Beyond Compression: Quantifying Spectral Accessibility in Vision Representations

Akayou A. Kitessa; Yijun Zhao

arxiv: 2606.03795 · v1 · pith:J627TV3Pnew · submitted 2026-06-02 · 💻 cs.CV

Beyond Compression: Quantifying Spectral Accessibility in Vision Representations

Akayou A. Kitessa , Yijun Zhao This is my paper

Pith reviewed 2026-06-28 10:41 UTC · model grok-4.3

classification 💻 cs.CV

keywords spectral accessibilityvision representationsfrequency recoverabilityCLIPDINOv2intermediate layersresidual spectral loss

0 comments

The pith

Vision representations make frequency information most linearly recoverable at intermediate layers rather than at the output.

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

The paper tracks how much band-limited spatial frequency content stays recoverable from frozen vision model activations on ImageNet and MS-COCO. It reports that recoverability rises to a peak in middle layers then declines toward the final embedding. A new residual measure separates the effect of learned projections from simple dimensionality reduction. The last step behaves differently by architecture: CLIP's projection mainly compresses without extra frequency bias, while DINOv2's class-token pooling removes energy across bands in a structured way.

Core claim

Spectral accessibility follows a non-monotonic trajectory across depth, peaking at intermediate layers before decreasing toward the output representation. The final transformation differs across architectures: CLIP's learned projection is spectrally neutral, with changes explained by compression, whereas DINOv2's [CLS] pooling induces a structured loss across the spectrum.

What carries the argument

Residual Spectral Loss (RSL), which quantifies changes in the linear recoverability of band-limited Fourier energy from representation vectors relative to a dimension-matched random projection baseline.

If this is right

Intermediate layers retain more recoverable frequency content than the final output and may therefore suit tasks that need high-frequency detail.
Pooling operations such as [CLS] token aggregation produce frequency-dependent losses that are not explained by compression alone.
Learned projections in models like CLIP mainly reduce dimension without imposing additional structured spectral bias.
Primary drivers of spectral change in modern vision encoders are layer depth and the final pooling or projection step.

Where Pith is reading between the lines

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

Feature extraction for frequency-sensitive downstream tasks could be improved by selecting activations from the peak-accessibility layer instead of the final embedding.
New pooling or projection designs could be evaluated by whether they avoid the structured spectral losses observed with class-token aggregation.

Load-bearing premise

Linear recoverability of band-limited Fourier energy from the representation vectors measures spectral accessibility without being confounded by dataset statistics or the choice of frequency bands.

What would settle it

If the same models on the same images show monotonic decline or flat recoverability when the frequency bands or the linear probe are altered, the reported non-monotonic pattern would not hold.

Figures

Figures reproduced from arXiv: 2606.03795 by Akayou A. Kitessa, Yijun Zhao.

**Figure 2.** Figure 2: Spatial-frequency accessibility (left) and Residual Spectral Loss (right) on ImageNet. Left panels plot per-band accessibility αk across layers; right panels show RSL with 95% bootstrap confidence intervals. COCO results show the same qualitative patterns (Appendix). 5 Results We evaluate spectral accessibility across CLIP ViT-L/14, CLIP ViT-B/32, and DINOv2 on ImageNet1K and COCO. Using RSL to factor out… view at source ↗

**Figure 3.** Figure 3: Spatial-frequency accessibility (left) and Residual Spectral Loss (right) on COCO. Left [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗

read the original abstract

Vision-language models map visual features into a shared embedding space through learned projection layers, yet it remains unclear how these transformations alter the structure of visual information. This study examines changes in representation through spatial-frequency accessibility, measured by the linear recoverability of band-limited Fourier energy from model representations. To isolate effects beyond dimensionality reduction, we introduce Residual Spectral Loss (RSL), which evaluates changes relative to a dimension-matched random projection baseline. To reduce confounding effects from optimization, the analysis uses pretrained models with all parameters frozen. The experimental results show consistent frequency-dependent changes in accessibility across CLIP and DINOv2 on ImageNet and MS-COCO datasets. Spectral accessibility follows a non-monotonic trajectory across depth, peaking at intermediate layers before decreasing toward the output representation. The final transformation differs across architectures: CLIP's learned projection is spectrally neutral, with changes explained by compression, whereas DINOv2's [CLS] pooling induces a structured loss across the spectrum. These findings identify intermediate layers and pooling mechanisms as primary drivers of spectral transformation in modern vision encoders.

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.

Desk Editor's Note private letter to a colleague

The paper introduces Residual Spectral Loss to track frequency preservation through frozen vision encoders and reports non-monotonic depth effects plus architecture differences in the final layer, but the linear-probe measure may still be tied to dataset statistics.

read the letter

The main takeaway is that this work defines a new residual metric to separate spectral shifts from plain compression and applies it layer-wise to CLIP and DINOv2. It finds accessibility peaks at middle layers then drops, with CLIP's projection looking mostly neutral while DINOv2's pooling removes structured frequency content.

What stands out is the attempt to hold model parameters fixed and use a random-projection baseline so the comparison is not just about dimension count. Running the same analysis on ImageNet and MS-COCO is also a reasonable check for consistency.

The soft spot is the core assumption that linear R^2 on band-limited Fourier energy cleanly measures accessibility. If the probe dataset's own power spectrum correlates with the representation dimensions, the reported trajectories and the CLIP-DINOv2 split could partly reflect that correlation rather than intrinsic model behavior. The abstract gives no equations, band definitions, or controls that would let a reader check this directly.

The paper is aimed at people who pick intermediate layers for downstream tasks or who study how pooling and projection reshape visual features. It is narrow enough that a serious referee could evaluate the metric and the controls in one round.

