Researchers found a regular language for maximal lexicographic representatives in braid monoids.
problem Understanding the language of maximal lexicographic representatives in braid monoids.
method Detailed description of the smallest Finite State Automaton and analysis of the proportion of elements.
result The proportion of elements of length k whose maximal lexicographic representative finishes with the first generator tends to a number P_{n,1} ≥ 1/8 as k tends to infinity.
A new layer learns abstract relations from graph structure using finite-state automata.
problem Learning abstract relations from graph structure for program analysis.
method Relaxing the problem into learning finite-state automata policies on a graph-based POMDP and training these policies using implicit differentiation.
result GFSA layer finds shortcuts in grid-world graphs and reproduces simple static analyses on Python programs.
Transformers simulate finite-state automata with fewer layers.
problem How do shallow, non-recurrent Transformers simulate complex computations?
method Hierarchical reparameterization of recurrent dynamics to simulate automata.
result Polynomial-sized, O(logT)-depth solutions exist and are common. ISA learns subgoals for reinforcement learning agents.
problem Learning subgoals for efficient reinforcement learning.
method Induces a subgoal automaton from observation traces using inductive logic programming.
result ISA learns subgoals that improve RL performance and convergence.
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…
Method extracts knowledge from LSTM for sequence validation.
problem Validating sequences generated by unknown automata.
method Clustering hidden states to build a corresponding automaton.
result Automaton accurately predicts sequence validity.
Method extracts weighted automata from RNNs using state space regression.
problem Extracting weighted automata from RNNs for better model understanding.
method Regression on RNN state space to prioritize counterexample candidates.
result Quantitative/weighted extension of DFA extraction.
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 defines topology automaton for Barański carpets and proves Hölder equivalence conditions.
problem Tackles Hölder equivalence of Barański carpets.
method Defines topology automaton and applies method from previous studies.
result Obtains sufficient condition for Hölder equivalence of Barański carpets.
Study of group actions on CAT(0) cube complexes, focusing on marked length spectra.
problem Comparing marked length spectra of group actions on CAT(0) cube complexes.
method Use of finite-state automata and thermodynamic formalism for suspension flows over subshifts of finite type.
result Prove that the Manhattan curve is analytic and convex, and a straight line if and only if marked length spectra are homothetic.
New formulas derived for Jones polynomial of rational links.
problem Calculating the Jones polynomial of rational links.
method Colored Brylawski's tensor product formula for Tutte polynomials, finite automaton for crossing signs.
result Generalization of existing formulas for 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.
Reservoir computers and RNNs fall short of optimal prediction for stochastic PDFA.
problem Predicting stochastic processes generated by probabilistic deterministic finite-state automata.
method Generalized linear models, Reservoir computers, and Long Short-Term Memory (LSTM) RNNs were tested.
result Each method can fall short of maximal predictive accuracy by up to 50% after training.
DeepSynth synthesizes automata to guide deep RL agents through sparse, non-Markovian rewards.
problem Training deep RL agents with sparse, non-Markovian rewards and unknown high-level objectives.
method Employing a novel algorithm for synthesizing compact automata to uncover sequential structure from trace data.
result Reduces the number of iterations required for policy synthesis by two orders of magnitude and improves scalability.
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…
New neural stack and Turing Machine architectures prove stability and computational power.
problem Designing stable neural network architectures for Turing Machine simulation.
method Introducing neural stack and Turing Machine architectures, proving stability and computational equivalence.
result Differentiable nnTM with bounded neurons can simulate Turing Machine in real-time and is equivalent to UTM.
Paper details Hilbert-curve for high-performance data mining.
problem Efficiently mapping multi-dimensional data to one dimension.
method Defines Hilbert-curve using finite automaton and context-free grammar.
result Cache-oblivious algorithms for matrix operations and clustering.
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.
problem Determining the existence of anti-tori in square complexes associated with Mealy automata
method Associating a graph and a square complex with a Mealy automaton and proving the equivalence between bi-reversibility and aperiodicity of the graph
result The square complex contains an anti-torus if and only if the automaton is bi-reversible and the graph is aperiodic
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…
The paper distills a weighted automaton from RNNs for language modeling.
problem Tackles the gap between deep learning and grammatical inference.
method Uses a spectral approach to infer a weighted automaton from a trained RNN.
result Extracted weighted automata are good approximations of the RNNs, validating the approach.
Algorithm extracts deterministic PDFA from probabilistic models with improved performance.
problem Learning deterministic models from probabilistic ones with noise.
method Adapted L* algorithm for probabilistic settings, using conditional probabilities and local tolerance.
result Achieves better performance on WER and NDCG than spectral extraction of WFAs.
Paper verifies RNNs using automata learning and model checking.
problem Verifying the correctness of RNNs is challenging.
method Learn a deterministic finite automaton from RNN, use model checking for verification.
result Can discover and generalize counterexamples to faulty flows.
Deep learning models predict faster dune migration in arid regions.
problem Predicting the movement of sand dunes in arid regions.
method Tested two deep learning algorithms (GAN and CNN) on simulated data from a cellular automaton model.
result Deep learning models can predict dune migration at ten million times the speed of existing models.
RL algorithm uses LTL to specify goals for MDPs, ensuring policy satisfaction.
problem Ensuring safety-critical RL policies meet specified goals formally.
method Formulates goals using LTL, translates to LDGBA, shapes synchronous reward function.
result Algorithm synthesizes policies satisfying LTL goals with maximal probability.
