Fibrillar adhesion, observed in animals like beetles, spiders, and geckos, relies on nanoscopic or microscopic fibrils to enhance surface adhesion via 'contact splitting.' This concept has inspired engineering applications across robotics, transportation, and medicine. Recent studies suggest that functional grading of fibril properties can improve adhesion, but this is a complex design challenge that has only been explored in simplified geometries. While machine learning (ML) has gained traction in adhesive design, no previous attempts have targeted fibril-array scale optimization. In this study, we propose an ML-based tool that optimizes the distribution of fibril compliance to maximize adhesive strength. Our tool, featuring two deep neural networks (DNNs), recovers previous design results for simple geometries and introduces novel solutions for complex configurations. The Predictor DNN estimates adhesive strength based on random compliance distributions, while the Designer DNN optimizes compliance for maximum strength using gradient-based optimization. Our method significantly reduces test error and accelerates the optimization process, offering a high-performance solution for designing fibrillar adhesives and micro-architected materials aimed at fracture resistance by achieving equal load sharing (ELS).

We investigate practical and scalable algorithms for training large language models (LLMs) with user-level differential privacy (DP) in order to provably safeguard all the examples contributed by each user. We study two variants of DP-SGD with: (1) example-level sampling (ELS) and per-example gradient clipping, and (2) user-level sampling (ULS) and per-user gradient clipping. We derive a novel user-level DP accountant that allows us to compute provably tight privacy guarantees for ELS. Using this, we show that while ELS can outperform ULS in specific settings, ULS generally yields better results when each user has a diverse collection of examples. We validate our findings through experiments in synthetic mean estimation and LLM fine-tuning tasks under fixed compute budgets. We find that ULS is significantly better in settings where either (1) strong privacy guarantees are required, or (2) the compute budget is large. Notably, our focus on LLM-compatible training algorithms allows us to scale to models with hundreds of millions of parameters and datasets with hundreds of thousands of users.

A fundamental challenge for machine learning models is how to generalize learned models for out-of-distribution (OOD) data. Among various approaches, exploiting invariant features by Domain Adversarial Training (DAT) received widespread attention. Despite its success, we observe training instability from DAT, mostly due to over-confident domain discriminator and environment label noise. To address this issue, we proposed Environment Label Smoothing (ELS), which encourages the discriminator to output soft probability, which thus reduces the confidence of the discriminator and alleviates the impact of noisy environment labels. We demonstrate, both experimentally and theoretically, that ELS can improve training stability, local convergence, and robustness to noisy environment labels. By incorporating ELS with DAT methods, we are able to yield state-of-art results on a wide range of domain generalization/adaptation tasks, particularly when the environment labels are highly noisy.

We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past. We establish that when the underlying matrix has rank $r=1$, has positive bounded entries, and the graph $\mathcal{G}$ underlying the revealed entries has bounded degree and diameter which is at most logarithmic in the size of the matrix, both algorithms succeed in reconstructing the matrix approximately in polynomial time starting from an arbitrary initialization. We further provide simulation results which suggest that the second algorithm which is based on the message passing type updates, performs significantly better.