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Exploring perceptual straightness in learned visual representations

Anne Harrington, Vasha DuTell, Ayush Tewari, Mark Hamilton, Simon Stent, Ruth Rosenholtz, William T. Freeman

arXiv:2610.34678v1cs.LGcs.CV

TL;DR

Human visual representations straighten temporal trajectories, but many computer-vision models do not, motivating a way to assess straightness across models and tasks. The paper measures curvature in video representations and compares it across architectures, training approaches, and tasks. It reports that adversarial training and biologically inspired mechanisms can be associated with straighter representations, but the pattern depends on task and does not extend to every robustness approach.

  • Problem

    Human perceptual representations are straighter than pixel-space trajectories, while many computer-vision models do not straighten natural videos.

    Source: §1 · p. 1

  • Method

    The paper measures temporal curvature in video representations across network layers and compares models with different architectures, training schemes, and tasks.

    Source: §1 · p. 2, §3 · p. 3

  • Results

    Adversarial training reduces output curvature, but straightness does not generalize to every robustness approach; models with lower curvature have more stable predictions over time.

    Source: §8 · p. 9

  • Takeaways & Limitations

    Straightness is a simple, computationally cheap measure for comparing representational robustness and stability across image and video models and tasks.

    Source: §8 · p. 9

    For frame-prediction models, straight representations at or near the output are not favorable because predictions should vary dynamically with video motion.

    Source: §6 · p. 8

Abstract

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Humans have been shown to use a "straightened" encoding to represent the natural visual world as it evolves in time (H\'enaff et al. 2019). In the context of discrete video sequences, "straightened" means that changes between frames follow a more linear path in representation space at progressively deeper levels of processing. While deep convolutional networks are often proposed as models of human visual processing, many do not straighten natural videos. In this paper, we explore the relationship between network architecture, differing types of robustness, biologically-inspired filtering mechanisms, and representational straightness in response to time-varying input; we identify strengths and limitations of straightness as a useful way of evaluating neural network representations. We find that (1) adversarial training leads to straighter representations in both CNN and transformer-based architectures but (2) this effect is task-dependent, not generalizing to tasks such as segmentation and frame-prediction, where straight representations are not favorable for predictions; and nor to other types of robustness. In addition, (3) straighter representations impart temporal stability to class predictions, even for out-of-distribution data. Finally, (4) biologically-inspired elements increase straightness in the early stages of a network, but do not guarantee increased straightness in downstream layers of CNNs. We show that straightness is an easily computed measure of representational robustness and stability, as well as a hallmark of human representations with benefits for computer vision models.

1 INTRODUCTION

Natural visual input traces trajectories over time, and human perceptual representations are straighter than pixel-space trajectories. The section asks whether computer-vision models can acquire this property and explores architecture, training, and early visual mechanisms as possible influences.

1 INTRODUCTION

  • Human perceptual trajectories are straighter than pixel-space trajectories, a property proposed to help with extrapolation such as predicting future visual states.Many computer-vision models achieve high recognition accuracy yet fail to capture aspects of human vision, and ImageNet-trained AlexNet does not straighten representations.Source: §1 · p. 1
  • The introduction frames representational straightness as a candidate property for models intended to reflect human visual processing.It notes that biologically inspired V1-like transformations yield straighter representations than the input domain, unlike popular computer-vision models such as AlexNet.Source: §1 · p. 1
  • The study evaluates how architecture, training schemes, and task affect temporal straightness across network layers.It asks whether adversarial robustness in CNNs and transformers, or hard-coding an early representation, leads to straighter downstream representations.Source: §1 · p. 2

2 PREVIOUS WORK

Prior work has sought to align deep networks with human vision and evaluate that alignment, while studying adversarial robustness and temporal representation learning as related approaches. This paper examines straightness as a measure of robust, stable representations across tasks.

