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We devise achievable encoding schemes for distributed source compression for computing inner products, symmetric matrix products, and more generally, square matrix products, which are a class of nonlinear transformations. To that end, our approach relies on devising nonlinear mappings of distributed sources, which are then followed by the structured linear encoding scheme, introduced by K\"orner and Marton. For different computation scenarios, we contrast our findings on the achievable sum rate with the state of the art to demonstrate the possible savings in compression rate. When the sources have special correlation structures, it is possible to achieve unbounded gains, as demonstrated by the analysis and numerical simulations.

The distributed computing literature considers multiple options for modeling communication. Most simply, communication is categorized as either synchronous or asynchronous. Synchronous communication assumes that messages get delivered within a publicly known timeframe and that parties' clocks are synchronized. Asynchronous communication, on the other hand, only assumes that messages get delivered eventually. A more nuanced approach, or a middle ground between the two extremes, is given by the partially synchronous model, which is arguably the most realistic option. This model comes in two commonly considered flavors: (i) The Global Stabilization Time (GST) model: after an (unknown) amount of time, the network becomes synchronous. This captures scenarios where network issues are transient. (ii) The Unknown Latency (UL) model: the network is, in fact, synchronous, but the message delay bound is unknown. This work formally establishes that any time-agnostic property that can be achieved by a protocol in the UL model can also be achieved by a (possibly different) protocol in the GST model. By time-agnostic, we mean properties that can depend on the order in which events happen but not on time as measured by the parties. Most properties considered in distributed computing are time-agnostic. The converse was already known, even without the time-agnostic requirement, so our result shows that the two network conditions are, under one sensible assumption, equally demanding.

Information pooling has been extensively formalised across various logical frameworks in distributed systems, characterized by diverse information-sharing patterns. These approaches generally adopt an intersection perspective, aggregating all possible information, regardless of whether it is known or unknown to the agents. In contrast, this work adopts a unique stance, emphasising that sharing knowledge means distributing what is known, rather than what remains uncertain. This paper introduces new modal logics for knowledge pooling and sharing, ranging from a novel language of knowledge pooling to a dynamic mechanism for knowledge sharing. It also outlines their axiomatizations and discusses a potential framework for permissible knowledge pooling.

Most dataset distillation methods struggle to accommodate large-scale datasets due to their substantial computational and memory requirements. In this paper, we present a curriculum-based dataset distillation framework designed to harmonize scalability with efficiency. This framework strategically distills synthetic images, adhering to a curriculum that transitions from simple to complex. By incorporating curriculum evaluation, we address the issue of previous methods generating images that tend to be homogeneous and simplistic, doing so at a manageable computational cost. Furthermore, we introduce adversarial optimization towards synthetic images to further improve their representativeness and safeguard against their overfitting to the neural network involved in distilling. This enhances the generalization capability of the distilled images across various neural network architectures and also increases their robustness to noise. Extensive experiments demonstrate that our framework sets new benchmarks in large-scale dataset distillation, achieving substantial improvements of 11.1\% on Tiny-ImageNet, 9.0\% on ImageNet-1K, and 7.3\% on ImageNet-21K. The source code will be released to the community.

The contextual integrity model is a widely accepted way of analyzing the plurality of norms that are colloquially called "privacy norms". Contextual integrity systematically describes such norms by distinguishing the type of data concerned, the three social agents involved (subject, sender, and recipient) and the transmission principle governing the transfer of information. It allows analyzing privacy norms in terms of their impact on the interaction of those agents with one another. This paper places contextual integrity in a strict game theoretic framework. When such description is possible it has three key advantages: Firstly, it allows indisputable utilitarian justification of some privacy norms. Secondly, it better relates privacy to topics which are well understood by stakeholders whose education is predominantly quantitative, such as engineers and economists. Thirdly, it is an absolute necessity when describing ethical constraints to machines such as AI agents. In addition to describing games which capture paradigmatic informational norms, the paper also analyzes cases in which the game, per se, does not encourage normative behavior. The paper discusses two main forms of mechanisms which can be applied to the game in such cases, and shows that they reflect accepted privacy regulation and technologies.

