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Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally…
Our starting point is the observation that if graphs in a class C have low descriptive complexity in first order logic, then the isomorphism problem for C is solvable by a fast parallel algorithm (essentially, by a simple combinatorial…
Motivation: Alignment-free (AF) distance/similarity functions are a key tool for sequence analysis. Experimental studies on real datasets abound and, to some extent, there are also studies regarding their control of false positive rate…
We present a general framework for designing efficient data structures for high-dimensional pattern-matching problems ($\exists \;? i\in[n], f(x_i,y)=1$) through communication models in which $f(x,y)$ admits sublinear communication…
Graph isomorphism testing is usually approached via the comparison of graph invariants. Two popular alternatives that offer a good trade-off between expressive power and computational efficiency are combinatorial (i.e., obtained via the…
This paper studies the matched network inference problem, where the goal is to determine if two networks, defined on a common set of nodes, exhibit a specific form of stochastic similarity. Two notions of similarity are considered: (i)…
Estimating the uncertainty of a model's prediction on a test point is a crucial part of ensuring reliability and calibration under distribution shifts. A minimum description length approach to this problem uses the predictive normalized…
Subgraph isomorphism, also known as subgraph matching, is typically regarded as an NP-complete problem. This complexity is further compounded in practical applications where edge weights are real-valued and may be affected by measurement…
This paper describes one objective function for learning semantically coherent feature embeddings in multi-output classification problems, i.e., when the response variables have dimension higher than one. In particular, we consider the…
Learning feature correspondence is a foundational task in computer vision, holding immense importance for downstream applications such as visual odometry and 3D reconstruction. Despite recent progress in data-driven models, feature…
We study the question of how much classical communication is needed when Alice is given a classical description of a quantum state $|\psi\rangle$ for Bob to recover any expectation value $\langle \psi | M |\psi\rangle$ given an observable…
We simulate correlation measurements of entangled photons numerically. The model employed is strictly local. The correlation is determined by its classical expression with one decisive difference: we sum up coincidences for each pair…
We study the communication complexity of symmetric XOR functions, namely functions $f: \{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}$ that can be formulated as $f(x,y)=D(|x\oplus y|)$ for some predicate $D: \{0,1,...,n\} \rightarrow…
Index Coding has received considerable attention recently motivated in part by real-world applications and in part by its connection to Network Coding. The basic setting of Index Coding encodes the problem input as an undirected graph and…
Boolean Satisfiability Problem (SAT) is one of the core problems in computer science. As one of the fundamental NP-complete problems, it can be used - by known reductions - to represent instances of variety of hard decision problems.…
We present a modular, extensible likelihood framework for spectroscopic inference based on synthetic model spectra. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints…
A connected undirected graph $G = (V,E)$ is lower conformally rigid if uniform edge weights maximize the second smallest Laplacian eigenvalue $\lambda_2(w)$ over all normalized edge weights $w$, and upper conformally rigid if uniform edge…
We develop a method for training neural networks on Boolean data in which the values at all nodes are strictly $\pm 1$, and the resulting models are typically equivalent to networks whose nonzero weights are also $\pm 1$. The method…
The combination of integrability and crossing symmetry has proven to give tight non-perturbative bounds on some planar structure constants in $\mathcal{N}$=4 SYM, particularly in the setup of defect observables built on a Wilson-Maldacena…
The algebraic degree is an important parameter of Boolean functions used in cryptography. When a function in a large number of variables is not given explicitly in algebraic normal form, it might not be feasible to compute its degree.…