in prevalent cohort studies with follow-up, the time-to-event outcome is subject to left truncation leading to selection bias. for estimation of the distribution of time-to-event, conventional methods adjusting for left truncation tend to rely on the (quasi-)independence assumption that the truncation time and the event time are ``independent" on the observed region. this assumption is violated when there is dependence between the truncation time and the event time possibly induced by measured covariates. inverse probability of truncation weighting leveraging covariate information can be used in this case, but it is sensitive to misspecification of the truncation model. in this work, we apply the semiparametric theory to find the efficient influence curve of an expected  (arbitrarily transformed) survival time in the presence of covariate-induced dependent left truncation. we then use it to construct estimators that are shown to enjoy double-robustness properties. our work represents the first attempt to construct doubly robust estimators in the presence of left truncation, which does not fall under the established framework of coarsened data where doubly robust approaches are developed. we provide technical conditions for the asymptotic properties that appear to not have been carefully examined in the literature for time-to-event data, and study the estimators via extensive simulation. we apply the estimators to two data sets from practice, with different right-censoring patterns.

 in this talk, i will discuss two topics that i have been exploring at the intersection of deep learning and dynamical systems.
    i will first present my recent research on ml-based dynamics learning and surrogate modeling. to circumvent difficulties faced by dynamics models from first principles or standard neural networks, a recent research direction has been considering a hybrid approach, where physics laws and geometric properties are encoded in the design of the deep learning architectures or in the learning process. available physics prior knowledge can be used to construct physics-constrained neural networks with improved design and efficiency and a better generalization capacity, which can take advantage of the function approximation power of deep learning methods to deal with incomplete knowledge. here, i will introduce two different ways to incorporate prior knowledge about the structure of a dynamical system in a strong way to obtain structure-preserving deep learning architectures for dynamics learning and surrogate modeling.
    in the second part of the talk, i will discuss a specific way to leverage deep learning techniques to accelerate the computation of high-resolution solutions of parametric partial differential equations. in numerous contexts, high-resolution solutions are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain using traditional numerical integration methods due to limited computational resources. here, i will introduce a new approach based on the use of neural operators to obtain high-resolution solution operators.

a group is said to be frobenius stable if every function from the group to unitaries that is "almost multiplicative" in the point-frobenius norm topology is "close" to a genuine representation of the group in the same topology. in this talk, i will summarize my proof that finitely generated nilpotent groups are frobenius stable if and only if they are virtually cyclic. i will also explain what the same techniques say about operator norm. this generalizes explicit counterexamples developed by voiculescu and kazhdan. 

i will introduce some interacting particle systems on finite graphs and cayley graphs of countable groups, and discuss how sofic entropy helps understand them.

more specifically, we consider two notions of statistical equilibrium: an "equilibrium state" maximizes a functional called the pressure while a "gibbs state" satisfies a local equilibrium condition. on amenable groups (for example, integer lattices) these notions are equivalent, under some assumptions on the interaction. barbieri and meyerovitch have recently shown that one direction holds for general sofic groups: equilibrium states are always gibbs.

i will show that the converse fails in the simplest nontrivial case: the free boundary ising state on a free group (an infinite regular tree) is gibbs but not equilibrium. i will also discuss what this says about gibbs states on finite locally-tree-like graphs: it is well-known that their local statistics are described by some gibbs state on the infinite tree, but in fact they must locally look like a mixture of equilibrium states. this constraint can be used to compute local limits of finitary gibbs states for a few interactions.

we consider general mixed $p$-spin mean field spin glass models and provide a method to prove that the spectral gap of the dirichlet form associated with the gibbs measure is of order one at sufficiently high temperature. our proof is based on an iteration scheme relating the spectral gap of the $n$-spin system to that of suitably conditioned subsystems. based on joint work w/ c. brennecke, c. xu, and h-t yau

in this talk i’ll discuss recent work studying benign overfitting in two-layer relu networks trained using gradient descent and hinge loss on noisy data for binary classification. unlike logistic or exponentially tailed losses the implicit bias in this setting is poorly understood and therefore our results and techniques are distinct from other recent and concurrent works on this topic. in particular, we consider linearly separable data for which a relatively small proportion of labels are corrupted and identify conditions on the margin of the clean data which give rise to three distinct training outcomes: benign overfitting, in which zero loss is achieved and with high probability test data is classified correctly; overfitting, in which zero loss is achieved but test data is misclassified with probability lower bounded by a constant; and non-overfitting, in which clean points, but not corrupt points, achieve zero loss and again with high probability test data is classified correctly. our analysis provides a fine-grained description of the dynamics of neurons throughout training and reveals two distinct phases: in the first phase clean points achieve close to zero loss, in the second phase clean points oscillate on the boundary of zero loss while corrupt points either converge towards zero loss or are eventually zeroed by the network. we prove these results using a combinatorial approach that involves bounding the number of clean versus corrupt updates across these phases of training.