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We investigate a family of approximate multi-step proximal point methods, accelerated by implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
Classically, the time complexity of a first-order method is estimated by its number of gradient computations. In this paper, we study a more refined complexity by taking into account the `lingering' of gradients: once a gradient is computed…
We propose a presentation of classical propositional tableaux elaborated by application of methods that are noteworthy in program design, namely program derivation with separation of concerns. We start by deriving from a straightforward…
We state the graph-theoretic computational problem of finding tight paths in a directed, edge-weighted graph, as well as its simplification of finding tight pairs. These problems are motivated by the need of algorithms that find so-called…
We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
The convergence of deep learning and formal mathematics has spurred research in formal verification. Statement autoformalization, a crucial first step in this process, aims to translate informal descriptions into machine-verifiable…
The discrete gradient methods are integrators designed to preserve invariants of ordinary differential equations. From a formal series expansion of a subclass of these methods, we derive conditions for arbitrarily high order. We derive…
Deep learning has become the state-of-art tool in many applications, but the evaluation and training of deep models can be time-consuming and computationally expensive. The conditional computation approach has been proposed to tackle this…
In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision…
Arc-standard derivations over projective dependency trees can be interpreted as the incremental construction of lexicalized ordered trees with contiguous yields. Each \textsc{shift}, \textsc{leftarc}, and \textsc{rightarc} transition…
We present a logic for the specification of static analysis problems that goes beyond the logics traditionally used. Its most prominent feature is the direct support for both inductive computations of behaviors as well as co-inductive…
We refine the weighted type graph technique for proving termination of double pushout (DPO) graph transformation systems. We increase the power of the approach for graphs, we generalize the technique to other categories, and we allow for…
We examine several aspects of explicability of a classification system built from neural networks. The first aspect is the pairwise explicability, which is the ability to provide the most accurate prediction when the range of possibilities…
Learning processes by exploiting restricted domain knowledge is an important task across a plethora of scientific areas, with more and more hybrid training methods additively combining data-driven and model-based approaches. Although the…
Gradient-based techniques are becoming increasingly critical in quantitative fields, notably in statistics and computer science. The utility of these techniques, however, ultimately depends on how efficiently we can evaluate the derivatives…
Direct Preference Optimization (DPO) has emerged as a de-facto approach for aligning language models with human preferences. Recent work has shown DPO's effectiveness relies on training data quality. In particular, clear quality differences…
Causal discovery from observational data is a fundamental task in artificial intelligence, with far-reaching implications for decision-making, predictions, and interventions. Despite significant advances, existing methods can be broadly…
In this article we extend the framework of rough paths to processes of variable H\"older exponent or variable order paths. We show how a class of multiple discrete delay differential equations driven by signals of variable order are…
In this work, we show that for linearly constrained optimization problems the primal-dual hybrid gradient algorithm, analyzed by Chambolle and Pock [3], can be written as an entirely primal algorithm. This allows us to prove convergence of…
We propose Dual Approximation Policy Optimization (DAPO), a framework that incorporates general function approximation into policy mirror descent methods. In contrast to the popular approach of using the $L_2$-norm to measure function…