Federated learning is a distributed paradigm that aims at training models using samples distributed across multiple users in a network while keeping the samples on users' devices with the aim of efficiency and protecting users privacy. In such settings, the training data is often statistically heterogeneous and manifests various distribution shifts across users, which degrades the performance of the learnt model. The primary goal of this paper is to develop a robust federated learning algorithm that achieves satisfactory performance against distribution shifts in users' samples. To achieve this goal, we first consider a structured affine distribution shift in users' data that captures the device-dependent data heterogeneity in federated settings. This perturbation model is applicable to various federated learning problems such as image classification where the images undergo device-dependent imperfections, e.g.

Multiple Instance Learning (MIL) is a sub-domain of classification problems with positive and negative labels and a bag of inputs, where the label is positive if and only if a positive element is contained within the bag, and otherwise is negative. Training in this context requires associating the bag-wide label to instance-level information, and implicitly contains a causal assumption and asymmetry to the task (i.e., you can't swap the labels without changing the semantics). MIL problems occur in healthcare (one malignant cell indicates cancer), cyber security (one malicious executable makes an infected computer), and many other tasks. In this work, we examine five of the most prominent deep-MIL models and find that none of them respects the standard MIL assumption. They are able to learn anti-correlated instances, i.e., defaulting to positive labels until seeing a negative counter-example, which should not be possible for a correct MIL model.

We propose a new approach to automated theorem proving where an AlphaZero-style agent is self-training to refine a generic high-level expert strategy expressed as a nondeterministic program. An analogous teacher agent is self-training to generate tasks of suitable relevance and difficulty for the learner. This allows leveraging minimal amounts of domain knowledge to tackle problems for which training data is unavailable or hard to synthesize. As a specific illustration, we consider loop invariant synthesis for imperative programs and use neural networks to refine both the teacher and solver strategies.

This paper examines replication portfolio construction in incomplete markets - a key problem in financial engineering with applications in pricing, hedging, balance sheet management, and energy storage planning. We model this as a two-player game between an investor and the market, where the investor makes strategic bets on future states while the market reveals outcomes. Inspired by the success of Monte Carlo Tree Search in stochastic games, we introduce an AlphaZero-based system and compare its performance to deep hedging - a widely used industry method based on gradient descent. Through theoretical analysis and experiments, we show that deep hedging struggles in environments where the $Q$-function is not subject to convexity constraints - such as those involving non-convex transaction costs, capital constraints, or regulatory limitations - converging to local optima. We construct specific market environments to highlight these limitations and demonstrate that AlphaZero consistently finds near-optimal replication strategies. On the theoretical side, we establish a connection between deep hedging and convex optimization, suggesting that its effectiveness is contingent on convexity assumptions. Our experiments further suggest that AlphaZero is more sample-efficient - an important advantage in data-scarce, overfitting-prone derivative markets.

Sparse Bayesian learning (SBL) associates to each weight in the underlying linear model a hyperparameter by assuming that each weight is Gaussian distributed with zero mean and precision (inverse variance) equal to its associated hyperparameter. The method estimates the hyperparameters by marginalizing out the weights and performing (marginalized) maximum likelihood (ML) estimation. SBL returns many hyperparameter estimates to diverge to infinity, effectively setting the estimates of the corresponding weights to zero (i.e., pruning the corresponding weights from the model) and thereby yielding a sparse estimate of the weight vector. In this letter, we analyze the marginal likelihood as function of a single hyperparameter while keeping the others fixed, when the Gaussian assumptions on the noise samples and the weight distribution that underlies the derivation of SBL are weakened. We derive sufficient conditions that lead, on the one hand, to finite hyperparameter estimates and, on the other, to infinite ones. Finally, we show that in the Gaussian case, the two conditions are complementary and coincide with the pruning condition of fast SBL (F-SBL), thereby providing additional insights into this algorithm.

