Discovering shared interpretable operations in image compression autoencoders

arXiv:2607.04839 · eess.IV, cs.MM, eess.SP · Submitted 2026-07-06 · Read on arXiv

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Introduction to the show: ident: Electrical Engineering. The day in electrical engineering: signals, systems and the hardware that carries them.

Rosa: I'm Rosa.

Dev: And I'm Dev, here with Taro.

Rosa: We're looking at the paper: "Discovering shared interpretable operations in image compression autoencoders".

Dev: Here's the gist of the paper. Deep learning-based image compression models face practical limitations due to their size and computational cost <ref:2607.04839#pg2> In this work, we study bias-free autoencoders for the image compression task, to investigate whether universal structures exist that could help simplify these data-adaptive models <ref:2607.04839#pg6>.

Rosa: Investigating Universal Behaviors The paper investigates whether universal behaviors can be detected from the internal operations of bias-free autoencoders through Jacobian analysis <ref:2607.04839#pg2> If such behaviors exist, they may be extracted to design low-complexity image compression models inspired by high-complexity deep learning architectures <ref:2607.04839#pg2>.

Dev: The authors investigate whether deep learning autoencoders trained for image compression learn universal compression behaviors that generalize across images, or whether the model must fully adapt to each specific input <ref:2607.04839#pg3>.

Rosa: This investigation is motivated by Mohan et al., who use Jacobian matrices derived from bias-free autoencoders with ReLU activations to explain the model’s behavior as a set of image-adaptable linear filters <ref:2607.04839#pg3>.

Paper summary: Rosa: We've seen that this paper investigates whether universal behaviors can be detected from the internal operations of bias-free autoencoders through Jacobian analysis. The core thesis is that if these universal behaviors exist, they might be extracted to design low-complexity image compression models inspired by high-complexity deep learning architectures.

Dev: The authors are looking at conventional autoencoders for compression, which optimize the rate-distortion trade-off defined by min genc(x) - p(genc(x)) + lambda x - gdec(genc(x)) two two where genc is the encoder and gdec is the decoder <ref:2607.04839#pg2,optimize the rate-distortion trade-off>.

Taro: They are treating these modules as analogous to a DCT matrix and its inverse, but they are implemented using learned non-linear operations instead of fixed transforms.

Rosa: Because these neural networks are black boxes, they can't be easily explained, but by examining the rows of the Jacobian for each input image, they can extract linear, adaptive filters specific to that image.

Dev: They extend this analysis to compression models by writing both modules separately as in Equations (three) and (four), allowing them to analyze genc(x) and gdec(x) independently <ref:2607.04839#pg2,as in Equations (3) and (4>.

Taro: The investigation then focuses on verifying whether the ordering of the most important Jacobian rows corresponds to highly correlated filters across different images.

Rosa: They define a score for feature importance, s x,(i) = a x,(i) times y i, and they average this over patches' dataset P to get a global measure s i. This helps them rank the filters based on their importance in reconstructing x.

Dev: They then check correlation scores where c i is the mean pairwise Pearson correlation between flattened magnitude spectra across all patch pairs. The agreement between the rankings R s and R c, measured by NDCG@k and Kendall’s tau, confirms that energetic and correlated filters are mostly the same up to a threshold k star.

Taro: This is important because it links the learned importance scores directly to structural consistency across different images.

Rosa: If these top- k filters are highly correlated, then they may be transferable across images, leading them to compute an averaged filter representation J enc* over a subset of image Jacobians.

Dev: This average Jacobian matrix J enc* shows strong similarities across models with different lambda values, and the most important filters tend to emphasize vertical and horizontal structures, as well as color-related characteristics.

Taro: So they are finding that even when you tune parameters like lambda in a model, the underlying essential features—like those emphasizing structure—remain consistent.

Rosa: The paper concludes by comparing this Jacobian approach with classical transform methods like DCT and KLT, showing that it achieves good performance at low BPP rates and a better PSNR–BPP trade-off across all quantization steps.

Dev: But they also flag a limitation: replacing all sufficient network features with Jacobians can degrade performance, which points toward the need for more sophisticated or hybrid strategies.

Conclusion: Rosa: So, looking at "Discovering shared interpretable operations in image compression autoencoders," the main implication is that we can interpret these black-box models by finding specific, shared filters within them.

Dev: The authors found that a subset of encoder operations is shared across images and can be interpreted as image filters. These are the filters that are most consistent across images and also contribute most to reconstruction energy.

Taro: In simple terms, it means we don't have to train a completely new, complex model from scratch for every new image if we can use these shared structures.

Rosa: It suggests that using the average filters across images for both encoding and decoding gives results very close to the original model, especially when you only keep the most energetic components at low bit rates.

Dev: The work is limited because it was specifically analyzing bias-free ReLU-based architectures, and they plan to extend this analysis to more general models in the future.

Taro: So while this technique is promising for compression, we need to be careful because replacing everything with Jacobians isn't always the best path; we still need a good strategy for how we select those features.

