# Understanding Learning Dynamics Through Structured Representations

arXiv: https://arxiv.org/abs/2508.02126 · HTML: https://mlsanity.com/paper/2508.02126/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 28 references that are in the map.
- First posted on arXiv 4 Aug 2025.

## Builds on (most cited first, 25 of 25)

- [Understanding plasticity in neural networks](https://mlsanity.com/paper/2303.01486/) (2023)
- [On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topology](https://mlsanity.com/paper/2302.02941/) (2023)
- [Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability](https://mlsanity.com/paper/2209.15594/) (2022)
- [Signal Propagation in Transformers: Theoretical Perspectives and the Role of Rank Collapse](https://mlsanity.com/paper/2206.03126/) (2022)
- [How Transformers Learn Causal Structure with Gradient Descent](https://mlsanity.com/paper/2402.14735/) (2024)
- [How Does Information Bottleneck Help Deep Learning?](https://mlsanity.com/paper/2305.18887/) (2023)
- [How Do Transformers Learn Topic Structure: Towards a Mechanistic Understanding](https://mlsanity.com/paper/2303.04245/) (2023)
- [Disentangling the Causes of Plasticity Loss in Neural Networks](https://mlsanity.com/paper/2402.18762/) (2024)
- [Gradient flow dynamics of shallow ReLU networks for square loss and orthogonal inputs](https://mlsanity.com/paper/2206.00939/) (2022)
- [Anti-Symmetric DGN: a stable architecture for Deep Graph Networks](https://mlsanity.com/paper/2210.09789/) (2022)
- [The Implicit Regularization of Dynamical Stability in Stochastic Gradient Descent](https://mlsanity.com/paper/2305.17490/) (2023)
- [Neural Redshift: Random Networks are not Random Functions](https://mlsanity.com/paper/2403.02241/) (2024)
- [The SSL Interplay: Augmentations, Inductive Bias, and Generalization](https://mlsanity.com/paper/2302.02774/) (2023)
- [Stochastic Collapse: How Gradient Noise Attracts SGD Dynamics Towards Simpler Subnetworks](https://mlsanity.com/paper/2306.04251/) (2023)
- [The Neural Race Reduction: Dynamics of Abstraction in Gated Networks](https://mlsanity.com/paper/2207.10430/) (2022)
- [Is a Modular Architecture Enough?](https://mlsanity.com/paper/2206.02713/) (2022)
- [Implicit Regularization in Hierarchical Tensor Factorization and Deep Convolutional Neural Networks](https://mlsanity.com/paper/2201.11729/) (2022)
- [Structured Neural Networks for Density Estimation and Causal Inference](https://mlsanity.com/paper/2311.02221/) (2023)
- [Singular Value Perturbation and Deep Network Optimization](https://mlsanity.com/paper/2203.03099/) (2022)
- [Designing Stable Neural Networks using Convex Analysis and ODEs](https://mlsanity.com/paper/2306.17332/) (2023)
- [Low-Rank Learning by Design: the Role of Network Architecture and Activation Linearity in Gradient Rank Collapse](https://mlsanity.com/paper/2402.06751/) (2024)
- [Deep Architecture Connectivity Matters for Its Convergence: A Fine-Grained Analysis](https://mlsanity.com/paper/2205.05662/) (2022)
- [Learning Stable Graph Neural Networks via Spectral Regularization](https://mlsanity.com/paper/2211.06966/) (2022)
- [Relational Constraints On Neural Networks Reproduce Human Biases towards Abstract Geometric Regularity](https://mlsanity.com/paper/2309.17363/) (2023)
- [Structured Transformations for Stable and Interpretable Neural Computation](https://mlsanity.com/paper/2508.00127/) (2025)

## Built on by (most cited first, 1 of 1)

- [Cross-Model Semantics in Representation Learning](https://mlsanity.com/paper/2508.03649/) (2025)

## Abstract (arXiv)

While modern deep networks have demonstrated remarkable versatility, their training dynamics remain poorly understood--often driven more by empirical tweaks than architectural insight. This paper investigates how internal structural choices shape the behavior of learning systems. Building on prior efforts that introduced simple architectural constraints, we explore the broader implications of structure for convergence, generalization, and adaptation. Our approach centers on a family of enriched transformation layers that incorporate constrained pathways and adaptive corrections. We analyze how these structures influence gradient flow, spectral sensitivity, and fixed-point behavior--uncovering mechanisms that contribute to training stability and representational regularity. Theoretical analysis is paired with empirical studies on synthetic and structured tasks, demonstrating improved robustness, smoother optimization, and scalable depth behavior. Rather than prescribing fixed templates, we emphasize principles of tractable design that can steer learning behavior in interpretable ways. Our findings support a growing view that architectural design is not merely a matter of performance tuning, but a critical axis for shaping learning dynamics in scalable and trustworthy neural systems.