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arxiv: 2605.23410 · v1 · pith:QRK7HZICnew · submitted 2026-05-22 · 💻 cs.LG · cs.CV

What Linear Probes Miss: Multi-View Probing for Weight-Space Learning

Eunwoo Heo , Kyeongkook Seo , Jaejun Yoo This is my paper

Pith reviewed 2026-05-25 05:00 UTC · model grok-4.3

classification 💻 cs.LG cs.CV
keywords weight-space learningmodel probingmulti-view probingGram matrixpermutation-equivariant representationsModel Jungle benchmarkLoRA adapters
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The pith

MVProbe fuses first-order and Gram-based probes to represent model weights more completely than single-view methods.

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

The paper tackles the Model Jungle problem where shared model checkpoints lack documentation, making direct weight-space analysis necessary yet computationally heavy. Single-view linear probes extract only first-order structures and miss the row-column correlation patterns that higher-order views can capture. MVProbe adds Gram-based interaction views and derives a standardization and fusion rule from the scaling behavior of different probe orders so each branch contributes without bias. The method is tested on a benchmark covering ResNet, vision transformers, and large generative LoRA adapters, where it improves identification accuracy over the prior state-of-the-art single-view probe.

Core claim

The paper claims that a multi-perspective probing framework synthesizing first-order signals with interaction-aware Gram-based views, using a standardization and fusion strategy derived from the scaling laws of different probing orders, produces superior permutation-equivariant representations for weight-space learning.

What carries the argument

MVProbe multi-view probing framework that fuses first-order probe vectors with Gram-based views through scaling-law-derived standardization.

If this is right

  • MVProbe enables more accurate identification of undocumented models directly from their parameters.
  • The same multi-view approach improves performance on both discriminative backbones and large generative LoRA adapters.
  • Principled fusion based on probing-order scaling laws provides a general recipe for balancing multiple probe branches.
  • Higher-order correlation patterns become accessible without processing full-scale model weights.

Where Pith is reading between the lines

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

  • The scaling-law analysis of probe orders could be reused to design probes for other parameter spaces such as diffusion model weights.
  • Improved weight representations may help detect unauthorized model copies or unintended merges across repositories.
  • Extending the Gram-based branch to capture three-way or higher tensor interactions is a direct next measurement.

Load-bearing premise

The assumption that a principled standardization and fusion strategy derived from scaling laws will ensure balanced contributions from first-order and Gram-based branches without introducing bias or overfitting to the benchmark.

What would settle it

Run MVProbe and the prior single-view probe on a new collection of checkpoints drawn from architectures absent from the original benchmark and check whether the accuracy gap disappears or reverses.

Figures

Figures reproduced from arXiv: 2605.23410 by Eunwoo Heo, Jaejun Yoo, Kyeongkook Seo.

Figure 1
Figure 1. Figure 1: Overview of MVProbe. Given a weight matrix X ∈ R m×n , MVProbe extracts probe responses from four complementary views. (a) First-order probing: learnable probes U and V produce row- and column-space responses XU and X⊤V. We also compute XZ and X⊤W as intermediate projections for the second-order branches. (b) Second-order probing: applying X⊤ and X once more yields Gram-based responses X⊤XZ and XX⊤W, captu… view at source ↗
Figure 2
Figure 2. Figure 2: Conceptual illustration of Theorem 4.1. With the same probe matrix U, two distinct weight matrices X1 and X2 may produce first-order probe responses that are indistinguishable under standard probing. Theorem 4.1 shows that second-order, Gram-based representations can separate such cases. Theorem 4.1 (Expressiveness of Second-Order Probes). Let U ∈ R n×r be a probe matrix with rank(U) = r < n. Define the fi… view at source ↗
Figure 3
Figure 3. Figure 3: Layer-wise performance comparison. MVProbe (solid lines) vs. ProbeX (dashed lines) across all layers. Shaded bands indicate the performance volatility. MVProbe maintains higher accuracy across most layers and shows less sensitivity to layer selection. 5.3. Ablation Study: Branch Contributions We analyze the contribution of each probing branch in Ta￾ble 2. Each row shows the performance when using only the … view at source ↗
Figure 4
Figure 4. Figure 4: Layer-wise performance on SD LoRA. MVProbe (solid lines) vs. ProbeX (dashed lines) across all layers on SD200 and SD1k (In-Distribution and Zero-shot). Shaded bands indicate per￾layer volatility; red arrows mark the largest gains [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Neuron-level interpretation of a weight matrix. Illustration for X ∈ R 3×2 (two input neurons, three output neurons). (a) XU corresponds to responses at each output neuron i, driven by its incoming weight pattern X:→i. (b) X⊤V corresponds to responses at each input neuron j, driven by its outgoing weight pattern Xj→:. (c) XX⊤W probes the row-similarity structure ⟨X:→i, X:→j ⟩. (d) X⊤XZ probes the column-si… view at source ↗
read the original abstract

