Pith. sign in

REVIEW 2 major objections 1 minor 15 references

Belief2-Attention extends standard attention by retaining and processing the projected value component alongside the perpendicular residual while adding a ZZ^T matrix to capture richer token correlations.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.3

2026-06-30 16:01 UTC pith:XDHKKTKG

load-bearing objection This is a small follow-up tweak to the author's own prior Belief-Attention that reuses the projected component and adds ZZ^T, but the abstract supplies no equations or numbers so the gains remain uncheckable. the 2 major comments →

arxiv 2606.00077 v1 pith:XDHKKTKG submitted 2026-05-22 cs.CV cs.AI

Improved Belief-Attention in Vision Task

Guoqiang Zhang This is my paper
classification cs.CV cs.AI
keywords Belief-Attentionattention mechanismtransformerimage classificationimage segmentationtoken correlationorthogonal projection
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper conducts an ablation study to show that the projected component after orthogonal projection of the weighted value vectors holds non-redundant information on token correlations. It proposes Belief2-Attention, which routes this projected component through an activation and linear mapping before merging, and augments the standard QK^T attention matrix with an extra ZZ^T matrix. This yields a module that is strictly more expressive than standard attention. Effectiveness is then demonstrated through experiments on image classification and segmentation tasks.

Core claim

By making use of both the perpendicular and projected components of the orthogonal projection of the softmax-weighted summation of V vectors, with the projected component passed through an activation function and linear mapping, and by introducing an additional inner-product matrix ZZ^T to the standard QK^T, Belief2-Attention captures richer token correlation information and is more expressive than standard attention.

What carries the argument

The Belief2-Attention module, which merges the perpendicular residual with a processed projected component and augments the attention matrix with ZZ^T.

Load-bearing premise

The projected component after orthogonal projection carries non-redundant information about token correlations that improves performance when retained and processed separately.

What would settle it

A controlled experiment on standard image classification or segmentation benchmarks in which Belief2-Attention achieves no accuracy improvement over standard attention would falsify the claim of greater effectiveness.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Belief2-Attention is more expressive than standard attention.
  • It improves accuracy on image classification tasks.
  • It improves accuracy on image segmentation tasks.
  • The projected component should be retained rather than discarded because it holds useful correlation information.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Attention designs in general could benefit from separately processing the components of an orthogonal decomposition of value vectors.
  • The two-layer FFN interpretation of the projected path suggests possible further extensions by varying the activation or depth of that sub-block.
  • The interaction between the added ZZ^T matrix and the original QK^T matrix may warrant explicit analysis in follow-up work.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The manuscript proposes Belief2-Attention as an extension of the authors' prior Belief-Attention. An ablation study is said to show that the projected component of the orthogonal projection of the softmax-weighted V carries non-redundant token-correlation information. This component is routed through an activation and linear map (framed as an internal two-layer FFN), and an additional ZZ^T term is added to the standard QK^T matrix. The authors state that Belief2-Attention is more expressive than standard attention and report verification on image classification and segmentation tasks.

Significance. If the ablation result generalizes and the expressivity claim can be made rigorous, the work would supply a concrete mechanism for retaining additional correlation information inside the attention block, potentially improving vision-transformer performance in a principled way. The internal-FFN framing of the projected-component path is a clear conceptual contribution that could be reused in other attention variants.

major comments (2)
  1. [Abstract] Abstract: the claim that 'It can be easily shown that Belief2-Attention is more expressive than standard Attention' is asserted without any derivation, equation, or explicit comparison to the baseline attention mechanism. Because this is the central theoretical justification for the architectural change, the absence of the argument is load-bearing.
  2. [Abstract] Abstract (ablation-study paragraph): the motivation for processing the projected component through the extra activation+linear block (and for introducing ZZ^T) rests entirely on an ablation whose quantitative results, models, datasets, and error bars are not supplied. If that observation is specific to the tested settings, the justification for the new routing and the expressivity claim collapses.
minor comments (1)
  1. [Abstract] The manuscript would benefit from a one-paragraph recap of the original Belief-Attention construction so that the extension can be evaluated without immediate reference to the cited prior work.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on the abstract. We address each major comment below and will revise the manuscript to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'It can be easily shown that Belief2-Attention is more expressive than standard Attention' is asserted without any derivation, equation, or explicit comparison to the baseline attention mechanism. Because this is the central theoretical justification for the architectural change, the absence of the argument is load-bearing.

