16 papers
When Do Attention Circuits Form? Developmental Trajectories of Capability and Attention-Sink Emergence Across Three 1B-ClassArchitectures
Yongzhong Xu
We track the developmental trajectory of attention-head circuit formation across three 1B-class language models spanning two architecture families (dense transformer, mixture-of-ex…
Closure-Validated Circuit Discovery in Attention Heads: Co-activation Proposes, Ablation Disposes
Yongzhong Xu
Interpretability increasingly treats groups of components, not individual units, as the basic object, and proposes to find them by clustering co-activation statistics. We ask wheth…
Pattern Selectivity is Not Task-Causal Structure: A Cross-Architecture Mechanistic Study of Composed-Task Circuits in 1B-Class Language Models
Yongzhong Xu
We test whether a single screen-and-ablate recipe -- identify attention-head circuits by task-pattern selectivity, then verify by causal ablation against a matched-random null -- p…
Spectral Probe-Circuits: A Three-Step Recipe for Identifying Attention-Head Circuits in Pretrained Transformers
Yongzhong Xu
We present a three-step recipe for identifying attention-head circuits in pretrained transformers. A per-head spectral signal -- the time-integrated participation ratio of each hea…
Feature Repulsion and Spectral Lock-in: An Empirical Study of Two-Layer Network Grokking
Yongzhong Xu
Tian (2025) proves a repulsion theorem (Theorem 6) for the matrix during the interactive feature-learning stage of grokking: si…
Gradient-Direction Sensitivity Reveals Linear-Centroid Coupling Hidden by Optimizer Trajectories
Yongzhong Xu
We show that replacing the rolling SVD of AdamW updates with a rolling SVD of loss gradients changes the diagnostic by 1-2 orders of magnitude. Performing SVD on the loss gradient…
The Lifecycle of the Spectral Edge: From Gradient Learning to Weight-Decay Compression
Yongzhong Xu
We decompose the spectral edge -- the dominant direction of the Gram matrix of parameter updates -- into its gradient and weight-decay components during grokking in two sequence ta…
Spectral Edge Dynamics Reveal Functional Modes of Learning
Yongzhong Xu
Training dynamics during grokking concentrate along a small number of dominant update directions -- the spectral edge -- which reliably distinguishes grokking from non-grokking reg…
The Geometry of Multi-Task Grokking: Transverse Instability, Superposition, and Weight Decay Phase Structure
Yongzhong Xu
Grokking -- the abrupt transition from memorization to generalization long after near-zero training loss -- has been studied mainly in single-task settings. We extend geometric ana…
Early-Warning Signals of Grokking via Loss-Landscape Geometry
Yongzhong Xu
Grokking -- the abrupt transition from memorization to generalization after prolonged training -- has been linked to confinement on low-dimensional execution manifolds in modular a…
Low-Dimensional and Transversely Curved Optimization Dynamics in Grokking
Yongzhong Xu
Grokking -- the delayed transition from memorization to generalization in small algorithmic tasks -- remains poorly understood. We present a geometric analysis of optimization dyna…
Spectral Edge Dynamics of Training Trajectories: Signal--Noise Geometry Across Scales
Yongzhong Xu
Despite hundreds of millions of parameters, transformer training trajectories evolve within only a few coherent directions. We introduce Spectral Edge Dynamics (SED) to quantify th…
Optimizer-Induced Low-Dimensional Drift and Transverse Dynamics in Transformer Training
Yongzhong Xu
We analyze cumulative parameter trajectories of transformer training under AdamW and identify a dominant low-dimensional drift direction ("backbone") that captures 60--80% of long-…
Spectral Edge Dynamics: An Analytical-Empirical Study of Phase Transitions in Neural Network Training
Yongzhong Xu
We develop the spectral edge analysis: phase transitions in neural network training -- grokking, capability gains, loss plateaus -- are controlled by the spectral gap of the rollin…
Global Low-Rank, Local Full-Rank: The Holographic Encoding of Learned Algorithms
Yongzhong Xu
Grokking -- the abrupt transition from memorization to generalization after extended training -- has been linked to the emergence of low-dimensional structure in learning dynamics.…
Low-Dimensional Execution Manifolds in Transformer Learning Dynamics: Evidence from Modular Arithmetic Tasks
Yongzhong Xu
We investigate the geometric structure of learning dynamics in overparameterized transformer models through carefully controlled modular arithmetic tasks. Our primary finding is th…