2 PREVIOUS WORK

  • Prior efforts to align deep networks with vision include V1-like receptive fields, foveation, neural activation properties, and predictive-coding error signals.Predictive coding has been used in networks trained for video-frame prediction.Source: §2 · p. 2
  • Straightness offers a quick quantitative way to assess alignment with human visual representations, whereas perceptual comparisons can require lengthy stimulus synthesis and human participants.The measure is particularly relevant to temporal stability.Source: §2 · p. 2
  • Adversarial training addresses image misclassification from adversarial examples and has been suggested to improve perceptual alignment, but is not biologically plausible.Adversarial robustness has also been studied for transfer learning, image generation, in-painting, and semantic segmentation; this paper tests whether it leads to straightened representations.Source: §2 · p. 3
  • Slow feature analysis encourages representations to change slowly over time, while earlier straightness constraints were explored for unsupervised video-frame prediction.This paper evaluates straightness as a metric for robust, stable representations learned for tasks.Source: §2 · p. 3

3 METHODS: MEASURING STRAIGHTNESS AS LOW CURVATURE

The method measures representational straightness through curvature along a video sequence. It computes angles between consecutive frame-difference vectors, averages them over time, and can compare a model representation with the pixel input.

3 METHODS: MEASURING STRAIGHTNESS AS LOW CURVATURE

  • Global curvature is the mean angle between successive frame-difference vectors across the T −1 time steps of a video sequence.The representation may be raw pixels or activations at any stage of a network.Source: §3 · p. 3
  • Representational straightness is evaluated as a reduction in curvature, with change in curvature defined as representational curvature minus pixel curvature.A negative change therefore indicates lower curvature in the representation than in the pixel input.Source: §3 · p. 3
  • The method applies the same curvature measure to representations at different stages of a processing pipeline, from pixel values to network layers.Figure 3 reports output-layer curvature relative to input-video curvature; for image-classification models, the output is the penultimate layer.Source: §3 · p. 3, Figure 3 · p. 4
  • Curvature measures the angle between consecutive frame-difference vectors, unlike cosine similarity, which measures the angle between frame vectors themselves.Figure 2 contrasts these two angles along a three-point temporal trajectory.Source: Figure 2 · p. 3, §3 · p. 4

4 CURVATURE AND ROBUSTNESS IN CONVOLUTIONAL OBJECT RECOGNITION MODELS

Across convolutional recognition models, adversarial training is associated with lower output curvature, while other robustness methods do not produce the same straightening. On VGGSound, the lower-curvature robust model also has more stable true-label predictions.

4 CURVATURE AND ROBUSTNESS IN CONVOLUTIONAL OBJECT RECOGNITION MODELS

  • Adversarially trained recognition models have lower output curvature than non-adversarial models, with most reducing curvature below the pixel input.Non-adversarially trained image-recognition models have the highest output curvature.Source: §4 · p. 4, Figure 4 · p. 5

4.1 ADVERSARIAL ATTACK TYPE, STRENGTH, AND CURVATURE

  • For l∞-trained ResNet50s, greater attack strength lowers output curvature; l2-trained models are straightest, with little curvature change across attack strengths.The authors suggest l2 models may be straighter because training permits greater ϵ; higher l2 ϵ values may be needed to test for differences.Source: §4.1 · pp. 4–5, Figure 5 · p. 5
  • For CIFAR-trained robust ResNet50s, greater curvature reduction correlates with higher APGD-CE AutoAttack accuracy for both l2 and l∞ attacks.Attack strength does not often translate to improved test-set accuracy, motivating this comparison of curvature with attack accuracy.Source: §4.1 · p. 6
  • Other evaluated robustness methods do not straighten natural videos like adversarial robustness, and do not provide the observed temporal representational stability.The evaluated methods include corruption robustness, shift-invariant robustness, and anti-aliasing CNNs.Source: §4.1 · p. 6

4.2 CURVATURE AND REPRESENTATIONAL STABILITY

  • On VGGSound videos, the adversarially robust ResNet50 has both lower curvature and lower variability in true-label probability than the standard model.The tested videos are out of distribution relative to the models’ image training data; the authors propose curvature as a computationally cheap proxy for temporal stability.Source: §4.2 · p. 6, Figure 6 · p. 6

5 CURVATURE IN VISUAL TRANSFORMER MODELS FOR OBJECT RECOGNITION

Standard and DINO ViT models increase curvature relative to pixel input, while DINO is less curved than the standard ViT. CrossViT briefly reduces curvature in one branch, but not after its paths recombine.

