相关论文: Symbolic Feedforward Networks for Probabilistic Fi…

Numerous neuro-symbolic approaches have recently been proposed typically with the goal of adding symbolic knowledge to the output layer of a neural network. Ideally, such losses maximize the probability that the neural network's predictions…

In this paper, we present connections between three models used in different research fields: weighted finite automata~(WFA) from formal languages and linguistics, recurrent neural networks used in machine learning, and tensor networks…

We revisit the complexity of procedures on SFAs (such as intersection, emptiness, etc.) and analyze them according to the measures we find suitable for symbolic automata: the number of states, the maximal number of transitions exiting a…

Neural networks (NN) have demonstrated remarkable capabilities in various tasks, but their computation-intensive nature demands faster and more energy-efficient hardware implementations. Optics-based platforms, using technologies such as…

Studying language models (LMs) in terms of well-understood formalisms allows us to precisely characterize their abilities and limitations. Previous work has investigated the representational capacity of recurrent neural network (RNN) LMs in…

We construct zero-error quantum finite automata (QFAs) for promise problems which cannot be solved by bounded-error probabilistic finite automata (PFAs). Here is a summary of our results: - There is a promise problem solvable by an exact…

A quantum finite-state automaton (QFA) is a theoretical model designed to simulate the evolution of a quantum system with finite memory in response to sequential input strings. We define the language of a QFA as the set of strings that lead…

Symbolic models have been recently used as a sound mathematical formalism for the formal verification and control design of purely continuous and hybrid systems. In this paper we propose a sequence of symbolic models that approximates a…

There is a wide gap between symbolic reasoning and deep learning. In this research, we explore the possibility of using deep learning to improve symbolic reasoning. Briefly, in a reasoning system, a deep feedforward neural network is used…

The Universal Approximation Theorem (UAT) guarantees universal function approximation but does not explain how residual models distribute approximation across layers. We reframe residual networks as a layer-wise approximation process that…

Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified…

Several authors have reported that the echo state network reproduces bifurcation diagrams of some nonlinear differential equations using the data for a few control parameters. We demonstrate that a simpler feedforward neural network can…

We present a correspondence and bisimulation between variants of parametrically polymorphic type systems and variants of finite control automata, such as FSA, PDA, tree automata and Turing machine. Within this correspondence we show that…

Consider a randomized algorithm that draws samples exactly from a distribution using recursion. Such an algorithm is called a perfect simulation, and here a variety of methods for building this type of algorithm are shown to derive from the…

The identification of a deterministic finite automaton (DFA) from labeled examples is a well-studied problem in the literature; however, prior work focuses on the identification of monolithic DFAs. Although monolithic DFAs provide accurate…

A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA $N$, there exists a process algebraic term $p$ such that its semantics is…

Computation is classically studied in terms of automata, formal languages and algorithms; yet, the relation between neural dynamics and symbolic representations and operations is still unclear in traditional eliminative connectionism.…

Animals are known to make efficient probabilistic inferences based on uncertain and noisy information from the outside world. Although it is known that generic neural networks can perform near-optimal point estimation by probabilistic…

Finite-State Transducers (FSTs) are effective models for string-to-string rewriting tasks, often providing the efficiency necessary for high-performance applications, but constructing transducers by hand is difficult. In this work, we…

Over the last decades, deep neural networks based-models became the dominant paradigm in machine learning. Further, the use of artificial neural networks in symbolic learning has been seen as increasingly relevant recently. To study the…