Research

My research combines approximation theory, statistical learning theory, harmonic analysis, and kernel methods to identify the structural conditions under which neural networks learn efficiently.

Learning rates for structured neural networks

My doctoral research established excess-risk bounds for classification, ranking, and pairwise learning. These analyses combine constructive approximation estimates with statistical complexity bounds to show how target regularity, network architecture, and data geometry determine learning rates.

Compositionality and learned representations

Current work investigates how low-dimensional representations, hierarchical composition, and sparsity can mitigate the curse of dimensionality. This work connects these structural properties to statistical and computational guarantees.

Recent Work

The illustrated projects below highlight selected recent work. A complete list of papers is available on the Publications page.

Feature learning with hyper-kernels

We developed hyper-kernel ridge regression to incorporate feature learning into kernel methods through a learnable matrix B, with KB(x,x′) = K(Bx,Bx′). For multi-index models f(x) = g(Bx), the method combines a learned low-dimensional representation with a nonlinear predictor.

Our analysis establishes statistical guarantees and convergence results for two alternating optimization algorithms, exploiting the structure of kernel methods.

Hyper-kernel regression paper

A hierarchical neural network mirroring a sparse compositional graph: low-dimensional components combine input features through successive layers.

Sparse compositional learning

Representing hierarchical targets by directed acyclic graphs, we study deep networks that exploit sparse compositional structure.

The resulting approximation and excess-risk bounds use Frobenius norms to control network complexity. They relate statistical performance to the structure of local components, accommodate overparameterized architectures, and identify conditions under which composition mitigates the curse of dimensionality.

Sparse compositional learning paper · NeurIPS 2026 (accepted)

Functional-learning pipeline: sampled input functions are discretized, encoded by a convolutional neural network into sparse coefficients, and mapped to the output by a deep neural network decoder.

Learning nonlinear functionals

Learning from function-valued inputs poses an infinite-dimensional problem. Our encoder–decoder architectures extract finite-dimensional representations from sampled inputs and use neural networks to approximate the target functional.

Spherical analysis and sparsity-aware constructions provide approximation guarantees that account for input regularity, discretization, and network architecture.

Sparse-aware networks · Spherical analysis

Future directions

Building on these results, I plan to investigate transformers as adaptive kernel machines, compositional representations for in-context learning, and the dynamics of feature learning during training. A central objective is to derive excess-risk bounds that distinguish the contributions of pretraining, context length, and computational accuracy.

Our work on representation alignment and its connections to multimodal learning motivates a complementary question: when can learned representations support transfer across models and tasks?

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