5 CURVATURE IN VISUAL TRANSFORMER MODELS FOR OBJECT RECOGNITION

  • Standard and DINO ViT models have output curvature above pixel input, with the increase consistent across their layers.The standard ViT does not reduce curvature on the tested natural video sequences.Source: §5 · p. 6, Figure 7 · p. 7
  • CrossViT reduces curvature below pixel input in one middle-stage branch, but its recombined output is more curved than pixel input.The other branch increases in curvature during the split stage.Source: Figure 7 · p. 7, §5 · p. 7
  • DINO-trained ViT is less curved than baseline ViT, but its representation remains more curved than the pixel input.The authors suggest self-supervised training may be better than supervised training for straight representations.Source: §5 · p. 7, Figure 7 · p. 7

6 CURVATURE AND ROBUSTNESS IN IMAGE SEGMENTATION AND FRAME PREDICTION MODELS

For segmentation and next-frame prediction, output straightness is not necessarily favorable because predictions must track frame-level changes. Segmentation models remain more curved than pixel input, while PredNet outputs stay close to input curvature.

6 CURVATURE AND ROBUSTNESS IN IMAGE SEGMENTATION AND FRAME PREDICTION MODELS

  • Adversarially robust segmentation models show only slightly reduced curvature versus non-robust counterparts, and all remain more curved than pixel input across layers.The authors argue that straightness is not desirable for segmentation maps that change frame by frame, making the effect task-dependent.Source: §6 · pp. 7–8, Figure 8 · p. 7
  • For next-frame prediction, the authors consider input-like output curvature favorable because predictions should reproduce the video’s frame-to-frame dynamics.This differs from straightness as a desired property for tasks such as object detection, where objects may persist across frames.Source: §6 · p. 8
  • All tested pretrained PredNet variants finish with output curvature close to input curvature, closer than the other models tested.Their curvature first increases in the first block, then decreases through the remaining network; the multi-frame-future variant only slightly reduces curvature.Source: §6 · p. 8
  • PredNet straightens more on in-distribution than out-of-distribution data, but the effect is small and does not change the overall trend.Adding a curvature constraint can straighten the model, but does not greatly affect final output curvature.Source: §6 · p. 8

7 CURVATURE IN BIOLOGICALLY INSPIRED MODELS

The section compares biologically inspired models across processing stages and finds that most progressively reduce curvature, but VOneNetCornets does not sustain its early straightening. This limits what biological front ends alone can achieve downstream.

7 CURVATURE IN BIOLOGICALLY INSPIRED MODELS

  • The compared models include non-parametric center-surround/Gabor and steerable-pyramid systems, a V1-fronted Cornets model, and adversarially trained CrossViT.The models are aligned to visual processing areas; CrossViT layers are matched to V4 and IT using BrainScore.Source: §7 · p. 8, Figure 9 · p. 9
  • Curvature progressively decreases through deeper layers in all biologically inspired models except VOneNetCornets.VOneNetCornets curvature falls through V1, then rises sharply after neural-stochasticity noise is added; removing noise reduces but does not eliminate the downstream increase.Source: §7 · p. 8
  • VOneNet's later curvature rise suggests that a biologically inspired front end alone is insufficient to straighten downstream representations.The authors note that VOneNet is reported as more robust to white-box attacks than a standard CNN, suggesting adversarial training—not robustness itself—may underlie straightening.Source: §7 · p. 8
  • The authors suggest that biologically plausible methods may need more constraints to achieve straight representations.Source: §7 · p. 9

8 DISCUSSION

The discussion presents curvature change as an efficient measure of some forms of robustness and temporal stability, while emphasizing that its relationship to robustness varies by task and training. Biological mechanisms can reduce curvature, but simple biologically inspired filters do not ensure low output curvature.

8 DISCUSSION

  • Strong white-box adversarial training reduces output curvature, and models with lower output curvature have better adversarial accuracy, but curvature reduction is not associated with robustness to image corruption or simple shift-invariance.Source: §8 · p. 9
  • Curvature reduction is task-dependent: adversarially robust object-recognition models straighten, whereas semantic-segmentation and frame-prediction models do not.The relationship also depends on training procedure, not architecture alone.Source: §8 · p. 9
  • Biologically inspired mechanisms reduce representational curvature, but adding non-parametric filters at a CNN input does not ensure lower output curvature.The authors frame straightness as a common thread between biologically inspired and adversarially robust models, with benefits and limits for temporally stable representations.Source: §8 · p. 9
  • The authors present curvature as an efficient, layer-wise way to compare representations and evaluate temporal stability, including in static image models.They describe perceptual straightening as a stepping-stone toward incorporating more temporal aspects into research aligning computer and human vision.Source: §8 · p. 9

9 REPRODUCIBILITY

The authors identify the models, stimuli, and curvature function as the materials needed to reproduce their results.