NSC classifies hybrid system states for time-bounded reachability, achieving high accuracy with minimal false negatives.
problem Classifying states in hybrid systems for time-bounded reachability.
method Neural State Classification using Deep Neural Networks.
result Achieved 99.25% to 99.98% accuracy with false-negative rates reduced to 0.0015 to 0 after tuning.
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…
Method trains policies for MDPs that satisfy LTL properties.
problem Training policies for MDPs that meet complex temporal logic constraints.
method Convert LTL to automaton, construct synchronised MDP, adapt reward function, apply neural Q-iteration.
result Synthesised policies satisfy specified LTL properties.
New algorithm learns deterministic policies in continuous domains using sign of advantage function.
problem Learning deterministic policies in continuous domains.
method Proposes a new trust region algorithm, Penalized NFAC (PeNFAC), based on a theoretical explanation of the advantage function.
result PeNFAC algorithm surpasses state-of-the-art algorithms in learning deterministic policies in classic control problems.
Compactifies stability conditions on triangulated categories, inspired by Teichmüller theory.
problem Moduli space of stability conditions on triangulated categories.
method Inspired by Thurston compactification of Teichmüller space, constructs maps to infinite projective space.
result Injective maps with compact closure, identifies categorical analogs of intersection functionals.
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…
The Open University studies student online behavior in virtual learning environments.
problem Improving retention rates in online modules.
method GUHA and Markov chain-based analysis of student activity.
result Both methods are valid for modeling student activities.
CURIE uses cellular automata to detect concept drift in data streams.
problem Detecting changes in data distribution (concept drift) in data streams.
method CURIE represents data stream distribution in a cellular automata grid and uses its neighborhood rule to detect changes.
result CURIE, when hybridized with base learners, performs competitively in detection metrics and classification accuracy.
Study on natural actor-critic for POMDPs with finite memory.
problem Learning in partially observed Markov decision processes with noisy observations.
method Finite actor-critic method with multi-step temporal difference learning.
result First non-asymptotic global convergence for POMDPs with function approximation.
State-regularized RNNs improve interpretability and performance on long-term memory tasks.
problem RNNs struggle with long-term memory and lack of interpretability.
method Introduce a stochastic state transition mechanism to limit state transitions to a finite set.
result State-regularized RNNs perform better on tasks requiring long-term memory.
The paper simplifies multi-agent RL dynamics in finite-state Markov games using homogenization.
problem Approximating complex multi-agent reinforcement learning dynamics in finite-state Markov games.
method Rescaling learning process by reducing learning rate and increasing update frequency, proving convergence to an ODE.
result The rescaled process converges to an ODE that approximates the agent's learning dynamics.
Extends effect variable concept to finite states for web search evaluation.
problem Finding effect of variant variables in changes of observable variables.
method Theoretical analysis and simultaneous distribution decomposition.
result States of extreme effect variable are minimally affected by variant and highly different in observable variable.
Finite presentations for skein algebras linked to gauge field theory.
problem Understanding finite presentations for skein algebras and their relationship to gauge field theory.
method Provided finite presentations and deduced properties of stated skein algebras.
result Stated skein algebras are Koszul and isomorphic to quantum moduli algebras in gauge field theory.
Paper uses RL to synthesize control policies for LTL objectives in uncertain environments.
problem Control policies for uncertain, probabilistic environments with temporal logic specifications.
method Model-free RL algorithm, LTL to LDBA translation, synchronous reward function, asymptotic satisfaction probability.
result RL algorithm maximizes satisfaction probability of LTL objectives in PL-MDPs.
Center identified in stated skein algebra for quantum traces.
problem Understanding the center of the stated skein algebra.
method Analyzing the algebra as a generalization of Kauffman bracket skein algebra, focusing on the case when the quantum parameter is a root of unity.
result Simple description and dimension calculation of the center over the center module.
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…
We extend a recent synchronization analysis of exact finite-state sources to nonexact sources for which synchronization occurs only asymptotically. Although the proof methods are quite different, the primary results remain the same. We find that an observer's average uncertainty in the source state vanishes exponential…
Recurrent neural networks trained on regular languages exhibit stable states that can recover from noise.
problem Stability of internal states in recurrent neural networks trained on regular languages.
method Empirical study with analysis of network activation and transitions between states.
result Recurrent neural networks trained on regular languages can recover from random perturbations and maintain stable states.
New method predicts state evolution for non-first-order algorithms on nonconvex problems.
problem Analyzing nonconvex optimization problems with random data.
method Developed a state evolution for a broader class of algorithms including first-order and saddle point updates.
result Established rigorous state evolution predictions and finite-sample guarantees for non-first-order methods.
We analyze how an observer synchronizes to the internal state of a finite-state information source, using the epsilon-machine causal representation. Here, we treat the case of exact synchronization, when it is possible for the observer to synchronize completely after a finite number of observations. The more difficult …
Estimates Markov chain parameters from a single long sequence, analyzing complexity based on mixing properties.
problem Estimating parameters of a discrete-state Markov chain kernel from a single long sequence of observations.
method Characterizes minimax sample complexity in finite and countably infinite cases, focusing on mixing properties.
result Sample complexity is governed by mixing properties, with finite-sample estimators available for finite-state cases.
Quantum states associated with subsets of product manifolds are separable.
problem Characterizing quantum states associated with subsets of product manifolds.
method Using holomorphic sections of quantum line bundles and restriction maps.
result Quantum states associated with finite unions of products are separable.