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Mark Landry

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3 published item(s)

preprint2026arXiv

TabH2O: A Unified Foundation Model for Tabular Prediction

We present TabH2O, a foundation model for tabular data that performs classification and regression in a single forward pass via in-context learning. TabH2O builds on the TabICL architecture with several key modifications: (1) unified training, a single model handles both classification and regression via a dual-head architecture, eliminating the need for separate models and reducing total pretraining cost; (2) single-stage pretraining, training stability improvements (bounded scalable softmax, inter-stage normalization, learnable residual scaling, logit soft-capping) eliminate the need for multi-stage curriculum learning, enabling training with full-length sequences from the start; and (3) noise-aware pretraining, synthetic datasets include explicit noise dimensions to teach the model robustness to irrelevant features. We evaluate TabH2O v1 (29.2M parameters) on the TALENT benchmark (300 datasets), where it achieves an average rank of 2.55 out of 6 evaluated methods, outperforming tuned CatBoost (4.07), H2O AutoML (4.18), and LightGBM (5.08), competitive with TabPFN v2.6 (2.74), and behind TabICL v2 (2.12), while placing in the top-3 on 81% of the testing datasets across classification and regression tasks.

preprint2020arXiv

Landscape Theory for Schrödinger Operators with General Hopping Terms on a Finite Lattice

Findings by M. L. Lyra, S. Mayboroda and M. Filoche relate invertibility and positivity of a class of discrete Schrödinger matrices with the existence of the "Landscape Function", which provides an upper bound on all eigenvectors simultaneously. Their argument is based on the variational principles. We consider an alternative method of proving these results, based on the power series expansion, and demonstrate that it naturally extends the original findings to the case of long range operators. The method of proof by power series expansion can also be employed in other scenarios, such as higher dimensional lattices.

preprint2020arXiv

The Multiple Points of Fractional Brownian Motion

Nils Tongring (1987) proved sufficient conditions for a compact set to contain $k$-tuple points of a Brownian motion. In this paper, we extend these findings to the fractional Brownian motion. Using the property of strong local nondeterminism, we show that if $B$ is a fractional Brownian motion in $\mathbb{R}^d$ with Hurst index $H$ such that $Hd=1$, and $E$ is a fixed, nonempty compact set in $\mathbb{R}^d$ with positive capacity with respect to the function $ϕ(s) = (\log_+(1/s))^k$, then $E$ contains $k$-tuple points with positive probability. For the $Hd > 1$ case, the same result holds with the function replaced by $ϕ(s) = s^{-k(d-1/H)}$.