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There is a wave of interest in using unsupervised neural networks for solving differential equations. The existing methods are based on feed-forward networks, {while} recurrent neural network differential equation solvers have not yet been…
Tabular data remains prevalent in high-stakes domains such as healthcare and finance, where predictive models are expected to provide both high accuracy and faithful, human-understandable reasoning. While symbolic models offer verifiable…
Many of the challenges facing today's reinforcement learning (RL) algorithms, such as robustness, generalization, transfer, and computational efficiency are closely related to compression. Prior work has convincingly argued why minimizing…
We developed a simulated environment to train deep reinforcement learning agents on a shortcut usage navigation task, motivated by the Dual Solutions Paradigm test used for human navigators. We manipulated the frequency with which agents…
We investigate the multi-dimensional Super Resolution problem on closed semi-algebraic domains for various sampling schemes such as Fourier or moments. We present a new semidefinite programming (SDP) formulation of the 1 -minimization in…
Self-consistency (SC), a widely used decoding strategy for chain-of-thought reasoning, shows significant gains across various multi-step reasoning tasks but comes with a high cost due to multiple sampling with the preset size. Its variants,…
Although the capabilities of large language models have been increasingly tested on complex reasoning tasks, their long-horizon planning abilities have not yet been extensively investigated. In this work, we provide a systematic assessment…
We show {\it semidefinite programming} (SDP) feasibility problem is equivalent to solving a {\it convex hull relaxation} (CHR) for a finite system of quadratic equations. On the one hand, this offers a simple description of SDP. On the…
Spatial cognition is essential for human intelligence, enabling problem-solving through visual simulations rather than solely relying on verbal reasoning. However, existing AI benchmarks primarily assess verbal reasoning, neglecting the…
Dominant areas of computer science and computation systems are intensively linked to the hypercube-related studies and interpretations. This article presents some transformations and analytics for some example algorithms and Boolean domain…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
Many computer vision problems can be formulated as binary quadratic programs (BQPs). Two classic relaxation methods are widely used for solving BQPs, namely, spectral methods and semidefinite programming (SDP), each with their own…
In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…
A new algorithm, denoted by RSRR, is presented for solving large-scale nonlinear eigenvalue problems (NEPs) with a focus on improving the robustness and reliability of the solution, which is a challenging task in computational science and…
Machine learning has become a fundamental approach for modeling, prediction, and control, enabling systems to learn from data and perform complex tasks. Reservoir computing is a machine learning tool that leverages high-dimensional…
The robust adaptive beamforming (RAB) problem for general-rank signal model with an additional positive semi-definite constraint is considered. Using the principle of the worst-case performance optimization, such RAB problem leads to a…
Deep learning models are often not easily adaptable to new tasks and require task-specific adjustments. The differentiable neural computer (DNC), a memory-augmented neural network, is designed as a general problem solver which can be used…
Query optimizers in RDBMSs search for execution plans expected to be optimal for given queries. They use parameter estimates, often inaccurate, and make assumptions that may not hold in practice. Consequently, they may select plans that are…
Reinforcement Learning (RL) policies are designed to predict actions based on current observations to maximize cumulative future rewards. In real-world applications (i.e., non-simulated environments), sensors are essential for measuring the…
Deep learning models for vision tasks are trained on large datasets under the assumption that there exists a universal representation that can be used to make predictions for all samples. Whereas high complexity models are proven to be…