arXiv subjects

Alexander N. Gorban

Publications and source records attributed to Alexander N. Gorban.

At least 37 records · Page 2Linked to original sources

arXiv2022

Situation-based memory in spiking neuron-astrocyte network

Mammalian brains operate in a very special surrounding: to survive they have to react quickly and effectively to the pool of stimuli patterns previously recognized as danger. Many learning tasks often encountered by living organisms involve a specific set-up centered around a relatively small set of patterns presented in a particular environment. For example, at a party, people recognize friends immediately, without deep analysis, just by seeing a fragment of their clothes. This set-up with reduced "ontology" is referred to as a "situation". Situations are usually local in space and time. In this work, we propose that neuron-astrocyte networks provide a network topology that is effectively adapted to accommodate situation-based memory. In order to illustrate this, we numerically simulate and analyze a well-established model of a neuron-astrocyte network, which is subjected to stimuli conforming to the situation-driven environment. Three pools of stimuli patterns are considered: external patterns, patterns from the situation associative pool regularly presented to the network and learned by the network, and patterns already learned and remembered by astrocytes. Patterns from the external world are added to and removed from the associative pool. Then we show that astrocytes are structurally necessary for an effective function in such a learning and testing set-up. To demonstrate this we present a novel neuromorphic model for short-term memory implemented by a two-net spiking neural-astrocytic network. Our results show that such a system tested on synthesized data with selective astrocyte-induced modulation of neuronal activity provides an enhancement of retrieval quality in comparison to standard spiking neural networks trained via Hebbian plasticity only. We argue that the proposed set-up may offer a new way to analyze, model, and understand neuromorphic artificial intelligence systems.

q-bio.NC↗

arXiv2021

High-dimensional separability for one- and few-shot learning

This work is driven by a practical question: corrections of Artificial Intelligence (AI) errors. These corrections should be quick and non-iterative. To solve this problem without modification of a legacy AI system, we propose special `external' devices, correctors. Elementary correctors consist of two parts, a classifier that separates the situations with high risk of error from the situations in which the legacy AI system works well and a new decision for situations with potential errors. Input signals for the correctors can be the inputs of the legacy AI system, its internal signals, and outputs. If the intrinsic dimensionality of data is high enough then the classifiers for correction of small number of errors can be very simple. According to the blessing of dimensionality effects, even simple and robust Fisher's discriminants can be used for one-shot learning of AI correctors. Stochastic separation theorems provide the mathematical basis for this one-short learning. However, as the number of correctors needed grows, the cluster structure of data becomes important and a new family of stochastic separation theorems is required. We refuse the classical hypothesis of the regularity of the data distribution and assume that the data can have a fine-grained structure with many clusters and peaks in the probability density. New stochastic separation theorems for data with fine-grained structure are formulated and proved. The multi-correctors for granular data are proposed. The advantages of the multi-corrector technology were demonstrated by examples of correcting errors and learning new classes of objects by a deep convolutional neural network on the CIFAR-10 dataset. The key problems of the non-classical high-dimensional data analysis are reviewed together with the basic preprocessing steps including supervised, semi-supervised and domain adaptation Principal Component Analysis.

cs.LG↗

arXiv2021

Scikit-dimension: a Python package for intrinsic dimension estimation

Dealing with uncertainty in applications of machine learning to real-life data critically depends on the knowledge of intrinsic dimensionality (ID). A number of methods have been suggested for the purpose of estimating ID, but no standard package to easily apply them one by one or all at once has been implemented in Python. This technical note introduces \texttt{scikit-dimension}, an open-source Python package for intrinsic dimension estimation. \texttt{scikit-dimension} package provides a uniform implementation of most of the known ID estimators based on scikit-learn application programming interface to evaluate global and local intrinsic dimension, as well as generators of synthetic toy and benchmark datasets widespread in the literature. The package is developed with tools assessing the code quality, coverage, unit testing and continuous integration. We briefly describe the package and demonstrate its use in a large-scale (more than 500 datasets) benchmarking of methods for ID estimation in real-life and synthetic data. The source code is available from https://github.com/j-bac/scikit-dimension , the documentation is available from https://scikit-dimension.readthedocs.io .