The papers deals with the problem of submodular maximization; specifically, it proposes a stochastic optimization algorithm for maximizing a specific family of submodular functions, i.e. weighted coverage, under matroid constraints. The algorithm operates on the multilinear extension of the weighted coverage function. This way, the authors are sacrificing accuracy by optimizing a concave function which is a bounded approximation of the target function. However, they gain theoretically supported bounds on the convergence rate and the running time, which they also showcase in the experiments. In general, the paper is well written, and the set of ideas that it uses are well put together. The experimental section, although brief, drives the point that the authors want to make.

The paper proves a very interesting result: For maximizing Deep Submodular Functions (DSF) with matroid constraints, one can provide efficient algorithms that, under mild assumptions on the singleton marginals, have approximation factor better than 1-1/e (and potentially approaching 1 when the rank of the matroid becomes large). This is given in Theorem 1 which I think is the main result of the paper. The basic idea behind the algorithm is that for DSFs there is a natural concave extension, equations (4), (5) that can be maximized by projected gradient ascent (this result has been proved in [3]). The authors show in Proposition 1 that this concave extension is close to the multilinear extension, and in section 4 they show that the projected gradient ascent algorithm can be implemented efficiently (e.g. the subgradient of the concave extension can be computed efficiently due to the deep structure). The paper is written well and the results are novel.

Sarah Silverman's lawsuit against OpenAI will advance with some of her legal team's claims dismissed. The comedian sued OpenAI and Meta in July 2023, claiming they trained their AI models on her books and other work without consent. Bloomberg reported on Tuesday that the unfair competition portion of the lawsuit will proceed. Judge Martínez-Olguín gave the plaintiffs until March 13 to amend the suit. US District Judge Araceli Martínez-Olguín threw out portions of the complaint from Silverman's legal team Monday, including negligence, unjust enrichment, DMCA violations and accusations of vicarious infringement.

Data-driven discovery of governing equations in computational science has emerged as a new paradigm for obtaining accurate physical models and as a possible alternative to theoretical derivations. The recently developed physics-informed neural networks (PINNs) have also been employed to learn governing equations given data across diverse scientific disciplines. Despite the effectiveness of PINNs for discovering governing equations, the physical models encoded in PINNs may be misspecified in complex systems as some of the physical processes may not be fully understood, leading to the poor accuracy of PINN predictions. In this work, we present a general approach to correct the misspecified physical models in PINNs for discovering governing equations, given some sparse and/or noisy data. Specifically, we first encode the assumed physical models, which may be misspecified, then employ other deep neural networks (DNNs) to model the discrepancy between the imperfect models and the observational data. Due to the expressivity of DNNs, the proposed method is capable of reducing the computational errors caused by the model misspecification and thus enables the applications of PINNs in complex systems where the physical processes are not exactly known. Furthermore, we utilize the Bayesian PINNs (B-PINNs) and/or ensemble PINNs to quantify uncertainties arising from noisy and/or gappy data in the discovered governing equations. A series of numerical examples including non-Newtonian channel and cavity flows demonstrate that the added DNNs are capable of correcting the model misspecification in PINNs and thus reduce the discrepancy between the physical models and the observational data. We envision that the proposed approach will extend the applications of PINNs for discovering governing equations in problems where the physico-chemical or biological processes are not well understood.

In the early 20th century, the psychoanalyst Carl Jung came up with the concept of the shadow--the human personality's darker, repressed side, which can burst out in unexpected ways. Surprisingly, this theme recurs in the field of artificial intelligence in the form of the Waluigi Effect, a curiously named phenomenon referring to the dark alter-ego of the helpful plumber Luigi, from Nintendo's Mario universe. Luigi plays by the rules; Waluigi cheats and causes chaos. An AI was designed to find drugs for curing human diseases; an inverted version, its Waluigi, suggested molecules for over 40,000 chemical weapons. All the researchers had to do, as lead author Fabio Urbina explained in an interview, was give a high reward score to toxicity instead of penalizing it.