arXiv research

We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite automata. We generate a set of biased sequences by applying a finite state auto…

Automaton models are often seen as interpretable models. Interpretability itself is not well defined: it remains unclear what interpretability means without first explicitly specifying objectives or desired attributes. In this paper, we identify the key properties used to interpret automata and propose a modification o…

Transformers simulate finite-state automata with fewer layers.

We present an interactive version of an evidence-driven state-merging (EDSM) algorithm for learning variants of finite state automata. Learning these automata often amounts to recovering or reverse engineering the model generating the data despite noisy, incomplete, or imperfectly sampled data sources rather than optim…

We show how well known rules of back propagation arise from a weighted combination of finite automata. By redefining a finite automata as a predictor we combine the set of all $k$-state finite automata using a weighted majority algorithm. This aggregated prediction algorithm can be simplified using symmetry, and we pro…

A framework for analyzing financial systems under scenario constraints.

Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, it is difficult to understand what exactly they learn. Second, they tend to work poorly on sequences requiring long-term memorization, despite having this capacity in principle. We aim to address both…

Paper verifies RNNs using automata learning and model checking.

Train track automata for fully irreducible elements in Out(F_r).

We present an algorithm for extraction of a probabilistic deterministic finite automaton (PDFA) from a given black-box language model, such as a recurrent neural network (RNN). The algorithm is a variant of the exact-learning algorithm L*, adapted to a probabilistic setting with noise. The key insight is the use of con…

Study immersions of punctured 4-manifolds for quantum automata applications.

Dual neural network architecture improves accuracy and interpretability.

Quantum cellular automata form a homology theory.

A new layer learns abstract relations from graph structure using finite-state automata.

This document investigates the integration of adaptive distinguishing sequences into the process of active automata learning (AAL). A novel AAL algorithm "ADT" (adaptive discrimination tree) is developed and presented. Since the submission of the original thesis, the presented algorithm has been integrated into LearnLi…

In this paper, we unravel a fundamental connection between weighted finite automata~(WFAs) and second-order recurrent neural networks~(2-RNNs): in the case of sequences of discrete symbols, WFAs and 2-RNNs with linear activation functions are expressively equivalent. Motivated by this result, we build upon a recent ext…

Recurrent neural networks trained on regular languages exhibit stable states that can recover from noise.

A fixed point theorem is proved for inverse transducers, leading to an automata-theoretic proof of the fixed point subgroup of an endomorphism of a finitely generated virtually free group being finitely generated. If the endomorphism is uniformly continuous for the hyperbolic metric, it is proved that the set of regula…

Reservoir computers (RCs) and recurrent neural networks (RNNs) can mimic any finite-state automaton in theory, and some workers demonstrated that this can hold in practice. We test the capability of generalized linear models, RCs, and Long Short-Term Memory (LSTM) RNN architectures to predict the stochastic processes g…

We introduce a new class of possibly noncompact n-dimensional manifolds without boundary associated to finite data which we call topological automata. This class is large enough to contain many interesting examples of open 2-dimensional and 3-dimensional manifolds of interest to low-dimensional topologists. Our main re…

In this work we present ISA, a novel approach for learning and exploiting subgoals in reinforcement learning (RL). Our method relies on inducing an automaton whose transitions are subgoals expressed as propositional formulas over a set of observable events. A state-of-the-art inductive logic programming system is used …

Paper proves hardness of learning various complex models under local pseudorandom generators.

We investigate the problem of reliable communication between two legitimate parties over deletion channels under an active eavesdropping (aka jamming) adversarial model. To this goal, we develop a theoretical framework based on probabilistic finite-state automata to define novel encoding and decoding schemes that ensur…

Designs a Cellular Automata rule for forming touching loop patterns.

CURIE uses cellular automata to detect concept drift in data streams.

Classifies knots in the Poincaré sphere, using fixed points and folding automata.

Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Stochastic acceptors or probabilistic automata are stochastic automata without output that can model components in machine learning scenarios. In this paper, we provide dynamic programming algorithms for the comput…

In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two dimensional grid. Active traders are characterised by the decision to buy, (+1), or sell, (-1), a …

We present a method to extract a weighted finite automaton (WFA) from a recurrent neural network (RNN). Our algorithm is based on the WFA learning algorithm by Balle and Mohri, which is in turn an extension of Angluin's classic \lstar algorithm. Our technical novelty is in the use of \emph{regression} methods for the s…

Understanding how a learned black box works is of crucial interest for the future of Machine Learning. In this paper, we pioneer the question of the global interpretability of learned black box models that assign numerical values to symbolic sequential data. To tackle that task, we propose a spectral algorithm for the …

We provide the first solution for model-free reinforcement learning of ω-regular objectives for Markov decision processes (MDPs). We present a constructive reduction from the almost-sure satisfaction of ω-regular objectives to an almost- sure reachability problem and extend this technique to learning how to control an …

We provide an algorithm to solve the word problem in all fundamental groups of closed 3-manifolds; in particular, we show that these groups are autostackable. This provides a common framework for a solution to the word problem in any closed 3-manifold group using finite state automata. We also introduce the notion of a…

MBQC linked to CQCA, yielding efficient Ansätze.

We propose an approach that connects recurrent networks with different orders of hidden interaction with regular grammars of different levels of complexity. We argue that the correspondence between recurrent networks and formal computational models gives understanding to the analysis of the complicated behaviors of rec…

Automata learning techniques automatically generate system models from test observations. These techniques usually fall into two categories: passive and active. Passive learning uses a predetermined data set, e.g., system logs. In contrast, active learning actively queries the system under learning, which is considered…

This paper formalizes Uniswap v3 using PTA and FST for rigorous analysis.

MPNPs use message passing to exploit relational structure in stochastic processes.

This note gives a brief survey of the minimum dilatation problem for pseudo-Anosov mapping classes, and the first explicit train track description of an infinite family of pseudo-Anosov mapping classes with orientable stable foliations and the conjectural minimum dilatation for closed surfaces of even genus $g \ge 2$.

This paper proposes DeepSynth, a method for effective training of deep Reinforcement Learning (RL) agents when the reward is sparse and non-Markovian, but at the same time progress towards the reward requires achieving an unknown sequence of high-level objectives. Our method employs a novel algorithm for synthesis of c…

With the advent of huges volumes of data produced in the form of fast streams, real-time machine learning has become a challenge of relevance emerging in a plethora of real-world applications. Processing such fast streams often demands high memory and processing resources. In addition, they can be affected by non-stati…

In order to satisfy safety conditions, an agent may be constrained from acting freely. A safe controller can be designed a priori if an environment is well understood, but not when learning is employed. In particular, reinforcement learned (RL) controllers require exploration, which can be hazardous in safety critical …

The paper distills a weighted automaton from RNNs for language modeling.

We discuss here the mean-field theory for a cellular automata model of meta-learning. The meta-learning is the process of combining outcomes of individual learning procedures in order to determine the final decision with higher accuracy than any single learning method. Our method is constructed from an ensemble of inte…

Hidden tree Markov models allow learning distributions for tree structured data while being interpretable as nondeterministic automata. We provide a concise summary of the main approaches in literature, focusing in particular on the causality assumptions introduced by the choice of a specific tree visit direction. We w…

Neural models for NLP typically use large numbers of parameters to reach state-of-the-art performance, which can lead to excessive memory usage and increased runtime. We present a structure learning method for learning sparse, parameter-efficient NLP models. Our method applies group lasso to rational RNNs (Peng et al.,…

Let $Γ$ be a subgroup of $PSL(2,R)$ generated by three parabolic transformations. The main goal of this paper is to present an algorithm to determine whether or not $Γ$ is discrete. Historically discreteness algorithms have been considered within several broader mathematical paradigms: the discreteness problem, the con…

Enhances reward specification in RL with a novel language-based approach.

Study of group actions on CAT(0) cube complexes, focusing on marked length spectra.