How to explain grokking
Explanation of grokking (delayed generalization) in learning is given by modeling grokking by the stochastic gradient Langevin dynamics (Brownian motion) and applying the ideas of thermodynamics.
cond-mat.stat-mech↗
arXiv subjects
S. V. Kozyrev
Publications and source records attributed to S. V. Kozyrev.
Predator-Prey Model: Driven Hunt for Accelerated Grokking
A machine learning method is proposed using two agents that simulate the biological behavior of a predator and a prey. In this method, the predator and the prey interact with each other - the predator chases the prey while the prey runs away from the predator - to perform an optimization on the landscape. This method allows, for the case of a ravine landscape (i.e., a landscape with narrow ravines and with gentle slopes along the ravines) to avoid getting optimization stuck in the ravine. For this, in the optimization over a ravine landscape the predator drives the prey along the ravine. Thus we also call this approach, for the case of ravine landscapes, the driven hunt method. For some examples of grokking (i.e., delayed generalization) problems we show that this method allows for achieving up to a hundred times faster learning compared to the standard learning procedure.
cs.NE↗
Lotka-Volterra Model with Mutations and Generative Adversarial Networks
A model of population genetics of the Lotka-Volterra type with mutations on a statistical manifold is introduced. Mutations in the model are described by diffusion on a statistical manifold with a generator in the form of a Laplace-Beltrami operator with a Fisher-Rao metric, that is, the model combines population genetics and information geometry. This model describes a generalization of the model of machine learning theory, the model of generative adversarial network (GAN), to the case of populations of generative adversarial networks. The introduced model describes the control of overfitting for generative adversarial networks.
q-bio.PE↗
Landau-Zener formula and non-secular transitions
The relationship between the Landau-Zener model (which describes transitions between energy levels for a time-dependent Hamiltonian) and non-secular master equations is discussed. This approach allows to describe the widely discussed in the literature on quantum photosynthesis resonance of the energy of the vibron and the difference of exciton energies for transitions between exciton states coupled to the vibron.
quant-ph↗
Quantum feedback control in quantum photosynthesis
A model of charge separation in quantum photosynthesis as a model of quantum feedback control in a system of interacting excitons and vibrons is introduced. Quantum feedback in this approach describes the Landau--Zener transition with decoherence. The model explains irreversibility in the process of charge separation for quantum photosynthesis -- direct transitions for this quantum control model will have probabilities close to one and reverse transitions will have probabilities close to zero. This can be considered as a model of quantum ratchet. Also this model explains coincidence of energy of the vibron paired to the transition and Bohr frequency of the transition.
quant-ph↗
Genome as a functional program
We discuss a model of genome as a program with functional architecture and consider the approach to Darwinian evolution as a learning problem for functional programming. In particular we introduce a model of learning for some class of functional programs. This approach is related to information geometry -- the learning model uses some kind of distance in the information space (the reduction graph of the model), we consider statistical sum over paths in the reduction graph and discuss relation of this sum to temperature learning.
cs.NE↗
q-Deformation and free statistics for interaction of a field and a particle
Emerging of free (or quantum Boltzmann) statistics for a model of quantum particle interacting with quantum field is described in the stochastic limit without dipole approximation. The quantum field is considered in a Gaussian (for example temperature) state. Entangled operators which describe interaction of the field and the particle satisfy the q-deformed relations which in the stochastic limit generate free statistics.
quant-ph↗
Model of vibrones in quantum photosynthesis as an analog of model of laser
Mechanism of vibronic amplification of transport of excitons was discussed in relation to quantum photosynthesis. Vibrones (some modes of vibrations of molecules) are observed experimentally in photosynthetic systems. In the present paper we discuss a model of vibronic amplification of quantum transfer where generation of vibrones as a coherent vibrational mode is described by an analog of semiclassical theory of laser. We consider two models --- a model of nonequilibrium three level system with vibronic mode, and some variant of a model of laser without inversion. We conjecture that dark states discussed in relation to quantum photosynthesis might be related to mechanism of vibronic "laser" without inversion which amplifies the transfer of excitons. We prove that in presence of vibronic mode transfer rate of excitons increases and compute dependence of the transfer rate on parameters of the model.
physics.chem-ph↗
Biology is a constructive physics
Yuri Manin's approach to Zipf's law (Kolmogorov complexity as energy) is applied to investigation of biological evolution. Model of constructive statistical mechanics where complexity is a contribution to energy is proposed to model genomics. Scaling laws in genomics are discussed in relation to Zipf's law. This gives a model of Eugene Koonin's Third Evolutionary Synthesis (physical model which should describe scaling in genomics).