Recent advancements in imitation learning have been largely fueled by the integration of sequence models, which provide a structured flow of information to effectively mimic task behaviours. Currently, Decision Transformer (DT) and subsequently, the Hierarchical Decision Transformer (HDT), presented Transformer-based approaches to learn task policies. Recently, the Mamba architecture has shown to outperform Transformers across various task domains. In this work, we introduce two novel methods, Decision Mamba (DM) and Hierarchical Decision Mamba (HDM), aimed at enhancing the performance of the Transformer models. Through extensive experimentation across diverse environments such as OpenAI Gym and D4RL, leveraging varying demonstration data sets, we demonstrate the superiority of Mamba models over their Transformer counterparts in a majority of tasks. Results show that HDM outperforms other methods in most settings. The code can be found at //github.com/meowatthemoon/HierarchicalDecisionMamba.

We consider estimation and inference using data collected from reinforcement learning algorithms. These algorithms, characterized by their adaptive experimentation, interact with individual units over multiple stages, dynamically adjusting their strategies based on previous interactions. Our goal is to evaluate a counterfactual policy post-data collection and estimate structural parameters, like dynamic treatment effects, which can be used for credit assignment and determining the effect of earlier actions on final outcomes. Such parameters of interest can be framed as solutions to moment equations, but not minimizers of a population loss function, leading to Z-estimation approaches for static data. However, in the adaptive data collection environment of reinforcement learning, where algorithms deploy nonstationary behavior policies, standard estimators do not achieve asymptotic normality due to the fluctuating variance. We propose a weighted Z-estimation approach with carefully designed adaptive weights to stabilize the time-varying estimation variance. We identify proper weighting schemes to restore the consistency and asymptotic normality of the weighted Z-estimators for target parameters, which allows for hypothesis testing and constructing uniform confidence regions. Primary applications include dynamic treatment effect estimation and dynamic off-policy evaluation.

In traditional semantics for classical logic and its extensions, such as modal logic, propositions are interpreted as subsets of a set, as in discrete duality, or as clopen sets of a Stone space, as in topological duality. A point in such a set can be viewed as a "possible world," with the key property of a world being primeness--a world makes a disjunction true only if it makes one of the disjuncts true--which classically implies totality--for each proposition, a world either makes the proposition true or makes its negation true. This chapter surveys a more general approach to logical semantics, known as possibility semantics, which replaces possible worlds with possibly partial "possibilities." In classical possibility semantics, propositions are interpreted as regular open sets of a poset, as in set-theoretic forcing, or as compact regular open sets of an upper Vietoris space, as in the recent theory of "choice-free Stone duality." The elements of these sets, viewed as possibilities, may be partial in the sense of making a disjunction true without settling which disjunct is true. We explain how possibilities may be used in semantics for classical logic and modal logics and generalized to semantics for intuitionistic logics. The goals are to overcome or deepen incompleteness results for traditional semantics, to avoid the nonconstructivity of traditional semantics, and to provide richer structures for the interpretation of new languages.

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.

We introduce an approach for deep reinforcement learning (RL) that improves upon the efficiency, generalization capacity, and interpretability of conventional approaches through structured perception and relational reasoning. It uses self-attention to iteratively reason about the relations between entities in a scene and to guide a model-free policy. Our results show that in a novel navigation and planning task called Box-World, our agent finds interpretable solutions that improve upon baselines in terms of sample complexity, ability to generalize to more complex scenes than experienced during training, and overall performance. In the StarCraft II Learning Environment, our agent achieves state-of-the-art performance on six mini-games -- surpassing human grandmaster performance on four. By considering architectural inductive biases, our work opens new directions for overcoming important, but stubborn, challenges in deep RL.