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ZX-diagrams are a powerful graphical language for the description of quantum processes with applications in fundamental quantum mechanics, quantum circuit optimization, tensor network simulation, and many more. The utility of ZX-diagrams relies on a set of local transformation rules that can be applied to them without changing the underlying quantum process they describe. These rules can be exploited to optimize the structure of ZX-diagrams for a range of applications. However, finding an optimal sequence of transformation rules is generally an open problem. In this work, we bring together ZX-diagrams with reinforcement learning, a machine learning technique designed to discover an optimal sequence of actions in a decision-making problem and show that a trained reinforcement learning agent can significantly outperform other optimization techniques like a greedy strategy or simulated annealing. The use of graph neural networks to encode the policy of the agent enables generalization to diagrams much bigger than seen during the training phase.

We study the problem of actively learning a non-parametric choice model based on consumers' decisions. We present a negative result showing that such choice models may not be identifiable. To overcome the identifiability problem, we introduce a directed acyclic graph (DAG) representation of the choice model. This representation provably encodes all the information about the choice model which can be inferred from the available data, in the sense that it permits computing all choice probabilities. We establish that given exact choice probabilities for a collection of item sets, one can reconstruct the DAG. However, attempting to extend this methodology to estimate the DAG from noisy choice frequency data obtained during an active learning process leads to inaccuracies. To address this challenge, we present an inclusion-exclusion approach that effectively manages error propagation across DAG levels, leading to a more accurate estimate of the DAG. Utilizing this technique, our algorithm estimates the DAG representation of an underlying non-parametric choice model. The algorithm operates efficiently (in polynomial time) when the set of frequent rankings is drawn uniformly at random. It learns the distribution over the most popular items among frequent preference types by actively and repeatedly offering assortments of items and observing the chosen item. We demonstrate that our algorithm more effectively recovers a set of frequent preferences on both synthetic and publicly available datasets on consumers' preferences, compared to corresponding non-active learning estimation algorithms. These findings underscore the value of our algorithm and the broader applicability of active-learning approaches in modeling consumer behavior.

We study the fully dynamic maximum matching problem. In this problem, the goal is to efficiently maintain an approximate maximum matching of a graph that is subject to edge insertions and deletions. Our focus is particularly on algorithms that maintain the edges of a $(1-\epsilon)$-approximate maximum matching for an arbitrarily small constant $\epsilon > 0$. Until recently, the fastest known algorithm for this problem required $\Theta(n)$ time per update where $n$ is the number of vertices. This bound was slightly improved to $n/(\log^* n)^{\Omega(1)}$ by Assadi, Behnezhad, Khanna, and Li [STOC'23] and very recently to $n/2^{\Omega(\sqrt{\log n})}$ by Liu [ArXiv'24]. Whether this can be improved to $n^{1-\Omega(1)}$ remains a major open problem. In this paper, we present a new algorithm that maintains a $(1-\epsilon)$-approximate maximum matching. The update-time of our algorithm is parametrized based on the density of a certain class of graphs that we call Ordered Ruzsa-Szemer\'edi (ORS) graphs, a generalization of the well-known Ruzsa-Szemer\'edi graphs. While determining the density of ORS (or RS) remains a hard problem in combinatorics, we prove that if the existing constructions of ORS graphs are optimal, then our algorithm runs in $n^{1/2+O(\epsilon)}$ time for any fixed $\epsilon > 0$ which would be significantly faster than existing near-linear in $n$ time algorithms.

We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition relations, which are treated similarly to the actions used in dynamic logics in order to define necessity and possibility operators. This leads to a higher degree of expressivity than that of many-sorted first-order logic. For example, one can finitely axiomatize both the finiteness and the reachability of models, neither of which are ordinarily possible in many-sorted first-order logic. We introduce syntactic entailment and study basic properties such as compactness and completeness, showing that the latter does not hold when standard finitary proof rules are used. Consequently, we define proof rules having both finite and countably infinite premises, and we provide conditions under which completeness can be proved. To that end, we generalize the forcing method introduced in model theory by Robinson from a single signature to a category of signatures, and we apply it to obtain a completeness result for signatures that are at most countable.

A model's capacity to generalize its knowledge to interpret unseen inputs with different characteristics is crucial to build robust and reliable machine learning systems. Language model evaluation tasks lack information metrics about model generalization and their applicability in a new setting is measured using task and language-specific downstream performance, which is often lacking in many languages and tasks. In this paper, we explore a set of efficient and reliable measures that could aid in computing more information related to the generalization capability of language models in cross-lingual zero-shot settings. In addition to traditional measures such as variance in parameters after training and distance from initialization, we also measure the effectiveness of sharpness in loss landscape in capturing the success in cross-lingual transfer and propose a novel and stable algorithm to reliably compute the sharpness of a model optimum that correlates to generalization.

It is well-known that extending the Hilbert axiomatic system for first-order intuitionistic logic with an exclusion operator, that is dual to implication, collapses the domains in the model into a constant domain. This makes it a very challenging problem to find a sound and complete proof system for first-order bi-intuitionistic logic with non-constant domains, that is also conservative over first-order intuitionistic logic. We solve this problem by presenting the first sound and complete proof system for first-order bi-intuitionistic logic with increasing domains. We formalize our proof system in a labeled polytree sequent calculus (a notational variant of nested sequents), and prove that it enjoys cut-elimination and is conservative over first-order intuitionistic logic. A key feature of our calculus is an explicit eigenvariable context, which allows us to control precisely the scope of free variables in a polytree structure. Semantically this context can be seen as encoding a notion of Scott's existence predicate for intuitionistic logic. This turns out to be crucial to avoid the collapse of domains and to prove the completeness of our proof system. The explicit consideration of the variable context in a formula sheds light on a previously overlooked dependency between the residuation principle and the existence predicate in the first-order setting, that may help explain the difficulty in obtaining a complete proof system for first-order bi-intuitionistic logic.

Qini curves have emerged as an attractive and popular approach for evaluating the benefit of data-driven targeting rules for treatment allocation. We propose a generalization of the Qini curve to multiple costly treatment arms, that quantifies the value of optimally selecting among both units and treatment arms at different budget levels. We develop an efficient algorithm for computing these curves and propose bootstrap-based confidence intervals that are exact in large samples for any point on the curve. These confidence intervals can be used to conduct hypothesis tests comparing the value of treatment targeting using an optimal combination of arms with using just a subset of arms, or with a non-targeting assignment rule ignoring covariates, at different budget levels. We demonstrate the statistical performance in a simulation experiment and an application to treatment targeting for election turnout.

Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.