multi-hop powers and matrix inverses or exponentials, graph adjacency and PageRank, and parameterized bilinear forms, plus a hybrid construction that reproduces attention-like behavior.
Load-bearing premise
The load-bearing premise is that every layer of a real CNN, RNN, GNN, or Transformer, including nonlinearities, normalization, and skip connections, can be absorbed exactly into the RPN 2 composition with only the interdependence matrix varying.
Editorial extensions
If this is right
- Choosing the identity interdependence function for both instances and attributes recovers the original RPN and, with it, the models already unified by RPN, including probabilistic graphical models, kernel SVMs, MLPs, and KANs.
- Using grid-patch interdependence reproduces CNN-style local receptive fields; varying patch shape and packing density gives a family of convolutional variants.
- Using chain interdependence functions reproduces RNN-style sequential processing, with multi-hop powers and $(I-A)^{-1}$ or $\exp(A)$ as computationally cheaper ways to propagate information along long sequences.
- Using graph adjacency, PageRank, or hybrid bilinear-plus-graph interdependence yields GNN, GAT-like, and Transformer-like behavior, so attention can be understood as one interdependence function choice.
- New backbones can be designed by selecting or fusing interdependence functions, and the reported experiments show such RPN 2 variants matching or outperforming standard backbones on image, language, time-series, and graph tasks.
Reading between the lines
- Beyond what the paper shows, the unification claim implies a concrete architecture-search agenda: treat the interdependence function class as the search space, with shared transformation and reconciliation components fixed, and measure whether such search finds backbones that beat hand-designed CNN and Transformer baselines.
- The chain and graph functions that sum powers of an adjacency-like matrix connect RPN 2 to graph-diffusion and PageRank ideas; learning the hop weights instead of fixing them would be a natural next step the paper motivates but does not implement.
- A shared RPN 2 model with per-modality interdependence functions could serve as a multimodal backbone without modality-specific heads; the paper discusses multimodal data but evaluates datasets one modality at a time.
- The paper's exact-equality claim should be tested by reimplementing a standard transformer as RPN 2 and checking forward-pass equality up to floating-point precision; until that check is run, the statement that these backbones differ only in interdependence function is a representation claim rather than a verified equivalence.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. This paper introduces RPN 2, an extension of the Reconciled Polynomial Network. The model represents a function as g(x|w) = ⟨κξ(x), ψ(w)⟩ + π(x), where κξ composes a data transformation κ with new attribute- and instance-level interdependence functions ξ that produce interdependence matrices applied to the input batch. The paper claims that this canonical form unifies CNN, RNN, GNN, and Transformer backbones and that the differences among these backbones primarily stem from how interdependence functions are defined. It also contributes a large catalog of interdependence functions, data compression and fusion functions, complexity estimates, a software toolkit update, and experiments on image, language, time-series, and graph benchmarks.
Significance. If the exact unification claim held, this would be a valuable conceptual contribution with practical implications for architecture design, and the open-source TINY BIG v0.2.0 toolkit is a concrete asset. The taxonomy of interdependence functions and the constructive matrix mappings for grid, chain, and graph structures are presented in a clear and useful way. However, the Transformer equivalence is asserted rather than demonstrated in the reviewed text, and the empirical evidence needed to support the performance claims is not present in the material provided. The central advertised novelty is therefore not yet established.
major comments (3)
- [Section 8.4, Eq. (28)] The unification of Transformers is asserted but not demonstrated. A standard Transformer encoder combines multi-head scaled dot-product softmax attention, per-head value and output projections, residual connections, and layer normalization. The RPN 2 form in Eq. (28) contains an interdependence matrix ξ, a transformation κ, a parameter reconciliation ψ, and a remainder π, but no exact derivation is given that rewrites the full Transformer forward pass in this form without placing the softmax nonlinearity and row normalization inside an opaque ξ and without changing κ and π per backbone. If softmax is absorbed into ξ, then ξ is no longer merely an interdependence matrix, and the claim that backbones differ primarily in their interdependence functions needs a precise and formal statement. Section 8.4 must provide explicit equivalence statements for all components of the Transformer encoder, or the central claim must be weakened.
