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Session-based Recommendation (SR) systems have recently achieved considerable success, yet their complex, "black box" nature often obscures why certain recommendations are made. Existing explanation methods struggle to pinpoint truly…
Motivated by Pryce's structural index reduction method for differential algebraic equations (DAEs), we show the complexity of the fixed-point iteration algorithm and propose a fixed-point iteration method with parameters. It leads to a…
The reconstruction of sparse signals from a limited set of measurements poses a significant challenge as it necessitates a solution to an underdetermined system of linear equations. Compressed sensing (CS) deals with sparse signal…
We study versions of the tree pigeonhole principle, $\mathsf{TT}^1$, in the context of Weihrauch-style computable analysis. The principle has previously been the subject of extensive research in reverse mathematics. Two outstanding…
Sequential design is a highly active field of research in active learning which provides a general framework for designing computer experiments with limited computational budgets. It aims to create efficient surrogate models to replace…
In this work, we establish separation theorems for several subsystems of the Ideal Proof System (IPS), an algebraic proof system introduced by Grochow and Pitassi (J. ACM, 2018). Separation theorems are well-studied in the context of…
Proximity gaps and correlated agreement have become central tools in the analysis of interactive oracle proofs of proximity (IOPPs) and code-based SNARKs. Informally, a proximity-gap statement says that for a structured set of words -- such…
We introduce SCORES, a recursive neural network for shape composition. Our network takes as input sets of parts from two or more source 3D shapes and a rough initial placement of the parts. It outputs an optimized part structure for the…
The determination of the number of mixture components (the order) of a finite mixture model has been an enduring problem in statistical inference. We prove that the closed testing principle leads to a sequential testing procedure (STP) that…
We introduce a sound and complete coinductive proof system for reachability properties in transition systems generated by logically constrained term rewriting rules over an order-sorted signature modulo builtins. A key feature of the…
We introduce a new cluster-cumulant expansion (CCE) based on the fixed points of iterative belief propagation (IBP). This expansion is similar in spirit to the loop-series (LS) recently introduced in [1]. However, in contrast to the latter,…
Proof-theoretic semantics (P-tS) is the paradigm of semantics in which meaning in logic is based on proof (as opposed to truth). A particular instance of P-tS for intuitionistic propositional logic (IPL) is its base-extension semantics…
In this paper, we analyze 2CNF formulas from the perspectives of Read-Once resolution (ROR) refutation schemes. We focus on two types of ROR refutations, viz., variable-once refutation and clause-once refutation. In the former, each…
In this work, we extend the sparse iterative covariance-based estimator (SPICE), by generalizing the formulation to allow for different norm constraints on the signal and noise parameters in the covariance model. For a given norm, the…
The ellipsoid method is an algorithm that solves the (weak) feasibility and linear optimization problems for convex sets by making oracle calls to their (weak) separation problem. We observe that the previously known method for showing that…
We generalize the reduction mechanism for linear programming problems and semidefinite programming problems from [arXiv:1410.8816] in two ways 1) relaxing the requirement of affineness and 2) extending to fractional optimization problems.…
Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…
An application area of vertex enumeration problem (VEP) is the usage within objective space based linear/convex {vector} optimization algorithms whose aim is to generate (an approximation of) the Pareto frontier. In such algorithms, VEP,…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
In this paper, we develop a new sequential regression modeling approach for data streams. Data streams are commonly found around us, e.g in a retail enterprise sales data is continuously collected every day. A demand forecasting model is an…