Towards the Three-Phase Dynamics of Generalization Power of a DNN

ICLR 2026 Conference SubmissionAnonymous Authors
Generalization AnalysisLearning DynamicsDeep Learning Theory
Abstract:

This paper addresses the core challenge in the field of symbolic generalization, i.e., how to define, quantify, and track the dynamics of generalizable and non-generalizable interactions encoded by a DNN throughout the training process. Specifically, this work builds upon the recent theoretical achievement in explainable AI, which proves that the detailed inference patterns of DNNs can be strictly rewritten as a small number of AND-OR interaction patterns. Based on this, we propose an efficient method to quantify the generalization power of each interaction, and we discover a distinct three-phase dynamics of the generalization power of interactions during training. In particular, the early phase of training typically removes noisy and non-generalizable interactions and learns simple and generalizable interactions. The second and the third phases tend to capture increasingly complex interactions that are harder to generalize. Experimental results verify that the learning of non-generalizable interactions is the direct cause for the gap between the training and testing losses.

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Overview

Overall Novelty Assessment

The paper proposes an efficient method to quantify generalization power of individual interactions in DNNs and discovers a three-phase learning dynamic. It resides in the 'Training Dynamics and Temporal Evolution of Interactions' leaf, which contains five papers total including the original work. This leaf sits within the broader 'Interaction-Based Explanation and Generalization Theory' branch, indicating a moderately populated research direction focused specifically on temporal aspects of interaction learning. The taxonomy shows this is a specialized but active area, distinct from static interaction extraction or domain-specific applications.

The paper's leaf neighbors include works examining two-phase dynamics, symbolic interaction evolution, and layerwise knowledge propagation. The broader parent branch encompasses core interaction theory, generalization power quantification methods, and analysis of confusing samples. Adjacent top-level branches explore information-theoretic perspectives, feature selection techniques, and architectural generalization strategies. The taxonomy structure reveals that while interaction-based explanations form a coherent research thread, this work's focus on three-phase temporal dynamics positions it at the intersection of theoretical interaction frameworks and empirical training analysis, bridging static quantification methods with dynamic learning characterization.

Among thirty candidates examined through semantic search, none clearly refuted any of the three core contributions. For the quantification method, ten candidates were reviewed with zero refutable overlaps. The three-phase dynamics discovery similarly examined ten papers without finding prior work describing this specific temporal pattern. The causal link between non-generalizable interactions and loss gaps also showed no clear refutation across ten candidates. This suggests the specific combination of efficient quantification, three-phase characterization, and causal analysis represents a novel synthesis, though the limited search scope means potentially relevant work outside the top-thirty semantic matches may exist.

Based on the examined literature, the work appears to offer substantive contributions within its specialized research area. The taxonomy reveals a moderately crowded field of interaction-based generalization studies, but the specific three-phase temporal characterization distinguishes this from prior two-phase analyses. The analysis covers top-thirty semantic matches plus citation expansion, providing reasonable confidence in novelty claims while acknowledging that exhaustive coverage of all related training dynamics research remains beyond scope. The lack of refutable candidates across all contributions suggests meaningful differentiation from examined prior work.

Taxonomy

Core-task Taxonomy Papers
38
3
Claimed Contributions
30
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: Quantifying and tracking generalization power of interactions in deep neural networks. The field encompasses diverse perspectives on how neural networks learn and generalize through feature interactions. The taxonomy reveals several major branches: Interaction-Based Explanation and Generalization Theory examines how interactions evolve during training and contribute to model performance; Information-Theoretic and Probabilistic Perspectives formalize generalization via concepts like information bottlenecks and Bayesian frameworks; Feature Interaction Detection and Selection Methods develop techniques to identify and leverage important feature combinations; Domain-Specific Interaction Modeling applies these ideas to specialized tasks; Generalization Enhancement strategies propose architectural and training innovations; and Alternative Representation and Complexity Frameworks explore different mathematical lenses for understanding learning dynamics. Works like Generalizable Interaction Primitives[1] and Interactive Concepts[2] illustrate how researchers formalize interaction structures, while Generalization Mystery[6] and Generalized Information Bottleneck[4] reflect theoretical efforts to explain why networks generalize. A particularly active line of research focuses on the temporal evolution of interactions during training. Three-Phase Dynamics[0] sits within this cluster, examining how interaction patterns shift across distinct learning phases. This work closely relates to Two-Phase Dynamics[18] and Symbolic Interactions Dynamics[11], which similarly track how networks transition between different learning regimes. Nearby, Layerwise Knowledge Change[3] and Tracking Knowledge Layers[36] investigate how knowledge propagates through network depth over time. The central tension across these studies concerns whether interaction dynamics follow universal patterns or depend heavily on architecture and task. Three-Phase Dynamics[0] contributes by identifying a three-stage progression, contrasting with the two-phase characterization in related work and offering a more granular view of how generalizable interactions emerge and stabilize during optimization.

Claimed Contributions

Efficient method to quantify generalization power of individual interactions

The authors introduce a method that quantifies the generalization power of each individual interaction encoded by a DNN by measuring its transferability to a baseline DNN trained on testing samples, avoiding computationally prohibitive exhaustive search across test samples.

10 retrieved papers
Discovery of three-phase dynamics of generalization power during training

The authors identify and characterize a three-phase pattern in how the generalization power of interactions evolves throughout DNN training: early removal of non-generalizable interactions and learning of simple generalizable ones, followed by learning increasingly complex and less generalizable interactions, and finally learning predominantly non-generalizable interactions that cause overfitting.

10 retrieved papers
Causal link between non-generalizable interactions and training-testing loss gap

The authors establish that non-generalizable interactions directly cause the gap between training and testing losses, demonstrating through experiments that removing these interactions significantly reduces this gap by primarily increasing training loss while minimally affecting testing loss.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Efficient method to quantify generalization power of individual interactions

The authors introduce a method that quantifies the generalization power of each individual interaction encoded by a DNN by measuring its transferability to a baseline DNN trained on testing samples, avoiding computationally prohibitive exhaustive search across test samples.

Contribution

Discovery of three-phase dynamics of generalization power during training

The authors identify and characterize a three-phase pattern in how the generalization power of interactions evolves throughout DNN training: early removal of non-generalizable interactions and learning of simple generalizable ones, followed by learning increasingly complex and less generalizable interactions, and finally learning predominantly non-generalizable interactions that cause overfitting.

Contribution

Causal link between non-generalizable interactions and training-testing loss gap

The authors establish that non-generalizable interactions directly cause the gap between training and testing losses, demonstrating through experiments that removing these interactions significantly reduces this gap by primarily increasing training loss while minimally affecting testing loss.