Two steps of gradient descent on first-layer weights in linear-width two-layer networks produce a spiked random matrix with floor(alpha2/(1/2-alpha1)) outliers, each a learned direction, and batch reuse allows capturing directions with information exponent exceeding one.
arXiv preprint arXiv:2301.02679 , year=
10 Pith papers cite this work. Polarity classification is still indexing.
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EGD equalizes gradient speeds across singular directions, eliminating or shortening grokking plateaus on modular addition and sparse parity problems.
An exposure-based split on BLiMP data reveals delayed generalization in five grammatical phenomena during LLM pre-training, with post-generalization shifts in concept vector predictiveness and attention patterns.
An auxiliary modulus during training reduces wrap-around issues and preserves train-test input distributions, enabling better accuracy and sample efficiency for large N and q in modular addition learning.
Diverse language models converge on similar periodic number features with a two-tier hierarchy of Fourier sparsity and geometric separability, acquired via language co-occurrences or multi-token arithmetic.
Deep sequence models develop geometric memory in embeddings that encodes novel global relationships, transforming l-fold composition tasks into 1-step navigation via a natural spectral bias connected to Node2Vec.
Eigenanalysis of the empirical NTK surfaces feature directions that align with Fourier features in modular addition networks and grammatical features in Gemma-3-270M, outperforming PCA baselines on activations.
Experiments on modular arithmetic with heavy label noise show that over-parameterized networks form a distributed internal generalization structure that can be extracted via frequency methods to achieve high accuracy despite 80% noise.
The paper introduces a taxonomy of AI safety for LLMs organized into Trustworthy AI, Responsible AI, and Safe AI perspectives, accompanied by a review of state-of-the-art methods, challenges, and future directions.
A mechanics of the learning process is emerging in deep learning theory, characterized by dynamics, coarse statistics, and falsifiable predictions across idealized settings, limits, laws, hyperparameters, and universal behaviors.
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Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent
Two steps of gradient descent on first-layer weights in linear-width two-layer networks produce a spiked random matrix with floor(alpha2/(1/2-alpha1)) outliers, each a learned direction, and batch reuse allows capturing directions with information exponent exceeding one.
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Egalitarian Gradient Descent: A Simple Approach to Accelerated Grokking
EGD equalizes gradient speeds across singular directions, eliminating or shortening grokking plateaus on modular addition and sparse parity problems.
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A Pre-Training Analogue of Grokking in Language Models: Tracing Delayed Grammatical Generalization
An exposure-based split on BLiMP data reveals delayed generalization in five grammatical phenomena during LLM pre-training, with post-generalization shifts in concept vector predictiveness and attention patterns.
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Learning Large-Scale Modular Addition with an Auxiliary Modulus
An auxiliary modulus during training reduces wrap-around issues and preserves train-test input distributions, enabling better accuracy and sample efficiency for large N and q in modular addition learning.
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Convergent Evolution: How Different Language Models Learn Similar Number Representations
Diverse language models converge on similar periodic number features with a two-tier hierarchy of Fourier sparsity and geometric separability, acquired via language co-occurrences or multi-token arithmetic.
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Deep sequence models tend to memorize geometrically; it is unclear why
Deep sequence models develop geometric memory in embeddings that encodes novel global relationships, transforming l-fold composition tasks into 1-step navigation via a natural spectral bias connected to Node2Vec.
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Feature Identification via the Empirical NTK
Eigenanalysis of the empirical NTK surfaces feature directions that align with Fourier features in modular addition networks and grammatical features in Gemma-3-270M, outperforming PCA baselines on activations.
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Unveiling Memorization-Generalization Coexistence: A Case Study on Arithmetic Tasks with Label Noise
Experiments on modular arithmetic with heavy label noise show that over-parameterized networks form a distributed internal generalization structure that can be extracted via frequency methods to achieve high accuracy despite 80% noise.
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AI Safety Landscape for Large Language Models: Taxonomy, State-of-the-art, and Future Directions
The paper introduces a taxonomy of AI safety for LLMs organized into Trustworthy AI, Responsible AI, and Safe AI perspectives, accompanied by a review of state-of-the-art methods, challenges, and future directions.
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There Will Be a Scientific Theory of Deep Learning
A mechanics of the learning process is emerging in deep learning theory, characterized by dynamics, coarse statistics, and falsifiable predictions across idealized settings, limits, laws, hyperparameters, and universal behaviors.