Rosa: That sounds right. The core idea is identifying these shared, important image filters that cut through the complexity of deep learning autoencoders.

University of Rennes · inria · CNRS

eess.IV, cs.MM, eess.SP

Submitted: 2026-07-06

Updated: 2026-10-29

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 80/100

The gist: Deep learning-based image compression models face practical limitations due to their size and computational cost <ref:2607.04839#pg2> In this work, we study bias-free autoencoders for the image

Key concepts

Bias-free Autoencoders: These are specific deep learning models used for image compression that do not have a bias term. They are studied to see if they learn universal patterns for compressing images, rather than just adapting perfectly to each individual picture.
Jacobian Analysis: This mathematical technique is used to examine the internal operations of the autoencoders. It helps researchers understand how the model transforms input data, revealing underlying linear filters that might represent universal compression behaviors.
Filter Importance Score: A score defined by combining gradient magnitude and feature value is used to rank which internal filters are most important for reconstructing an image. This ranking helps identify the key operations that drive image reconstruction quality.
Cross-Image Correlation: This involves measuring how similar the top-ranked filters are when comparing different images. Finding high correlation confirms that certain energetic and consistent filters exist across various natural images, supporting the idea of shared compression structures.

Terminology

Quantization — 9× in this paper · explained in 15 episodes
Jacobian Analysis — 8× in this paper · explained in 3 episodes
Decoder — 7× in this paper · explained in 2 episodes
International Conference on Learning Representations — 6× in this paper
Generalization — 4× in this paper · explained in 14 episodes
Discrete Cosine Transform — 3× in this paper
Ablation — 2× in this paper · explained in 1 episode
Core — 2× in this paper · explained in 2 episodes
Diffusion Model — 2× in this paper · explained in 10 episodes
Diffusion Models — 2× in this paper · explained in 9 episodes
Feature Importance — 2× in this paper · explained in 2 episodes
Latent Space — 2× in this paper · explained in 7 episodes
Universality — 2× in this paper · explained in 2 episodes
computational cost — 2× in this paper · explained in 2 episodes
Consistency — 1× in this paper · explained in 3 episodes
Explainability — 1× in this paper · explained in 4 episodes
International Conference on Computer Vision — 1× in this paper
Interpretability — 1× in this paper · explained in 15 episodes
Latent Representation — 1× in this paper · explained in 2 episodes
Localization — 1× in this paper · explained in 2 episodes
Reconstruction Error — 1× in this paper · explained in 2 episodes
Structural Consistency — 1× in this paper · explained in 2 episodes

Summary

Deep learning-based image compression models face practical limitations due to their size and computational cost <ref:2607.04839#pg2> In this work, we study bias-free autoencoders for the image compression task, to investigate whether universal structures exist that could help simplify these data-adaptive models <ref:2607.04839#pg6>.

Investigating Universal Behaviors

The paper investigates whether universal behaviors can be detected from the internal operations of bias-free autoencoders through Jacobian analysis <ref:2607.04839#pg2> If such behaviors exist, they may be extracted to design low-complexity image compression models inspired by high-complexity deep learning architectures <ref:2607.04839#pg2>. The authors investigate whether deep learning autoencoders trained for image compression learn universal compression behaviors that generalize across images, or whether the model must fully adapt to each specific input <ref:2607.04839#pg3>. This investigation is motivated by Mohan et al., who use Jacobian matrices derived from bias-free autoencoders with ReLU activations to explain the model’s behavior as a set of image-adaptable linear filters <ref:2607.04839#pg3>.

Extracting Feature Importance

The process for finding important features involves several steps based on Jacobian analysis <ref:2607.04839#pg4>. The authors define a score that combines the gradient magnitude with the feature value to rank filters by importance, defined as sx,(i) = ax,(i) · yi <ref:2607.04839#pg4> This score is used to rank features according to their importance in reconstructing x, and it is averaged over a patches’ dataset P to obtain a global importance measure si <ref:2607.04839#pg4>. The reconstruction quality is expected to increase smoothly as features are iteratively included from the most to the least important <ref:2607.04839#pg4>.

Verifying Cross-Image Correlation

To verify whether the ordering of the most important filters corresponds to highly correlated filters across different images, the authors analyze correlation scores <ref:2607.04839#pg5>. The correlation score ci is defined as the mean pairwise Pearson correlation between the flattened magnitude spectra across all patch pairs <ref:2607.04839#pg5>. The agreement between the rankings Rs and Rc, measured by NDCG@k and Kendall’s tau, confirms that energetic and correlated filters are mostly the same up to a threshold k∗ <ref:2607.04839#pg6>. This behavior is consistent with intuition from handcrafted transform coding where classical transforms concentrate signal energy into a few low-frequency coefficients which are simultaneously the most energetic, and the most consistent across natural images <ref:2607.04839#pg6>.