The explosive growth of open-source model repositories has created a Model Jungle, where checkpoints are frequently shared without adequate documentation or metadata. While weight-space learning offers a pathway to identify and analyze these models directly from their parameters, processing full-scale weights is computationally prohibitive. Probing-based methods have emerged as a lightweight alternative, extracting permutation-equivariant representations via learnable probe vectors. However, existing probing methods are limited by a single-view design: they capture first-order structures but fail to encode the rich, higher-order correlation patterns inherent in row-column interactions. To bridge this gap, we introduce MVProbe, a multi-perspective probing framework that synthesizes first-order signals with interaction-aware (Gram-based) views. Our approach is theoretically grounded; we analyze the scaling laws of different probing orders to derive a principled standardization and fusion strategy that ensures balanced contributions from all branches. On the Model Jungle benchmark, MVProbe consistently outperforms the state-of-the-art ProbeX across diverse architectures, including discriminative backbones (ResNet, SupViT, MAE, DINO) and large-scale generative LoRA adapters (Stable Diffusion LoRA).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that existing single-view linear probes for weight-space learning miss higher-order correlations in model weights, and introduces MVProbe as a multi-view framework that fuses first-order probes with Gram-based interaction views. The fusion is derived from an analysis of scaling laws across probing orders to produce a principled standardization that balances contributions; on the Model Jungle benchmark this yields consistent gains over the prior ProbeX method across ResNet, SupViT, MAE, DINO, and Stable Diffusion LoRA checkpoints.

Significance. If the claimed generalization holds, the work would meaningfully extend weight-space analysis by supplying richer, interaction-aware representations that remain computationally lightweight, directly addressing the practical problem of identifying and characterizing undocumented checkpoints in open model repositories.

major comments (2)
  1. [theoretical grounding / scaling-laws section (no equation numbers supplied in abstract)] The central claim that the standardization and fusion strategy is 'theoretically grounded' and produces unbiased, general contributions rests on the scaling-law analysis; however, the manuscript provides no explicit derivation or equations showing that the fitted parameters are obtained independently of the Model Jungle benchmark statistics (see the skeptic note on circularity). Without this separation, the reported outperformance over ProbeX risks being an artifact of benchmark-specific correlations among the evaluated architectures rather than an intrinsic weight-space property.
  2. [experiments / Model Jungle benchmark results] The experimental claim of consistent superiority across discriminative and generative models is load-bearing for the contribution, yet the provided text supplies neither dataset details, ablation results on the fusion weights, nor error bars; this prevents verification that the gains are robust rather than post-hoc choices on the same evaluation distribution.
minor comments (2)
  1. [method] Notation for the first-order and Gram-based branches should be introduced with explicit definitions before the fusion formula is presented.
  2. [abstract and introduction] The abstract states 'theoretically grounded' but contains no equations; the main text should include at least the key scaling-law relation and the resulting standardization expression.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the presentation of MVProbe's theoretical and experimental contributions. We respond to each major point below.

read point-by-point responses

  1. Referee: [theoretical grounding / scaling-laws section (no equation numbers supplied in abstract)] The central claim that the standardization and fusion strategy is 'theoretically grounded' and produces unbiased, general contributions rests on the scaling-law analysis; however, the manuscript provides no explicit derivation or equations showing that the fitted parameters are obtained independently of the Model Jungle benchmark statistics (see the skeptic note on circularity). Without this separation, the reported outperformance over ProbeX risks being an artifact of benchmark-specific correlations among the evaluated architectures rather than an intrinsic weight-space property.

    Authors: We agree that explicit equations demonstrating independence from the Model Jungle statistics are necessary to fully substantiate the theoretical grounding claim and rule out circularity. The scaling-law analysis in the manuscript was performed on synthetic weight matrices generated from controlled correlation models, independent of the benchmark; however, these details and the fitting procedure are not presented with sufficient formality. We will add a dedicated subsection containing the full derivation, the synthetic data protocol, and the independence argument in the revised manuscript. revision: yes

  2. Referee: [experiments / Model Jungle benchmark results] The experimental claim of consistent superiority across discriminative and generative models is load-bearing for the contribution, yet the provided text supplies neither dataset details, ablation results on the fusion weights, nor error bars; this prevents verification that the gains are robust rather than post-hoc choices on the same evaluation distribution.

    Authors: The Model Jungle benchmark composition (ResNet, SupViT, MAE, DINO, and Stable Diffusion LoRA checkpoints) is described in Section 4.1, with ablation results on fusion weights in Appendix C and error bars from 5 random seeds reported throughout the results. To address the concern that these elements are insufficiently prominent, we will add a concise dataset statistics table to the main text, expand the ablation discussion in Section 4, and explicitly reference the error bars in the figure captions and results narrative. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The provided abstract and excerpts claim that scaling laws of probing orders are analyzed to derive a standardization and fusion strategy, but contain no equations, self-citations, or explicit reductions showing that the fusion weights or standardization are fitted to the Model Jungle benchmark data, defined in terms of the target predictions, or imported via self-citation chains. The outperformance claim is presented as an empirical result on the benchmark following the method, with no load-bearing step reducing by construction to the inputs. The derivation is therefore treated as self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the fusion strategy and scaling-law standardization are referenced but not detailed.

pith-pipeline@v0.9.0 · 5730 in / 1056 out tokens · 30076 ms · 2026-05-25T05:00:57.812826+00:00 · methodology

discussion (0)

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