Related papers: Solving Marginal MAP Exactly by Probabilistic Circ…
Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…
Robust principal component analysis (RPCA) has drawn significant attentions due to its powerful capability in recovering low-rank matrices as well as successful appplications in various real world problems. The current state-of-the-art…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Given a graphical model, one essential problem is MAP inference, that is, finding the most likely configuration of states according to the model. Although this problem is NP-hard, large instances can be solved in practice. A major open…
We consider probabilistic circuits working over the real numbers, and using arbitrary semialgebraic functions of bounded description complexity as gates. In particular, such circuits can use all arithmetic operations +, -, x, /,…
The possibility of using non-deterministic circuit components has been gaining significant attention in recent years. The modeling and simulation of their circuits require novel approaches, as now the state of a circuit at an arbitrary…
Permutational Quantum Computing (PQC) [\emph{Quantum~Info.~Comput.}, \textbf{10}, 470--497, (2010)] is a natural quantum computational model conjectured to capture non-classical aspects of quantum computation. An argument backing this…
Probabilistic Circuits (PCs) are deep generative models that support exact and efficient probabilistic inference. Yet in autoregressive language modeling, PCs still lag behind Transformer-based large language models (LLMs), suggesting an…
A probabilistic circuit (PC) succinctly expresses a function that represents a multivariate probability distribution and, given sufficient structural properties of the circuit, supports efficient probabilistic inference. Typically a PC…
Particle filtering is a numerical Bayesian technique that has great potential for solving sequential estimation problems involving non-linear and non-Gaussian models. Since the estimation accuracy achieved by particle filters improves as…
The representation of polynomials by arithmetic circuits evaluating them is an alternative data structure which allowed considerable progress in polynomial equation solving in the last fifteen years. We present a circuit based computation…
Active components, such as actuators, constitute a fundamental aspect of engineering systems, affording the freedom to shape system behavior as desired. However, this capability necessitates energy consumption, primarily in the form of…
Many algorithms for processing probabilistic networks are dependent on the topological properties of the problem's structure. Such algorithms (e.g., clustering, conditioning) are effective only if the problem has a sparse graph captured by…
Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking…
A minimum path cover (MPC) of a directed acyclic graph (DAG) $G = (V,E)$ is a minimum-size set of paths that together cover all the vertices of the DAG. Computing an MPC is a basic polynomial problem, dating back to Dilworth's and…
Probabilistic integral circuits (PICs) have been recently introduced as probabilistic models enjoying the key ingredient behind expressive generative models: continuous latent variables (LVs). PICs are symbolic computational graphs defining…
Squared tensor networks (TNs) and their extension as computational graphs--squared circuits--have been used as expressive distribution estimators, yet supporting closed-form marginalization. However, the squaring operation introduces…
Large-scale programmable photonic circuits are opening up new possibilities for information processing providing fast and energy-efficient means for matrix-vector multiplication. Here, we introduce a novel architecture of photonic circuits…
This paper proposes a method for solving multivariate regression and classification problems using piecewise linear predictors over a polyhedral partition of the feature space. The resulting algorithm that we call PARC (Piecewise Affine…