cs.LG↗

arXiv2021

Demystification of Few-shot and One-shot Learning

Few-shot and one-shot learning have been the subject of active and intensive research in recent years, with mounting evidence pointing to successful implementation and exploitation of few-shot learning algorithms in practice. Classical statistical learning theories do not fully explain why few- or one-shot learning is at all possible since traditional generalisation bounds normally require large training and testing samples to be meaningful. This sharply contrasts with numerous examples of successful one- and few-shot learning systems and applications. In this work we present mathematical foundations for a theory of one-shot and few-shot learning and reveal conditions specifying when such learning schemes are likely to succeed. Our theory is based on intrinsic properties of high-dimensional spaces. We show that if the ambient or latent decision space of a learning machine is sufficiently high-dimensional than a large class of objects in this space can indeed be easily learned from few examples provided that certain data non-concentration conditions are met.

cs.LG↗

arXiv2021

Transition states and entangled mass action law

The classical approaches to the derivation of the (generalized) Mass Action Law (MAL) assume that the intermediate transition state (i) has short life time and (ii) is in partial equilibrium with the initial reagents of the elementary reaction. The partial equilibrium assumption (ii) means that the reverse decomposition of the intermediates is much faster than its transition through other channels to the products. In this work we demonstrate how avoiding this partial equilibrium assumption modifies the reaction rates. This kinetic revision of transition state theory results in an effective `entanglement' of reaction rates, which become linear combinations of different MAL expressions.

physics.chem-ph↗

arXiv2021

General stochastic separation theorems with optimal bounds

Phenomenon of stochastic separability was revealed and used in machine learning to correct errors of Artificial Intelligence (AI) systems and analyze AI instabilities. In high-dimensional datasets under broad assumptions each point can be separated from the rest of the set by simple and robust Fisher's discriminant (is Fisher separable). Errors or clusters of errors can be separated from the rest of the data. The ability to correct an AI system also opens up the possibility of an attack on it, and the high dimensionality induces vulnerabilities caused by the same stochastic separability that holds the keys to understanding the fundamentals of robustness and adaptivity in high-dimensional data-driven AI. To manage errors and analyze vulnerabilities, the stochastic separation theorems should evaluate the probability that the dataset will be Fisher separable in given dimensionality and for a given class of distributions. Explicit and optimal estimates of these separation probabilities are required, and this problem is solved in present work. The general stochastic separation theorems with optimal probability estimates are obtained for important classes of distributions: log-concave distribution, their convex combinations and product distributions. The standard i.i.d. assumption was significantly relaxed. These theorems and estimates can be used both for correction of high-dimensional data driven AI systems and for analysis of their vulnerabilities. The third area of application is the emergence of memories in ensembles of neurons, the phenomena of grandmother's cells and sparse coding in the brain, and explanation of unexpected effectiveness of small neural ensembles in high-dimensional brain.

cs.AI↗

arXiv2020

Formation of working memory in a spiking neuron network accompanied by astrocytes

We propose a biologically plausible computational model of working memory (WM) implemented by the spiking neuron network (SNN) interacting with a network of astrocytes. SNN is modelled by the synaptically coupled Izhikevich neurons with a non-specific architecture connection topology. Astrocytes generating calcium signals are connected by local gap junction diffusive couplings and interact with neurons by chemicals diffused in the extracellular space. Calcium elevations occur in response to the increase of concentration of a neurotransmitter released by spiking neurons when a group of them fire coherently. In turn, gliotransmitters are released by activated astrocytes modulating the strengths of synaptic connections in the corresponding neuronal group. Input information is encoded as two-dimensional patterns of short applied current pulses stimulating neurons. The output is taken from frequencies of transient discharges of corresponding neurons. We show how a set of information patterns with quite significant overlapping areas can be uploaded into the neuron-astrocyte network and stored for several seconds. Information retrieval is organised by the application of a cue pattern representing the one from the memory set distorted by noise. We found that successful retrieval with level of the correlation between recalled pattern and ideal pattern more than 90% is possible for multi-item WM task. Having analysed the dynamical mechanism of WM formation, we discovered that astrocytes operating at a time scale of a dozen of seconds can successfully store traces of neuronal activations corresponding to information patterns. In the retrieval stage, the astrocytic network selectively modulates synaptic connections in SNN leading to the successful recall. Information and dynamical characteristics of the proposed WM model agrees with classical concepts and other WM models.

