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The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. There is a considerable body of mathematical…
This article is concerned with the application of the program extraction technique to a new class of problems: the synthesis of decision procedures for the classical satisfiability problem that are correct by construction. To this end, we…
Past years have witnessed rapid developments in Neural Machine Translation (NMT). Most recently, with advanced modeling and training techniques, the RNN-based NMT (RNMT) has shown its potential strength, even compared with the well-known…
Effectively modeling non-stationary dynamics in probabilistic multivariate time series(MTS) forecasting requires balancing expressiveness with robustness. Existing parametric approaches benefit from strong inductive biases but lack…
In this paper, we extend an available neural network verification technique to support a wider class of piece-wise linear activation functions. Furthermore, we extend the algorithms, which provide in their original form exact respectively…
Neural Turing Machines (NTMs) are an instance of Memory Augmented Neural Networks, a new class of recurrent neural networks which decouple computation from memory by introducing an external memory unit. NTMs have demonstrated superior…
The reviewed paper describes an analog device that empirically solves small instances of the NP-complete Subset Sum Problem (SSP). The authors claim that this device can solve the SSP in polynomial time using polynomial space, in principle,…
We study a polynomial-time decision problem in which each input encodes a depth-$N$ causal execution in which a single non-duplicable token must traverse an ordered sequence of steps, revealing at most $O(1)$ bits of routing information at…
This work establishes a rigorous theoretical foundation for analyzing deep learning systems by leveraging Infinite Time Turing Machines (ITTMs), which extend classical computation into transfinite ordinal steps. Using ITTMs, we reinterpret…
The Curry-Howard correspondence is often called the proofs-as-programs result. I offer a generalization of this result, something which may be called machines as programs. Utilizing this insight, I introduce two new Turing Machines called…
Finite-state models, such as finite-state machines (FSMs), aid software engineering in many ways. They are often used in formal verification and also can serve as visual software models. The latter application is associated with the…
We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general.…
The last decade has witnessed growth in the computational requirements for training deep neural networks. Current approaches (e.g., data/model parallelism, pipeline parallelism) parallelize training tasks onto multiple devices. However,…
This paper demonstrates the relativity of Computability and Nondeterministic; the nondeterministic is just Turing's undecidable Decision rather than the Nondeterministic Polynomial time. Based on analysis about TM, UM, DTM, NTM, Turing…
Deep learning (DL) is transforming industry as decision-making processes are being automated by deep neural networks (DNNs) trained on real-world data. Driven partly by rapidly-expanding literature on DNN approximation theory showing they…
Quantitatively evaluating and comparing the performance of robotic solutions that are designed to work under a variety of conditions is inherently challenging because they need to be evaluated under numerous precisely repeatable conditions…
We introduce determinantal sieving, a new, remarkably powerful tool in the toolbox of algebraic FPT algorithms. Given a polynomial $P(X)$ on a set of variables $X=\{x_1,\ldots,x_n\}$ and a linear matroid $M=(X,\mathcal{I})$ of rank $k$,…
Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…
We show that deciding whether a sparse univariate polynomial has a p-adic rational root can be done in NP for most inputs. We also prove a polynomial-time upper bound for trinomials with suitably generic p-adic Newton polygon. We thus…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…