I would send it to review if the full methods section shows the bands and the random baseline are handled without obvious leakage from the data distribution.

Referee Report

2 major / 2 minor

Summary. The paper introduces Residual Spectral Loss (RSL) to quantify changes in spectral accessibility of visual information in frozen pretrained vision encoders (CLIP, DINOv2) beyond dimensionality reduction. Accessibility is operationalized as the linear recoverability (R²) of band-limited Fourier energy from representation vectors, evaluated relative to a dimension-matched random-projection baseline on ImageNet and MS-COCO. Results indicate a non-monotonic depth trajectory (peaking at intermediate layers) and architecture-specific final-layer effects: CLIP's projection is spectrally neutral (changes attributable to compression), while DINOv2's [CLS] pooling produces structured spectral loss.

Significance. If the RSL measure proves unconfounded, the work supplies a concrete, reproducible diagnostic for how pooling and projection stages reshape spatial-frequency content in modern vision backbones. The frozen-model protocol and explicit random-projection control are strengths that allow isolation of architectural effects; the non-monotonic depth finding, if robust, would directly inform layer selection for tasks sensitive to high-frequency detail.

major comments (2)

[Methods (RSL definition and experimental setup)] The central claim that RSL isolates intrinsic spectral transformations (rather than dataset-specific correlations) rests on the assumption that linear probe performance for band-limited energy is independent of the empirical power spectrum of the probe images and the chosen frequency-band partitioning. No ablation is described that varies band definitions or substitutes a dataset with different frequency statistics while holding the representations fixed; without such a control the reported non-monotonic trajectories and CLIP-vs-DINOv2 distinction could be artifacts of the ImageNet/MS-COCO statistics.
[§4 (baseline construction)] The random-projection baseline is presented as parameter-free and architecture-independent, yet the paper does not report whether the baseline R² itself varies systematically with the depth or pooling operation under study. If the baseline already encodes depth-dependent spectral bias (e.g., via the statistics of the frozen feature maps), then the residual RSL values may not cleanly separate compression from structured loss.

minor comments (2)

Notation for the frequency bands and the exact linear-probe formulation (ridge parameter, train/test split) should be stated explicitly rather than left to supplementary material.
Figure captions should include the precise number of frequency bands, the dimensionality of each representation, and error-bar definition (e.g., std over seeds or images).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments highlighting potential confounds in the RSL definition and baseline. We respond point-by-point below and commit to revisions that directly address the concerns while preserving the core contributions.

read point-by-point responses

Referee: [Methods (RSL definition and experimental setup)] The central claim that RSL isolates intrinsic spectral transformations (rather than dataset-specific correlations) rests on the assumption that linear probe performance for band-limited energy is independent of the empirical power spectrum of the probe images and the chosen frequency-band partitioning. No ablation is described that varies band definitions or substitutes a dataset with different frequency statistics while holding the representations fixed; without such a control the reported non-monotonic trajectories and CLIP-vs-DINOv2 distinction could be artifacts of the ImageNet/MS-COCO statistics.

Authors: We acknowledge the value of explicit controls for band partitioning and dataset frequency statistics. The current experiments already evaluate the same frozen representations on two datasets with materially different frequency content (object-centric natural images in ImageNet versus more varied scene content in MS-COCO), and the non-monotonic depth trajectories are qualitatively consistent across both. Nevertheless, we did not vary the frequency-band definitions themselves. In the revision we will add an ablation that re-partitions the spectrum using different numbers of bands and cutoff frequencies while holding all representations fixed, and we will report whether the reported trajectories and architecture distinctions remain stable. This addition will directly test the independence assumption. revision: yes
Referee: [§4 (baseline construction)] The random-projection baseline is presented as parameter-free and architecture-independent, yet the paper does not report whether the baseline R² itself varies systematically with the depth or pooling operation under study. If the baseline already encodes depth-dependent spectral bias (e.g., via the statistics of the frozen feature maps), then the residual RSL values may not cleanly separate compression from structured loss.

Authors: The random-projection baseline is formed by applying a single random linear matrix directly to the preprocessed input image pixels to produce a vector whose dimension exactly matches the target layer output; the matrix is drawn once per dimension and is never applied to any intermediate feature map. Consequently the baseline R² depends only on input statistics and target dimension, not on depth, pooling, or any frozen-model representation. Because the construction is deliberately input-based, it cannot inherit depth-dependent spectral biases from the encoder. We will revise §4 to state this construction explicitly, add a supplementary figure showing baseline R² as a function of dimension only, and confirm that residual RSL therefore isolates structured loss beyond compression. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation uses independent random-projection baseline on frozen models

full rationale

The paper defines RSL as linear recoverability of band-limited Fourier energy relative to a dimension-matched random projection baseline, then applies the measure to frozen pretrained CLIP and DINOv2 models. No equation or claim reduces the reported non-monotonic depth trajectory or final-layer differences to a fitted constant or self-citation by construction. The baseline is parameter-independent and external to the models under test, so the central empirical observations remain non-tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The work rests on standard Fourier analysis and introduces one new evaluation quantity without reported free parameters or additional postulated entities.

axioms (1)

standard math Band-limited Fourier energy can be linearly recovered from representation vectors to quantify accessibility
Core measurement definition used throughout the abstract.

invented entities (1)

Residual Spectral Loss (RSL) no independent evidence
purpose: Quantify spectral changes relative to dimension-matched random projection baseline
New metric introduced to isolate effects beyond compression

pith-pipeline@v0.9.1-grok · 5711 in / 1201 out tokens · 47351 ms · 2026-06-28T10:41:38.519560+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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work page internal anchor Pith review Pith/arXiv arXiv

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Dong Yin, Raphael Gontijo Lopes, Jonathon Shlens, Ekin D

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