q-bio.NC↗

arXiv2020

Trajectories, bifurcations and pseudotime in large clinical datasets: applications to myocardial infarction and diabetes data

Large observational clinical datasets become increasingly available for mining associations between various disease traits and administered therapy. These datasets can be considered as representations of the landscape of all possible disease conditions, in which a concrete pathology develops through a number of stereotypical routes, characterized by `points of no return' and `final states' (such as lethal or recovery states). Extracting this information directly from the data remains challenging, especially in the case of synchronic (with a short-term follow up) observations. Here we suggest a semi-supervised methodology for the analysis of large clinical datasets, characterized by mixed data types and missing values, through modeling the geometrical data structure as a bouquet of bifurcating clinical trajectories. The methodology is based on application of elastic principal graphs which can address simultaneously the tasks of dimensionality reduction, data visualization, clustering, feature selection and quantifying the geodesic distances (pseudotime) in partially ordered sequences of observations. The methodology allows positioning a patient on a particular clinical trajectory (pathological scenario) and characterizing the degree of progression along it with a qualitative estimate of the uncertainty of the prognosis. Overall, our pseudo-time quantification-based approach gives a possibility to apply the methods developed for dynamical disease phenotyping and illness trajectory analysis (diachronic data analysis) to synchronic observational data. We developed a tool $ClinTrajan$ for clinical trajectory analysis implemented in Python programming language. We test the methodology in two large publicly available datasets: myocardial infarction complications and readmission of diabetic patients data.

stat.AP↗

arXiv2020

Blessing of dimensionality at the edge

In this paper we present theory and algorithms enabling classes of Artificial Intelligence (AI) systems to continuously and incrementally improve with a-priori quantifiable guarantees - or more specifically remove classification errors - over time. This is distinct from state-of-the-art machine learning, AI, and software approaches. Another feature of this approach is that, in the supervised setting, the computational complexity of training is linear in the number of training samples. At the time of classification, the computational complexity is bounded by few inner product calculations. Moreover, the implementation is shown to be very scalable. This makes it viable for deployment in applications where computational power and memory are limited, such as embedded environments. It enables the possibility for fast on-line optimisation using improved training samples. The approach is based on the concentration of measure effects and stochastic separation theorems and is illustrated with an example on the identification faulty processes in Computer Numerical Control (CNC) milling and with a case study on adaptive removal of false positives in an industrial video surveillance and analytics system.

cs.LG↗

arXiv2020

Fractional norms and quasinorms do not help to overcome the curse of dimensionality

The curse of dimensionality causes the well-known and widely discussed problems for machine learning methods. There is a hypothesis that using of the Manhattan distance and even fractional quasinorms lp (for p less than 1) can help to overcome the curse of dimensionality in classification problems. In this study, we systematically test this hypothesis. We confirm that fractional quasinorms have a greater relative contrast or coefficient of variation than the Euclidean norm l2, but we also demonstrate that the distance concentration shows qualitatively the same behaviour for all tested norms and quasinorms and the difference between them decays as dimension tends to infinity. Estimation of classification quality for kNN based on different norms and quasinorms shows that a greater relative contrast does not mean better classifier performance and the worst performance for different databases was shown by different norms (quasinorms). A systematic comparison shows that the difference of the performance of kNN based on lp for p=2, 1, and 0.5 is statistically insignificant.

