A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Paper defines topology automaton for Barański carpets and proves Hölder equivalence conditions.
The language of maximal lexicographic representatives of elements in the positive braid monoid with generators is a regular language. We describe with great detail the smallest Finite State Automaton accepting such language, and study the proportion of elements of length whose maximal lexicographic repres…
A new layer learns abstract relations from graph structure using finite-state automata.
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 …
New formulas derived for Jones polynomial of rational links.
In this paper we study Thurston's automaton on the braid groups via binary operations. These binary operations are obtained from the construction of this automaton. We study these operations and find some connections between them in a "skew lattice" spirit.
Transformers simulate finite-state automata with fewer layers.
We introduce a general method to extract knowledge from a recurrent neural network (Long Short Term Memory) that has learnt to detect if a given input sequence is valid or not, according to an unknown generative automaton. Based on the clustering of the hidden states, we explain how to build and validate an automaton t…
Representative investors whose behaviour is modelled by a deterministic finite automaton generate complexity both in the time series of each asset and in the cross-sectional correlation when the rule governing their behaviour is schizophrenic, meaning the investor must hold multiple seemingly contradictory beliefs simu…
We discuss algorithms for estimating the Shannon entropy h of finite symbol sequences with long range correlations. In particular, we consider algorithms which estimate h from the code lengths produced by some compression algorithm. Our interest is in describing their convergence with sequence length, assuming no limit…
Autostackability for finitely generated groups is defined via a topological property of the associated Cayley graph which can be encoded in a finite state automaton. Autostackable groups have solvable word problem and an effective inductive procedure for constructing van Kampen diagrams with respect to a canonical fini…
Paper details Hilbert-curve for high-performance data mining.
A full Mealy automaton is associated with a graph and a square complex, which contains an anti-torus if and only if the automaton is bi-reversible and the graph is aperiodic.
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…
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…
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 of group actions on CAT(0) cube complexes, focusing on marked length spectra.
The paper distills a weighted automaton from RNNs for language modeling.
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…
Paper verifies RNNs using automata learning and model checking.
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…
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…
New neural stack and Turing Machine architectures prove stability and computational power.
Braids can be represented geometrically as laminations of punctured disks. The geometric complexity of a braid is the minimal complexity of a lamination that represents it, and tight laminations are representatives of minimal complexity. These laminations give rise to a normal form of braids, via a relaxation algorithm…
Compactifies stability conditions on triangulated categories, inspired by Teichmüller theory.
Reinforcement Learning (RL) is a widely employed machine learning architecture that has been applied to a variety of control problems. However, applications in safety-critical domains require a systematic and formal approach to specifying requirements as tasks or goals. We propose a model-free RL algorithm that enables…
In recent years, distance education has enjoyed a major boom. Much work at The Open University (OU) has focused on improving retention rates in these modules by providing timely support to students who are at risk of failing the module. In this paper we explore methods for analysing student activity in online virtual l…
We study the problem of online path learning with non-additive gains, which is a central problem appearing in several applications, including ensemble structured prediction. We present new online algorithms for path learning with non-additive count-based gains for the three settings of full information, semi-bandit and…
Most people are risk-averse (risk-seeking) when they expect to gain (lose). Based on a generalization of ``expected utility theory'' which takes this into account, we introduce an automaton mimicking the dynamics of economic operations. Each operator is characterized by a parameter q which gauges people's attitude unde…
A dry decade in the Navajo Nation has killed vegetation, dessicated soils, and released once-stable sand into the wind. This sand now covers one-third of the Nation's land, threatening roads, gardens and hundreds of homes. Many arid regions have similar problems: global warming has increased dune movement across farmla…
We propose a method for efficient training of Q-functions for continuous-state Markov Decision Processes (MDPs) such that the traces of the resulting policies satisfy a given Linear Temporal Logic (LTL) property. LTL, a modal logic, can express a wide range of time-dependent logical properties (including "safety") that…
In the context of learning deterministic policies in continuous domains, we revisit an approach, which was first proposed in Continuous Actor Critic Learning Automaton (CACLA) and later extended in Neural Fitted Actor Critic (NFAC). This approach is based on a policy update different from that of deterministic policy g…
Reinforcement Learning (RL) has emerged as an efficient method of choice for solving complex sequential decision making problems in automatic control, computer science, economics, and biology. In this paper we present a model-free RL algorithm to synthesize control policies that maximize the probability of satisfying h…
CURIE uses cellular automata to detect concept drift in data streams.
We introduce the State Classification Problem (SCP) for hybrid systems, and present Neural State Classification (NSC) as an efficient solution technique. SCP generalizes the model checking problem as it entails classifying each state of a hybrid automaton as either positive or negative, depending on whether or not …
Faster Tsetlin Machines use clause indexing to speed inference and learning.
Convolutional networks struggle to learn Game of Life, even with lottery ticket weights.
Machine learning predicts critical points for directed percolation models.
Finite vector bundles over complex manifolds are trivializable via finite covers.
Abstract: Non-residually finite hyperbolic groups imply non-residually finite rigid hyperbolic groups.
Finite type and finitely generated homotopy groups for manifold automorphisms.
The study proves how groups can be split with limited complexity.
Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work [2] residual finiteness of quandles was introduced, and it was proved that free quandles and knot quandles are residually finite. In this paper, we extend these resul…
In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residual finiteness of quandles arising from residually finite groups (conjugation, core and Alexander quandles) is established. Further, residual…
Study of uncountable family of finitely generated groups.
Study on minimal submanifolds with finite curvature in Euclidean space.
Finite rigid sets found in complex of curves for surfaces.
Study on finite entropy and energy in Kähler geometry.