- [Section 8, Eq. (24)] The claim that 'the fundamental distinctions among these backbone models primarily stem from their diverse approaches to defining the interdependence functions' requires that the other components of the canonical form be held fixed or shown to be common. The paper does not establish this. The constructive mappings for CNN, RNN, and GNN use backbone-specific ingredients beyond ξ: patch geometry and compression for CNNs, temporal sharing and remainder terms for RNNs, and graph adjacency plus normalization for GNNs. If κ, ψ, or π vary between backbones, the distinctions are not primarily due to interdependence functions alone. A formal statement of what is fixed across backbones and what is allowed to vary is needed before the advertised conceptual conclusion is supported.
- [Section 9 and Abstract] The empirical claims in the abstract and introduction cannot be verified from the reviewed text. The abstract says RPN 2 'significantly outperforms' the previous RPN and that RPN 2-based models 'enhance existing backbones,' while Section 1 says RPN 2 'achieves performance comparable to leading models like CNNs, RNNs, and GCNs.' The reviewed portions do not include the experimental setup, result tables, baselines, standard deviations, or ablations needed to assess either claim. These materials must be included, and the apparent inconsistency between 'significantly outperforms' and 'comparable' should be resolved.
minor comments (3)
- [Section 4.2] There is a grammatical error near the end of the section: 'the codomain dimensions m′ and b′ must are explicitly specified' should read 'must be explicitly specified.'
- [Figure 19] Entries 7 and 8 in the data expansion list are both labeled 'Lucas Expansion'; one of them appears to be mislabeled and should be corrected.
- [Eq. (30)] The notation in Eq. (30) for the multi-head and multi-channel fusion is difficult to parse because the head and channel indices H, C are introduced without a fully explicit indexing convention; a cleaner definition of the fusion argument would improve readability.
Circularity Check
Central unification claim is partly self-definitional: RPN 2 is defined with a free interdependence function xi, and backbones are instantiated by choosing xi, so the 'finding' that backbones differ in xi is to some extent built into the template; Transformer/GAT equivalences are announced with 'akin to' rather than proven, and the empirical benchmarking is independent.
-
self definitional
[Abstract; Section 4.2, Eq. (26)-(27)]
"Our analysis reveals that the fundamental distinctions among these backbone models primarily stem from their diverse approaches to defining the interdependence functions. ... kappa_xi(X) = A_xi_i^top kappa(X A_xi_a) in R^{b' x D} ... A_xi_a = xi_a(X) in R^{m x m'}, and A_xi_i = xi_i(X) in R^{b x b'}."
The canonical RPN 2 form is a template in which the interdependence function xi is free to absorb all inter-instance/attribute structure. Each backbone is 'unified' by selecting a different xi (grid, chain, graph, bilinear/attention matrix). Therefore the conclusion that backbones differ primarily in xi is entailed by the way the representation was filled in: any operation expressible as X times a matrix produced from X can be put into xi. The paper does not derive from independent definitions of CNN/RNN/GNN/Transformer that their differences must reduce to xi; it assigns each a xi and then reads the distinction back out.
-
renaming known result
[Section 5.1.7 and Section 5.3.2; announced Section 8.4]
"To illustrate, we present the bilinear interdependence function with low-rank parameter reconciliation, which will also be used to construct the Transformer model with the RPN 2 model architecture. ... this hybrid interdependence function endows the RPN 2 model with capabilities akin to those of the Graph Attention Network (GAT) [76], which uses a linear attention mechanism, and Graph-BERT [91], which utilizes a transformer-based attention mechanism."
Self-attention and graph attention are re-expressed as a 'parameterized bilinear' or 'hybrid graph' interdependence matrix. The 'unification' then consists of renaming the attention-score matrix as an interdependence function and placing it in xi. The paper itself says 'akin to', not 'equal to', so the exact reduction of Transformer/GAT to the canonical form is not demonstrated; the claimed insight is carried by the naming/placement of xi rather than by a derivation from the backbones' own definitions.
full rationale
The paper is not a pure exercise in circularity: RPN 2's architecture, the new interdependence functions, and the benchmark experiments stand on their own, and the identity-interdependence reduction to RPN is a genuine containment result. The circular flavor is concentrated in the advertised unification claim. Because RPN 2's definition (Eq. 24-28) gives xi the role of the variable that changes across instantiations, saying that CNN/RNN/GNN/Transformer 'primarily differ in their interdependence functions' is largely a restatement of how the author chose to instantiate the template, especially when the Transformer/attention mappings are sketched ('will be used to construct', 'akin to') rather than proved as exact equivalences. This is a partial, construction-level circularity affecting the paper's headline conceptual contribution, but it does not invalidate the empirical comparisons, which are external benchmarks with fitted models. Hence score 4 rather than 8-10.