9 REPRODUCIBILITY

  • The models, stimuli, and curvature function are identified as sufficient to reproduce the results.Model links are in the supplemental Network Comparison Spreadsheet; stimulus sources are in Sec A.2.2 and the HenaffBio code base, and curvature is calculated using Secs 3 and A.1.Source: §9 · p. 10

A.1 CURVATURE VS COSINE SIMILARITY

This appendix relates cosine similarity for vectors and video frames to cosine curvature. It defines curvature through the angle between consecutive normalized vectors.

A.1 CURVATURE VS COSINE SIMILARITY

  • Vector cosine similarity is the dot product of vectors A and B divided by the product of their norms.Source: §A.1 · p. 15
  • For video frames, cosine similarity is the dot product of consecutive frames divided by the product of their norms.Source: §A.1 · p. 15
  • Cosine curvature is the cosine similarity of consecutive normalized vectors and equals the cosine of curvature.Source: §A.1 · p. 15

A.2 MODELS

The appendix describes the models and curvature-analysis choices used to compare representations, then tests how curvature relates to robustness and frame prediction. Adversarial training reduced curvature more consistently than other robustness approaches, while curvature-constrained PredNet models straightened selected layers but had worse prediction error than the original model.

A.2.2 MODEL ANALYSIS PROCEDURE

  • The analysis used pretrained models, activations from intermediate and final layers, and 12 psychophysically validated 11-frame natural videos; analyses ran on CPU, with a GPU speeding feature extraction.Curvature was computed from flattened activations and compared with pixel-space video curvature; layer dimensions were not equalized, and PCA did not greatly change trends such as adversarial training’s effect.Source: §A.2.2 · p. 15, §A.2.3 · p. 15

A.2.4 EFFECT OF PCA ON MODEL CURVATURE

  • Across the tested principal-component counts, standard ResNet50 had higher natural-video curvature than adversarially robust ResNet50.Figure 10 compares layer-wise curvature using 2, 5, 10, and 100 principal components, with pixel-level PCA also used when components were fewer than the 11 video frames.Source: Figure 10 · p. 16

A.3 FINAL STAGE CURVATURES

  • Across model families, final-stage curvature was similar to curvature in their output representation layers; the reported layer was just before classification because it is commonly used as a backbone.The comparison figures cover classification architectures and segmentation models across several datasets.Source: §A.3 · p. 17, Figure 11 · p. 17, Figure 12 · p. 17

A.4 MATCHING MODELS CURVATURE COMPARISON PLOTS

A.5 ADVERSARIAL ACCURACY AND CURVATURE

  • Stronger adversarial attacks decreased curvature, but test accuracy did not predict curvature reduction across models; within a model’s training/test set, higher accuracy predicted smaller output-curvature reduction.The figure notes that adversarial training can also decrease within-domain test accuracy.Source: Figure 23 · p. 23

A.6 CURVATURE IN NON-ADVERSARIALLY ROBUST NETWORKS

  • Adversarial robustness strongly reduced curvature below input levels, whereas shift invariance reduced it only slightly and corruption robustness did not reduce it.The AlexNet result was an exception among tested adversarially trained models; its small size may limit benefits from adversarial attacks.Source: Figure 24 · p. 24, Figure 25 · p. 24, Figure 26 · p. 25

A.8 PREDNET PREDICTIONS

  • PredNet models were trained on KITTI and evaluated on KITTI and Hénाफ et al. stimuli; Figure 29 provides example predictions for the original and straightened models.The straightened PredNet was trained with a curvature penalty on its R2 layer.Source: §A.7 · p. 26, Figure 29 · p. 28

A.7 PREDNET STRAIGHTNESS FOR IN AND OUT OF DISTRIBUTION DATA

  • Curvature-constrained PredNet reduced curvature in R2 and R3, but its 0.00976 MSE exceeded the original model’s 0.00687 while remaining below frame-copying’s 0.02122.The constrained models straightened only two layers overall; the original and straightened models were trained on KITTI.Source: Figure 28 · p. 26, §A.7 · p. 27

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