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Influence Dynamics and Stagewise Data Attribution

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📄 Abstract

Abstract: Current training data attribution (TDA) methods treat the influence one sample has on another as static, but neural networks learn in distinct stages that exhibit changing patterns of influence. In this work, we introduce a framework for stagewise data attribution grounded in singular learning theory. We predict that influence can change non-monotonically, including sign flips and sharp peaks at developmental transitions. We first validate these predictions analytically and empirically in a toy model, showing that dynamic shifts in influence directly map to the model's progressive learning of a semantic hierarchy. Finally, we demonstrate these phenomena at scale in language models, where token-level influence changes align with known developmental stages.

Authors (4)

Jin Hwa Lee

Matthew Smith

Maxwell Adam

Jesse Hoogland

Submitted

October 14, 2025

arXiv Category

cs.LG

arXiv PDF

Key Contributions

This paper introduces a framework for stagewise data attribution, grounded in singular learning theory, to address the static nature of current methods. It predicts and validates that influence can change non-monotonically across distinct learning stages, aligning with the model's progressive learning of a semantic hierarchy. The phenomena are demonstrated at scale in language models, showing token-level influence changes that correspond to known developmental stages.

Business Value

Improved interpretability of large models can lead to better debugging, bias detection, and more trustworthy AI systems, crucial for high-stakes applications.

Paper Metadata

Innovation Type

New Framework/Methodology

Deployment Feasibility

Moderate, as it provides a framework for analysis rather than a direct deployment tool.

Limitations Addressed

Current data attribution methods treat influence as static, failing to capture the dynamic, stagewise nature of neural network learning.

Performance Gains

Qualitative demonstration of dynamic influence shifts aligning with learning stages.

Technical Tags

data attributionstagewise learningsingular learning theoryinfluence dynamicslanguage modelssemantic hierarchydevelopmental transitionsnon-monotonic influencetoken-level influencedynamic shifts

Research Topics

Machine Learning InterpretabilityDeep Learning TheoryCausal InferenceNatural Language Processing

Methods & Architectures

Singular Learning TheoryAnalytical ValidationEmpirical ValidationStagewise Data Attribution Framework Language Models

Applications & Tasks

Machine Learning Natural Language Processing AI Interpretability Data AttributionUnderstanding Model Learning DynamicsInterpreting Model Behavior Attributing Influence of Training DataUnderstanding Learning StagesAnalyzing Dynamic Influence Patterns

Related Fields

Machine Learning InterpretabilityCausalityDeep Learning TheoryNatural Language Processing

Keywords

data attributionstagewise learningsingular learning theoryinfluence dynamicslanguage modelsinterpretabilitydeep learningsemantic hierarchydevelopmental stagesnon-monotonictoken influencedynamic analysiscausalitymodel behaviorNLP

Academic Context

#Machine Learning Interpretability#Deep Learning Theory#Causal Inference#Natural Language Processing

Commercial Potential

Potential Products

Model interpretability toolsDebugging platforms for LLMs

Target Industries

TechnologyAI DevelopmentResearch

Use Case Examples

Understanding why a language model makes certain predictionsIdentifying influential training data points at different learning stages

Competitive Edge

Offers a novel, dynamic approach to data attribution that accounts for the temporal evolution of learning, unlike static methods.

Market Opportunity

Growing market for AI interpretability and debugging tools.

Revenue Models

SaaS for AI development platformsconsulting services.

Resource Requirements

Compute Needs

Likely requires significant computation for large-scale language model analysis.

Data Requirements

Large language models and their training data.

Deployment Constraints

Requires access to model internals and training dynamics.

Scalability

Demonstrated at scale in language models.

Production Readiness

Maturity Level

Research/Experimental

Time to Market

1-3 years for tool development.

Patent Potential

Moderate, for the stagewise attribution framework.

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