A Probabilistic Theory of Deep Learning
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Abstract (arXiv)
A grand challenge in machine learning is the development of computational algorithms that match or outperform humans in perceptual inference tasks that are complicated by nuisance variation. For instance, visual object recognition involves the unknown object position, orientation, and scale in object recognition while speech recognition involves the unknown voice pronunciation, pitch, and speed. Recently, a new breed of deep learning algorithms have emerged for high-nuisance inference tasks that routinely yield pattern recognition systems with near- or super-human capabilities. But a fundamental question remains: Why do they work? Intuitions abound, but a coherent framework for understanding, analyzing, and synthesizing deep learning architectures has remained elusive. We answer this question by developing a new probabilistic framework for deep learning based on the Deep Rendering Model: a generative probabilistic model that explicitly captures latent nuisance variation. By relaxing the generative model to a discriminative one, we can recover two of the current leading deep learning systems, deep convolutional neural networks and random decision forests, providing insights into their successes and shortcomings, as well as a principled route to their improvement.
Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Apr 2015.
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Citing papers per year: 2021: 4; 2022: 1; 2023: 1; 2024: 1; 2025: 2; 2026: 2.
11 papers.
- 2023How Deep Neural Networks Learn Compositional Data: The Random Hierarchy Modelcited by 70
- 2021The staircase property: How hierarchical structure can guide deep learningcited by 62
- 2022The Neural Race Reduction: Dynamics of Abstraction in Gated Networkscited by 37
- 2021Improving Transformers with Probabilistic Attention Keyscited by 28
- 2024Probing the Latent Hierarchical Structure of Data via Diffusion Modelscited by 25
- 2021When are Deep Networks really better than Decision Forests at small sample sizes, and how?cited by 6
- 2021Category-orthogonal object features guide information processing in recurrent neural networks trained for object categorizationcited by 2
- 2025Noise Sensitivity and Learning Lower Bounds for Hierarchical Functionscited by 2
- 2026Statistical Properties of Training & Generalizationcited by 2
- 2026Self-supervised local learning rules learn the hidden hierarchical structure of high-dimensional datacited by 1
- 2025FL-CLEANER: byzantine and backdoor defense by CLustering Errors of Activation maps in Non-iid fedErated leaRningcited by 0
- 2026Statistical Properties of Training & Generalization18 Jun 2026
- 2026Self-supervised local learning rules learn the hidden hierarchical structure of high-dimensional data18 May 2026
- 2025Noise Sensitivity and Learning Lower Bounds for Hierarchical Functions7 Feb 2025
- 2025FL-CLEANER: byzantine and backdoor defense by CLustering Errors of Activation maps in Non-iid fedErated leaRning21 Jan 2025
- 2024Probing the Latent Hierarchical Structure of Data via Diffusion Models17 Oct 2024
- 2023How Deep Neural Networks Learn Compositional Data: The Random Hierarchy Model5 Jul 2023
- 2022The Neural Race Reduction: Dynamics of Abstraction in Gated Networks21 Jul 2022
- 2021Category-orthogonal object features guide information processing in recurrent neural networks trained for object categorization15 Nov 2021
- 2021Improving Transformers with Probabilistic Attention Keys16 Oct 2021
- 2021When are Deep Networks really better than Decision Forests at small sample sizes, and how?31 Aug 2021
- 2021The staircase property: How hierarchical structure can guide deep learning24 Aug 2021