Related papers: Sum of Squares Circuits

Parameterized Quantum Circuits (PQCs) are essential to quantum machine learning and optimization algorithms. The expressibility of PQCs, which measures their ability to represent a wide range of quantum states, is a critical factor…

Probabilistic Circuits (PCs) have emerged as an efficient framework for representing and learning complex probability distributions. Nevertheless, the existing body of research on PCs predominantly concentrates on data-driven parameter…

We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…

Squared tensor networks (TNs) and their generalization as parameterized computational graphs -- squared circuits -- have been recently used as expressive distribution estimators in high dimensions. However, the squaring operation introduces…

Tensor-network techniques have enjoyed outstanding success in physics, and have recently attracted attention in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding…

Probabilistic representations, such as Bayesian and Markov networks, are fundamental to much of statistical machine learning. Thus, learning probabilistic representations directly from data is a deep challenge, the main computational…

We present a novel tractable generative model that extends Sum-Product Networks (SPNs) and significantly boosts their power. We call it Sum-Product-Quotient Networks (SPQNs), whose core concept is to incorporate conditional distributions…

Parameterized quantum circuits (PQCs) are fundamental to quantum machine learning (QML), quantum optimization, and variational quantum algorithms (VQAs). The expressibility of PQCs is a measure that determines their capability to harness…

Casting neural networks in generative frameworks is a highly sought-after endeavor these days. Contemporary methods, such as Generative Adversarial Networks, capture some of the generative capabilities, but not all. In particular, they lack…

In this paper, we present a robust adaptive model predictive control (MPC) scheme for linear systems subject to parametric uncertainty and additive disturbances. The proposed approach provides a computationally efficient formulation with…

Understanding and explaining the structure of generated test inputs is essential for effective software testing and debugging. Existing approaches--including grammar-based fuzzers, probabilistic Context-Free Grammars (pCFGs), and Large…

Strongly simulating a quantum circuit, that is, computing an output amplitude, amounts to summing the circuit's Feynman paths, a weighted count over assignments to the Boolean ``path'' variables. The circuit's gates induce correlations…

Several authors have proposed spatially-coupled (or convolutional-like) variants of product codes (PCs). In this paper, we focus on a parametrized family of generalized PCs that recovers some of these codes (e.g., staircase and block-wise…

Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even…

The design of parametric quantum circuits (PQCs) for efficient use in variational quantum simulations (VQS) is subject to two competing factors. On one hand, the set of states that can be generated by the PQC has to be large enough to…

Probabilistic circuits (PCs) are a promising avenue for probabilistic modeling, as they permit a wide range of exact and efficient inference routines. Recent ``deep-learning-style'' implementations of PCs strive for a better scalability,…

Designing models that are both expressive and preserve known invariances of tasks is an increasingly hard problem. Existing solutions tradeoff invariance for computational or memory resources. In this work, we show how to leverage…

While abstract interpretation is not theoretically restricted to specific kinds of properties, it is, in practice, mainly developed to compute linear over-approximations of reachable sets, aka. the collecting semantics of the program. The…

Probabilistic graphical models (PGMs) are powerful tools for solving systems of complex relationships over a variety of probability distributions. However, while tree-structured PGMs always result in efficient and exact solutions, inference…

We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic, and computational implications of the presence of discrete…