cs.LG↗

arXiv2020

Informational Space of Meaning for Scientific Texts

In Natural Language Processing, automatic extracting the meaning of texts constitutes an important problem. Our focus is the computational analysis of meaning of short scientific texts (abstracts or brief reports). In this paper, a vector space model is developed for quantifying the meaning of words and texts. We introduce the Meaning Space, in which the meaning of a word is represented by a vector of Relative Information Gain (RIG) about the subject categories that the text belongs to, which can be obtained from observing the word in the text. This new approach is applied to construct the Meaning Space based on Leicester Scientific Corpus (LSC) and Leicester Scientific Dictionary-Core (LScDC). The LSC is a scientific corpus of 1,673,350 abstracts and the LScDC is a scientific dictionary which words are extracted from the LSC. Each text in the LSC belongs to at least one of 252 subject categories of Web of Science (WoS). These categories are used in construction of vectors of information gains. The Meaning Space is described and statistically analysed for the LSC with the LScDC. The usefulness of the proposed representation model is evaluated through top-ranked words in each category. The most informative n words are ordered. We demonstrated that RIG-based word ranking is much more useful than ranking based on raw word frequency in determining the science-specific meaning and importance of a word. The proposed model based on RIG is shown to have ability to stand out topic-specific words in categories. The most informative words are presented for 252 categories. The new scientific dictionary and the 103,998 x 252 Word-Category RIG Matrix are available online. Analysis of the Meaning Space provides us with a tool to further explore quantifying the meaning of a text using more complex and context-dependent meaning models that use co-occurrence of words and their combinations.

cs.CL↗

arXiv2020

On Adversarial Examples and Stealth Attacks in Artificial Intelligence Systems

In this work we present a formal theoretical framework for assessing and analyzing two classes of malevolent action towards generic Artificial Intelligence (AI) systems. Our results apply to general multi-class classifiers that map from an input space into a decision space, including artificial neural networks used in deep learning applications. Two classes of attacks are considered. The first class involves adversarial examples and concerns the introduction of small perturbations of the input data that cause misclassification. The second class, introduced here for the first time and named stealth attacks, involves small perturbations to the AI system itself. Here the perturbed system produces whatever output is desired by the attacker on a specific small data set, perhaps even a single input, but performs as normal on a validation set (which is unknown to the attacker). We show that in both cases, i.e., in the case of an attack based on adversarial examples and in the case of a stealth attack, the dimensionality of the AI's decision-making space is a major contributor to the AI's susceptibility. For attacks based on adversarial examples, a second crucial parameter is the absence of local concentrations in the data probability distribution, a property known as Smeared Absolute Continuity. According to our findings, robustness to adversarial examples requires either (a) the data distributions in the AI's feature space to have concentrated probability density functions or (b) the dimensionality of the AI's decision variables to be sufficiently small. We also show how to construct stealth attacks on high-dimensional AI systems that are hard to spot unless the validation set is made exponentially large.

cs.LG↗

arXiv2020

Singularities of transient processes in dynamics and beyond

This note is a brief review of the analysis of long transients in dynamical systems. The problem of long transients arose in many disciplines, from physical and chemical kinetic to biology and even social sciences. Detailed analysis of singularities of various `relaxation times' associated long transients with bifurcations of $ω$-limit sets, homoclinic structures (intersections of $α$- and $ω$-limit sets) and other peculiarities of dynamics. This review was stimulated by the analysis of anomalously long transients in ecology published recently by A. Morozov and S. Petrovskii with co-authors.

cond-mat.stat-mech↗

arXiv2020

Personality Traits and Drug Consumption. A Story Told by Data

This is a preprint version of the first book from the series: "Stories told by data". In this book a story is told about the psychological traits associated with drug consumption. The book includes: - A review of published works on the psychological profiles of drug users. - Analysis of a new original database with information on 1885 respondents and usage of 18 drugs. (Database is available online.) - An introductory description of the data mining and machine learning methods used for the analysis of this dataset. - The demonstration that the personality traits (five factor model, impulsivity, and sensation seeking), together with simple demographic data, give the possibility of predicting the risk of consumption of individual drugs with sensitivity and specificity above 70% for most drugs. - The analysis of correlations of use of different substances and the description of the groups of drugs with correlated use (correlation pleiades). - Proof of significant differences of personality profiles for users of different drugs. This is explicitly proved for benzodiazepines, ecstasy, and heroin. - Tables of personality profiles for users and non-users of 18 substances. The book is aimed at advanced undergraduates or first-year PhD students, as well as researchers and practitioners. No previous knowledge of machine learning, advanced data mining concepts or modern psychology of personality is assumed. For more detailed introduction into statistical methods we recommend several undergraduate textbooks. Familiarity with basic statistics and some experience in the use of probabilities would be helpful as well as some basic technical understanding of psychology.

