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.
Quantum cellular automata form a homology theory.
Study immersions of punctured 4-manifolds for quantum automata applications.
CURIE uses cellular automata to detect concept drift in data streams.
Designs a Cellular Automata rule for forming touching loop patterns.
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 …
MBQC linked to CQCA, yielding efficient Ansätze.
MPNPs use message passing to exploit relational structure in stochastic processes.
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…
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…
Train track automata for fully irreducible elements in Out(F_r).
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…
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…
Physically-based overland flow models are computationally demanding, hindering their use for real-time applications. Therefore, the development of fast (and reasonably accurate) overland flow models is needed if they are to be used to support flood mitigation decision making. In this study, we investigate the potential…
This article introduces both a new algorithm for reconstructing epsilon-machines from data, as well as the decisional states. These are defined as the internal states of a system that lead to the same decision, based on a user-provided utility or pay-off function. The utility function encodes some a priori knowledge ex…
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…
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…
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 verifies RNNs using automata learning and model checking.
Transformers simulate finite-state automata with fewer layers.
Classifies knots in the Poincaré sphere, using fixed points and folding automata.
We introduce gym-city, a Reinforcement Learning environment that uses SimCity 1's game engine to simulate an urban environment, wherein agents might seek to optimize one or a combination of any number of city-wide metrics, on gameboards of various sizes. We focus on population, and analyze our agents' ability to genera…
A framework for analyzing financial systems under scenario constraints.
In this paper we generalize cellular algebras by allowing different partial orderings relative to fixed idempotents. For these relative cellular algebras we classify and construct simple modules, and we obtain other characterizations in analogy to cellular algebras. We also give several examples of algebras that are re…
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…
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 -state finite automata using a weighted majority algorithm. This aggregated prediction algorithm can be simplified using symmetry, and we pro…
This article introduces descriptive cellular homology on cell complexes, which is an extension of J.H.C. Whitehead's CW topology. A main result is that a descriptive cellular complex is a topology on fibres in a fibre bundle. An application of two forms of cellular homology is given in terms of the persistence of shape…
The study classifies cellular pseudomanifolds and their properties.
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…
We present a construction of cellular BF theory (in both abelian and non-abelian variants) on cobordisms equipped with cellular decompositions. Partition functions of this theory are invariant under subdivisions, satisfy a version of the quantum master equation, and satisfy Atiyah-Segal-type gluing formula with respect…
Optimizes natural frequencies of cellular composites with various microstructures.
For leveled spatial graphs, we find a surface embedding that allows cellular embedding.
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…
We give examples of harmonic cellular maps between negatively curved manifolds which are not diffeomorphisms but are homotopic to diffeomorphisms.
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…
The notion of cellular stratified spaces was introduced in a joint work of the author with Basabe, González, and Rudyak [1009.1851] with the aim of constructing a cellular model of the configuration space of a sphere. In particular, it was shown that the classifying space (order complex) of the face poset of a totally …
Main subject of the paper is a (strong) Morse function on a compact manifold with boundary. We construct a cellular structure and discuss its algebraic properties in this paper. Also we get an estimation on Arnold's question on a number of critical points of a Morse function with given boundary condition.
Dual neural network architecture improves accuracy and interpretability.
In this work we develop a cellular equivariant homology functor and apply it to prove an equivariant Euler-Poincare formula and an equivariant Lefschetz theorem.
The paper extends Gaussian processes to model complex interactions in cellular complexes.
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 …
ChemCPA predicts cellular responses to novel drugs using transfer learning.
Machine learning algorithms can be fooled by small well-designed adversarial perturbations. This is reminiscent of cellular decision-making where ligands (called antagonists) prevent correct signalling, like in early immune recognition. We draw a formal analogy between neural networks used in machine learning and model…
New findings on hyperbolicity of augmented links in thickened surfaces.
In many complex dynamical systems, artificial or natural, one can observe self-organization of patterns emerging from local rules. Cellular automata, like the Game of Life (GOL), have been widely used as abstract models enabling the study of various aspects of self-organization and morphogenesis, such as the emergence …
This paper introduces a new system for discovering patterns in morphogenetic systems using modular architecture and unsupervised learning.
Electron Cryo-Tomography (ECT) allows 3D visualization of subcellular structures at the submolecular resolution in close to the native state. However, due to the high degree of structural complexity and imaging limits, the automatic segmentation of cellular components from ECT images is very difficult. To complement an…
Classifies fake surfaces up to complexity 5.