    Authors: We agree the expressivity claim in the abstract requires explicit support. In the revision we will add a concise derivation or side-by-side comparison (in the abstract or a new short paragraph in Section 2) showing that the combination of the processed projected component and the additional ZZ^T term strictly enlarges the set of representable token-correlation functions relative to standard QK^T attention. revision: yes

  2. Referee: [Abstract] Abstract (ablation-study paragraph): the motivation for processing the projected component through the extra activation+linear block (and for introducing ZZ^T) rests entirely on an ablation whose quantitative results, models, datasets, and error bars are not supplied. If that observation is specific to the tested settings, the justification for the new routing and the expressivity claim collapses.

    Authors: The ablation demonstrating non-redundant information in the projected component is reported with concrete models, datasets, and metrics in the main experimental section. To address the concern about the abstract, we will insert a one-sentence summary of the key quantitative finding (including error bars) into the abstract paragraph and ensure all ablation details are clearly referenced. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on new ablation and task verification

full rationale

The paper cites prior self-authored work only to describe the base Belief-Attention mechanism, then introduces an independent ablation study on the projected component to motivate retaining it via an extra processing block. Belief2-Attention is defined by this extension plus the ZZ^T augmentation, with the expressivity observation following directly from the added term rather than any fitted parameter or unverified self-citation chain. Effectiveness claims rest on new experiments for classification and segmentation, providing external empirical content independent of the cited base. No load-bearing step reduces a claimed result to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. The construction appears to rest on standard linear-algebra facts about orthogonal decomposition and on the empirical claim that the projected component is informative.

axioms (1)
  • domain assumption The inner-product matrices QK^T and ZZ^T together capture richer token correlations than QK^T alone.
    Invoked when the authors state that adding ZZ^T captures richer correlation; no derivation is supplied in the abstract.

pith-pipeline@v0.9.1-grok · 5743 in / 1338 out tokens · 36209 ms · 2026-06-30T16:01:22.722851+00:00 · methodology

0 comments
read the original abstract

Recently, Belief-Attention \cite{Guoqiang25BeliefAttention} has been proposed by first performing an orthogonal projection of the softmax-based weighted summation of $V$ vectors with respect to the original $V$ vectors and then taking the perpendicular component as the residual signal in Transformer for performance improvement. In this paper, we first conduct an ablation study showing the projected component also carries information about the token correlation, which should not be ignored. We then propose to extend Belief-Attention by making use of both the perpendicular and projected components. In particular, the projected component goes through certain activation function and then a linear mapping before merging with the considered token. Conceptually speaking, the neural block for the projected component can be viewed as a two-layer feedforward network (FFN) within the new attention block. It is also noted that standard attention captures the token correlation via the inner-product matrix $QK^T$. We propose to introduce an additional inner-product matrix $ZZ^T$ to $QK^T$ to capture richer token correlation. We refer to the new module as Belief2-Attention. It can be easily shown that Belief2-Attention is more expressive than standard Attention. We then verify the effectiveness of Belief2-Attention for vision tasks of image classification and segmentation.

Figures

Figures reproduced from arXiv: 2606.00077 by Guoqiang Zhang.

Figure 2
Figure 2. Figure 2: Demonstration of Belief2-Attention, where MH refers to “multi-head attention". The two-layer FFN consists of two linear mappings, one for computing V from X and the other one for post￾processing φ(α ⊙ V ) where φ(·) is an (element-wise) activation function. an orthogonal projection of the softmax-based weighted summation of V vectors onto the original V vectors and then taking the perpendicular component a… view at source ↗
Figure 3
Figure 3. Figure 3: Impact of different residual signals in the attention layers of a Transformer being trained over CIFAR100 for image classification. The curve for weighted summation of V vectors is in fact the performance of the standard Attention layer. The first open-source in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Performance comparison for image segmentation over the ADE20K dataset. 4 Experimental Results We evaluated Belief2-Attention for three vision tasks: (1) image segmentation over the ADE20K dataset2 ; (2) image classification over ImageNet; (3) image classification over CIFAR100. All the experiments were conducted on a computer with a single Nvidia Geforce A6000 GPU with 48GB memory. For the 2nd and 3rd task… view at source ↗
Figure 5
Figure 5. Figure 5: Performance comparison for image classification over ImageNet of 1000 classes. 4.2 Image classification over ImageNet In this experiment, we adjusted the Vision Transformer model from the opensource3 for the image classification purpose over ImageNet. The original open-source is for training a diffusion model for image generation. The selected model type for our experiment is JiT-B/16. We replaced each sta… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages · 5 internal anchors