Assumptions & free parameters
free parameters (4)
- Patch packing hyperparameters (ph, pw, pd, dh, dw, dd)
- Low-rank rank r for bilinear interdependence
- PageRank damping factor alpha =
0.15 (default)
- Kernel bandwidth sigma for RBF and Laplacian kernels
assumptions (4)
- standard math Taylor's theorem justifies decomposing any sufficiently smooth function into an expansion and a remainder.
- domain assumption Data interdependence can be fully captured by multiplying the data batch by pairwise interdependence matrices.
- domain assumption Standard CNN, RNN, GNN, and Transformer operations can be represented exactly as a composition of an interdependence function, a transformation, and a remainder in RPN 2.
- ad hoc to paper The primary distinction between backbones is their interdependence function.
invented entities (2)
-
Data interdependence function (xi)
-
Interdependence matrix
Cite this review
Pith. "Pith review of RPN 2: On Interdependence Function Learning Towards Unifying and Advancing CNN, RNN, GNN, and Transformer." pith.science (2026). https://pith.science/paper/MJMSGUIW
@misc{pith2026241111162,
author = {Pith},
title = {Pith review of: RPN 2: On Interdependence Function Learning Towards Unifying and Advancing CNN, RNN, GNN, and Transformer},
year = {2026},
howpublished = {\url{https://pith.science/paper/MJMSGUIW}},
note = {Machine review of arXiv:2411.11162}
}
read the original abstract
This paper builds upon our previous work on the Reconciled Polynomial Network (RPN). The original RPN model was designed under the assumption of input data independence, presuming the independence among both individual instances within data batches and attributes in each data instance. However, this assumption often proves invalid for function learning tasks involving complex, interdependent data such as language, images, time series, and graphs. Ignoring such data interdependence may inevitably lead to significant performance degradation. To overcome these limitations, we introduce the new Reconciled Polynomial Network (version 2), namely RPN 2, in this paper. By incorporating data and structural interdependence functions, RPN 2 explicitly models data interdependence via new component functions in its architecture. This enhancement not only significantly improves RPN 2's learning performance but also substantially expands its unifying potential, enabling it to encompass a broader range of contemporary dominant backbone models within its canonical representation. These backbones include, but are not limited to, convolutional neural networks (CNNs), recurrent neural networks (RNNs), graph neural networks (GNNs), and Transformers. Our analysis reveals that the fundamental distinctions among these backbone models primarily stem from their diverse approaches to defining the interdependence functions. Furthermore, this unified representation opens up new opportunities for designing innovative architectures with the potential to surpass the performance of these dominant backbones.
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Created in BioRender. Zhang, J. (2024) BioRender.com/f39x623
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2024
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Confirmation
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2024
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Created in BioRender. Zhang, J. (2024) BioRender.com/j80y259
All Completed Graphics to be published in any publication (journals, textbooks, websites, etc.) must be accompanied by the following citation either as a caption, footnote or reference for each figure that includes a Completed Graphic: "Created in BioRender. Zhang, J. (2024) B...
2024
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[108]
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publish their Completed Graphics created in the BioRender Services containing both User Content and BioRender Content (as both are defined in the License Terms) in publications (journals, textbooks, websites, etc.); and
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sublicense such Completed Graphics under “open access” publication sublicensing models such as CC-BY 4.0 and more restrictive models, so long as the conditions set forth herein are fully met. Requirements of User:
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Created in BioRender. Zhang, J. (2024) BioRender.com/v74r180
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[112]
All terms of the License Terms including all Prohibited Uses are fully complied with. E.g. For Academic License Users, no commercial uses (beyond publication in journals, textbooks or websites) are permitted without obtaining or switching to a BioRender Industry Plan
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