Publications

Selected List

Training Dynamics of Deep Neural Networks (DNNs)

• Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise
• Signal propagation in transformers: Theoretical perspectives and the role of rank collapse

Loss Landscape of DNNs

• Loss Landscape Characterization of Neural Networks without Over-Parametrization
• Theoretical characterisation of the Gauss-Newton conditioning in Neural Networks

Generalization

• A Comprehensive Analysis on the Learning Curve in Kernel Ridge Regression
• Characterizing Overfitting in Kernel Ridgeless Regression Through the Eigenspectrum

Non-convex Optimization

• Sub-sampled Cubic Regularization for Non-convex Optimization

DNN Architectural Design

• Exponential convergence rates for Batch Normalization: The power of length-direction decoupling in non-convex optimization
• Batch Normalization Provably Avoids Rank Collapse for Randomly Initialised Deep Networks