  1. [1]

    https://pytorch.org/docs/stable/generated/torch.nn

    Pytorch implimentation of multi-head attention. https://pytorch.org/docs/stable/generated/torch.nn. 2023

    work page 2023

  2. [3]

    Longformer: The Long-Document Transformer

    I. Beltagy, M. E. Peters, and A. Cohan. Longformer: The lo ng-document transformer. arXiv:2004.05150v2, 2020

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  3. [4]

    T. Dao. Flashattention-2: Faster attention with better parallelism and work partitioning. arXiv preprint arXiv:2307.08691, 2023

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  4. [5]

    Dosovitskiy, L

    A. Dosovitskiy, L. Beyer, A. Kolesnikov, D. Weissenborn a, X. Zhai, T. Unterthiner, M. De- hghani, M. Minderer, G. Heigold, S. G. abd J. Uszkoreit, and N . Houlsby. An image is worth 16x16 words: Transformers for image recognition at scale. I n ICLR, 2021

    work page 2021

  5. [6]

    Hatamizadeh, J

    A. Hatamizadeh, J. Song, G. Liu, J. Kautz, and A. V ahdat. D iffiT: Diffusion Vision Transform- ers for Image Generation. In ECCV, 2024

    work page 2024

  6. [7]

    Kitaev, A

    N. Kitaev, A. Kaiser, and A. Levskaya. Reformer: The Effic ient Transformer. In ICLR, 2020

    work page 2020

  7. [8]

    Latif, A

    S. Latif, A. Zaidi, H. C. AZ, F. Shamshad, M. Shoukat, and J . Qadir. Transformers in speech processing: A survey. arXiv:2303.11607 [cs.CL], 2023

    work page arXiv 2023

  8. [10]

    Peebles and S

    W . Peebles and S. Xie. Scalable Diffusion Models with Tr ansformers. In ICCV, 2023

    work page 2023

  9. [11]

    A. Sun, W . Zhao, X. Han, C. Y ang, Z. Liu, C. Shi, and M. Sun. Burstattention: An efficient dis- tributed attention framework for extremely long sequences . arXiv:2403.09347 [cs.DC], 2023

    work page arXiv 2023

  10. [12]

    Llama 2: Open Foundation and Fine-Tuned Chat Models

    H. Touvron, L. Martin, P . A. K. Stone, A. Almahairi, Y . Babaei, N. Bashlykov, S. Batra, P . Bhar- gava, S. Bhosale, D. Bikel, L. Blecher, C. C. Ferrer, M. Chen,G. Cucurull, D. Esiobu, J. Fernan- des, J. Fu, W . Fu, B. Fuller, C. Gao, V . Goswami, N. Goyal, A. Hartshorn, S. Hosseini, R. Hou, H. Inan, M. Kardas, V . Kerkez, M. Khabsa, I. Kloumann, A. Kore...

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  11. [13]

    Attention Is All You Need

    A. V aswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and I. Polo- sukhin. Attention is all you need. arXiv:1706.03762 [cs. CL ], 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  12. [14]

    S. Wang, M. K. B. Z. Li, H. Fang, and H. Ma. Linformer: Self -attention with linear complexity. arXiv:2006.04768v3, 2020

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  13. [15]

    S. Zhai. Exclusive self attention. arXiv:2603.09078 [ cs.LG]

    work page arXiv

  14. [16]

    G. Zhang. Beliefformer: Belief-attention in transfor mer. https://openreview.net/forum?id=Ard2QzP AUK, 2025

    work page 2025

  15. [17]

    Zhang, J

    G. Zhang, J. P . Lewis, and W . B. Kleijn. Exact diffusion i nversion via bidirectional integration approximation. arXiv:2307.10829 [cs.CV], 2023. 10 CIFAR10 & CIFAR100 https://github.com/aanna0701/SPT_LSA_ViT Image segmentation https://github.com/rstrudel/segmenter Table 5: list of open-source repositories expoited in this paper. 11

    work page arXiv 2023