q-bio.PE↗
Quantum transport in degenerate systems
Transport in nonequilibrium degenerate quantum systems is investigated. Transfer rate depends on parameters of the system. In this paper we investigate dependence of the flow (transfer rate) on the angle between "bright" vectors (which define interaction of the system with the environment). We show that in some approximation for the system under investigation the flow is proportional to cosine squared of the angle between "bright" vectors. Earlier in arXiv:1603.07182 it was shown that in this degenerate quantum system excitation of non-decaying quantum "dark" states is possible, moreover the effectiveness of this process is proportional to sine squared of the angle between "bright" vectors (this phenomenon was discussed as a possible model of excitation of quantum coherences in quantum photosynthesis). Thus quantum transport and excitation of dark states are competing processes, dark states can be considered as a result of leakage of quantum states in quantum thermodynamic machine which performs the quantum transport.
quant-ph↗
$p$-Adic Mathematical Physics: The First 30 Years
$p$-Adic mathematical physics is a branch of modern mathematical physics based on the application of $p$-adic mathematical methods in modeling physical and related phenomena. It emerged in 1987 as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale, but then was extended to many other areas including biology. This paper contains a brief review of main achievements in some selected topics of $p$-adic mathematical physics and its applications, especially in the last decade. Attention is mainly paid to developments with promising future prospects.
math-ph↗
Flows in nonequilibrium quantum systems and quantum photosynthesis
A three level quantum system interacting with nonequilibrium environment is investigated. The stationary state of the system is found (both for non-coherent and coherent environment) and relaxation and decoherence to the stationary state is described. The stationary state of the system will be non-equilibrium and will generate flows. We describe the dependence of the flows on the state of the environment. We also discuss application of this model to the problem of quantum photosynthesis, in particular, to description of flows of excitons and generation of excitonic coherences.
quant-ph↗
Model of protein fragments and statistical potentials
We discuss a model of protein conformations where the conformations are combinations of short fragments from some small set. For these fragments we consider a distribution of frequencies of occurrence of pairs (sequence of amino acids, conformation), averaged over some balls in the spaces of sequences and conformations. These frequencies can be estimated due to smallness of epsilon-entropy of the set of conformations of protein fragments. We consider statistical potentials for protein fragments which describe the mentioned frequencies of occurrence and discuss model of free energy of a protein where the free energy is equal to a sum of statistical potentials of the fragments. We also consider contribution of contacts of fragments to the energy of protein conformation, and contribution from statistical potentials of some hierarchical set of larger protein fragments. This set of fragments is constructed using the distribution of frequencies of occurrence of short fragments. We discuss applications of this model to problem of prediction of the native conformation of a protein from its primary structure and to description of dynamics of a protein. Modification of structural alignment taking into account statistical potentials for protein fragments is considered and application to threading procedure for proteins is discussed.
q-bio.BM↗
Dark states in quantum photosynthesis
We discuss a model of quantum photosynthesis with degeneracy in the light-harvesting system. We consider interaction of excitons in chromophores with light and phonons (vibrations of environment). These interactions have dipole form but are different (are related to non-parallel vectors of "bright" states). We show that this leads to excitation of non-decaying "dark" states. We discuss relation of this model to the known from spectroscopical experiments phenomenon of existence of photonic echo in quantum photosynthesis.
physics.bio-ph↗
Cluster networks and Bruhat-Tits buildings
Clustering procedure for the case where instead of a fixed metric one applies a family of metrics is considered. In this case instead of a classification tree one obtains a classification network (a directed acyclic graph with non directed cycles). Relation to Bruhat-Tits buildings is discussed. Dimension of a general cluster system is considered.
math.MG↗
Hierarchical model of the actomyosin molecular motor based on ultrametric diffusion with drift
We discuss the approach to investigation of molecular machines using systems of integro--differential ultrametric (p-adic) reaction--diffusion equations with drift. This approach combines the features of continuous and discrete dynamic models. We apply this model to investigation of actomyosin molecular motor. The introduced system of equations is solved analytically using p-adic wavelet theory. We find explicit stationary solutions and behavior in the relaxation regime.
q-bio.BM↗
Quinary lattice model of secondary structures of polymers
In the standard approach to lattice proteins the models based on nearest neighbor interaction are used. In this kind of models it is difficult to explain the existence of secondary structures --- special preferred conformations of protein chains. In the present paper a new lattice model of proteins is proposed which is based on non-local cooperative interactions. In this model the energy of a conformation of a polymer is equal to the sum of energies of conformations of fragments of the polymer chain of the length five. It is shown that this quinary lattice model is able to describe at qualitative level secondary structures of proteins: for this model all conformations with minimal energy are combinations of lattice models of alpha--helix and beta--strand. Moreover for lattice polymers of the length not longer that 38 monomers we can describe all conformations with minimal energy.
cond-mat.soft↗
Application of p-adic analysis to time series
Time series defined by a p-adic pseudo-differential equation is investigated using the expansion of the time series over p-adic wavelets. Quadratic correlation function is computed. This correlation function shows a degree--like behavior and is locally constant for some time periods. It is natural to apply this kind of models for the investigation of avalanche processes and punctuated equilibrium as well as fractal-like analysis of time series generated by measurement of pressure in oil wells.
math-ph↗