Developing Low-Complexity Models

If the filters i (J(m)enc,x,(i,. for an image m ∈ D) ranked in the top-k of Rs are highly correlated, then they may be transferable across images <ref:2607.04839#pg6>. The authors compute an averaged filter representation over a subset of image Jacobians to obtain an average Jacobian matrix J∗enc <ref:2607.04839#pg6>. The resulting average top-10 filters show strong similarities across models with different λ values, and the most important filters tend to emphasize vertical and horizontal structures, as well as color-related characteristics <ref:2607.04839#pg6>.

Evaluating Rate-Distortion Trade-off

The final stage compares the Jacobian-based approach with classical transform methods like DCT and KLT. The Jacobian filtering method outperforms the transform-based and achieves PSNR values comparable to the original model, particularly at low BPP rates. The Jacobian approach is shown to achieve a better PSNR–BPP trade-off across all quantization steps <ref:2607.04839#pg6>. However, replacing all sufficient network features with Jacobians can degrade performance, suggesting that more sophisticated or hybrid strategies are needed <ref:2607.04839#pg6>.

Conclusion

The study concludes that a subset of encoder operations is shared across images and can be interpreted as image filters <ref:2607.04839#pg6>. The filters that are most consistent across images are also among those that contribute most to reconstruction energy <ref:2607.04839#pg6>. Using the average filters across images for both encoding and decoding presents results close to the original model, particularly at low bit rates when only the most energetic components are retained <ref:2607.04839#pg6>. The analysis is limited to bias-free ReLU-based architectures, and extension to more general models is planned <ref:2607.04839#pg6>.

References

[1] J. Balle, V. Laparra, and E. P. Simoncelli, “End-to-end optimized image compression,” in 5th International Conference on Learning Representations (ICLR), 2017, pp. 1–27

[2] J. Balle, D. Minnen, S. Singh, S. J. Hwang, and N. Johnston, “Variational image compression with a scale hyperprior,” in 6th International Conference on Learning Representations (ICLR), 2018, pp. 1–23

[3] Y. Yang, S. Mandt, and L. Theis, “An introduction to neural data compression,” Foundations and Trends in Computer Graphics and Vision, vol. 5, pp. 113–200, 2023

[4] M. Gilbert, M. Campos, and M. Campista, “Asymmetric autoencoders: An nn alternative for resource-constrained devices in iot networks,” Ad Hoc Networks, vol. 156, 02 2024

[5] Y. Yang and S. Mandt, “Computationally-efficient neural image compression with shallow decoders,” in 19th International Conference on Computer Vision (ICCV), 2023, pp. 1–23

[6] F. Liang, W. Yu, X. Liu, D. Griffith, and N. Golmie, “Toward edgebased deep learning in industrial internet of things,” IEEE Internet of Things Journal, vol. 7, no. 5, pp. 4329–4341, 2020

[7] V. Hassija, V. Chamola, A. Mahapatra, A. Singal, D. Goel, K. Huang, S. Scardapane, I. Spinelli, M. Mahmud, and A Hussaini “Interpreting black-box models: A review on explainable artificial intelligence,” Cognitive Computation, vol. 16, pp. 45–74, 2024

[8] S. Mohan, Z. Kadkhodaie, E. P. Simoncelli, and C Fernandez-Granda “Robust and interpretable blind image denoising via bias-free convolutional neural networks,” in 8th International Conference on Learning Representations (ICLR), 2020, pp. 1–22

[9] Z. Kadkhodaie, F. Guth, E. P. Simoncelli, and S Mallat “Generalization in diffusion models arises from geometry-adaptive harmonic representations,” in International Conference on Learning Representations (ICLR), 2024

[10] S M Lundberg and S-I Lee “A unified approach to interpreting model predictions,” in Advances in Neural Information Processing Systems (NeurIPS), 2017, pp. 4765–4774

[11] M T Ribeiro, S Singh, and C Guestrin “why should i trust you?: Explaining the predictions of any classifier,” in 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. ACM, 2016, pp. 1135–1144

[12] C M Rodrigues, N Boutry, and L Najman “Transforming gradientbased techniques into interpretable methods,” Pattern Recognition Letters, vol. 184, pp. 66–73, 2024 [Online]. Available: https://www.sciencedirect.

Improvements for AI systems

Bias-free autoencoders can be used to design low-complexity image compression models by extracting universal behaviors through Jacobian analysis, which allows for developing compression tools inspired by high-complexity deep learning architectures.
The improved system can perform image compression with better rate distortion trade-offs because the Jacobian filtering method outperforms transform-based methods like DCT and KLT, achieving comparable PSNR values to the original model, particularly at low bit rates.
A low-complexity compression model can be constructed by combining the top filters from different images, as this approach uses the most correlated filters from one image to process for both encoding and decoding.
The system can select sufficient features for reconstruction based on a stabilization point in PSNR, allowing the retention of only those features that are sufficient for reconstruction quality close to the maximum obtained by the model.
The system can achieve better performance at higher quantization steps by exploiting inter-channel correlations, even when compressing grayscale images, as neural network and Jacobian models maintain better rate-distortion trade-off even in this setting (single channel).