stat.AP↗

arXiv2020

High--Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality

High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the "curse of dimensionality" states: many problems become exponentially difficult in high dimensions. Recently, the other side of the coin, the "blessing of dimensionality", has attracted much attention. It turns out that generic high-dimensional datasets exhibit fairly simple geometric properties. Thus, there is a fundamental tradeoff between complexity and simplicity in high dimensional spaces. Here we present a brief explanatory review of recent ideas, results and hypotheses about the blessing of dimensionality and related simplifying effects relevant to machine learning and neuroscience.

cs.LG↗

arXiv2019

LScDC-new large scientific dictionary

In this paper, we present a scientific corpus of abstracts of academic papers in English -- Leicester Scientific Corpus (LSC). The LSC contains 1,673,824 abstracts of research articles and proceeding papers indexed by Web of Science (WoS) in which publication year is 2014. Each abstract is assigned to at least one of 252 subject categories. Paper metadata include these categories and the number of citations. We then develop scientific dictionaries named Leicester Scientific Dictionary (LScD) and Leicester Scientific Dictionary-Core (LScDC), where words are extracted from the LSC. The LScD is a list of 974,238 unique words (lemmas). The LScDC is a core list (sub-list) of the LScD with 104,223 lemmas. It was created by removing LScD words appearing in not greater than 10 texts in the LSC. LScD and LScDC are available online. Both the corpus and dictionaries are developed to be later used for quantification of meaning in academic texts. Finally, the core list LScDC was analysed by comparing its words and word frequencies with a classic academic word list 'New Academic Word List (NAWL)' containing 963 word families, which is also sampled from an academic corpus. The major sources of the corpus where NAWL is extracted are Cambridge English Corpus (CEC), oral sources and textbooks. We investigate whether two dictionaries are similar in terms of common words and ranking of words. Our comparison leads us to main conclusion: most of words of NAWL (99.6%) are present in the LScDC but two lists differ in word ranking. This difference is measured.

cs.CL↗

arXiv2019

Symphony of high-dimensional brain

This paper is the final part of the scientific discussion organised by the Journal "Physics of Life Rviews" about the simplicity revolution in neuroscience and AI. This discussion was initiated by the review paper "The unreasonable effectiveness of small neural ensembles in high-dimensional brain". Phys Life Rev 2019, doi 10.1016/j.plrev.2018.09.005, arXiv:1809.07656. The topics of the discussion varied from the necessity to take into account the difference between the theoretical random distributions and "extremely non-random" real distributions and revise the common machine learning theory, to different forms of the curse of dimensionality and high-dimensional pitfalls in neuroscience. V. K{ů}rkov{á}, A. Tozzi and J.F. Peters, R. Quian Quiroga, P. Varona, R. Barrio, G. Kreiman, L. Fortuna, C. van Leeuwen, R. Quian Quiroga, and V. Kreinovich, A.N. Gorban, V.A. Makarov, and I.Y. Tyukin participated in the discussion. In this paper we analyse the symphony of opinions and the possible outcomes of the simplicity revolution for machine learning and neuroscience.

q-bio.NC↗

arXiv2019

Basic, simple and extendable kinetic model of protein synthesis

Protein synthesis is one of the most fundamental biological processes, which consumes a significant amount of cellular resources. Despite existence of multiple mathematical models of translation, varying in the level of mechanistical details, surprisingly, there is no basic and simple chemical kinetic model of this process, derived directly from the detailed kinetic model. One of the reasons for this is that the translation process is characterized by indefinite number of states, thanks to existence of polysomes. We bypass this difficulty by applying a trick consisting in lumping multiple states of translated mRNA into few dynamical variables and by introducing a variable describing the pool of translating ribosomes. The simplest model can be solved analytically under some assumptions. The basic and simple model can be extended, if necessary, to take into account various phenomena such as the interaction between translating ribosomes, limited amount of ribosomal units or regulation of translation by microRNA. The model can be used as a building block (translation module) for more complex models of cellular processes. We demonstrate the utility of the model in two examples. First, we determine the critical parameters of the single protein synthesis for the case when the ribosomal units are abundant. Second, we demonstrate intrinsic bi-stability in the dynamics of the ribosomal protein turnover and predict that a minimal number of ribosomes should pre-exists in a living cell to sustain its protein synthesis machinery, even in the absence of proliferation.

q-bio.MN↗