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Federico Benitez

Publications and source records attributed to Federico Benitez.

13 recordsLinked to original sources

Dendritic structure enables powerful plasticity

Over the past decades, it has become increasingly clear that the complex morphology of cortical neurons is more than just a quirk of evolution, and that dendritic compartments serve as computational elements in their own right, rather than just providing connections between nerve cell bodies. While most computational studies discuss the enhanced representational capabilities of multi-compartment models as compared to point neurons, we focus here on the implications of neuronal morphology for synaptic plasticity. We argue that the ability of single neurons to simultaneously encode multiple pieces of information gives synapses local access to more than just the classical Hebbian pre- and postsynaptic terms, and with much greater specificity and reaction speed than permitted by other globally modulated factors. Based on a comparative review of recent dendritic learning models, we show how such neuronal compartmentalization can provide synapses with the means for calculating various forms of error signals, which in turn give rise to powerful real-time and fully local instantiations of deep learning through gradient descent. Implemented within cortical microcircuits capable of propagating and manipulating these errors, compartmentalized neurons thus ultimately enable the learning of far more complex tasks than are achievable by globally modulated Hebbian plasticity alone.

q-bio.NC

A Variational Latent Equilibrium for Learning in Neuronal Circuits

Brains remain unrivaled in their ability to recognize and generate complex spatiotemporal patterns. While AI is able to reproduce some of these capabilities, deep learning algorithms remain largely at odds with our current understanding of brain circuitry and dynamics. This is prominently the case for backpropagation through time (BPTT), the go-to algorithm for learning complex temporal dependencies. In this work we propose a general formalism to approximate BPTT in a controlled, biologically plausible manner. Our approach builds on, unifies and extends several previous approaches to local, time-continuous, phase-free spatiotemporal credit assignment based on principles of energy conservation and extremal action. Our starting point is a prospective energy function of neuronal states, from which we calculate real-time error dynamics for time-continuous neuronal networks. In the general case, this provides a simple and straightforward derivation of the adjoint method result for neuronal networks, the time-continuous equivalent to BPTT. With a few modifications, we can turn this into a fully local (in space and time) set of equations for neuron and synapse dynamics. Our theory provides a rigorous framework for spatiotemporal deep learning in the brain, while simultaneously suggesting a blueprint for physical circuits capable of carrying out these computations. These results reframe and extend the recently proposed Generalized Latent Equilibrium (GLE) model.

q-bio.NC

Backpropagation through space, time, and the brain

How physical networks of neurons, bound by spatio-temporal locality constraints, can perform efficient credit assignment, remains, to a large extent, an open question. In machine learning, the answer is almost universally given by the error backpropagation algorithm, through both space and time. However, this algorithm is well-known to rely on biologically implausible assumptions, in particular with respect to spatio-temporal (non-)locality. Alternative forward-propagation models such as real-time recurrent learning only partially solve the locality problem, but only at the cost of scaling, due to prohibitive storage requirements. We introduce Generalized Latent Equilibrium (GLE), a computational framework for fully local spatio-temporal credit assignment in physical, dynamical networks of neurons. We start by defining an energy based on neuron-local mismatches, from which we derive both neuronal dynamics via stationarity and parameter dynamics via gradient descent. The resulting dynamics can be interpreted as a real-time, biologically plausible approximation of backpropagation through space and time in deep cortical networks with continuous-time neuronal dynamics and continuously active, local synaptic plasticity. In particular, GLE exploits the morphology of dendritic trees to enable more complex information storage and processing in single neurons, as well as the ability of biological neurons to phase-shift their output rate with respect to their membrane potential, which is essential in both directions of information propagation. For the forward computation, it enables the mapping of time-continuous inputs to neuronal space, effectively performing a spatio-temporal convolution. For the backward computation, it permits the temporal inversion of feedback signals, which consequently approximate the adjoint variables necessary for useful parameter updates.

q-bio.NC

ELiSe: Efficient Learning of Sequences in Structured Recurrent Networks

Behavior can be described as a temporal sequence of actions driven by neural activity. To learn complex sequential patterns in neural networks, memories of past activities need to persist on significantly longer timescales than the relaxation times of single-neuron activity. While recurrent networks can produce such long transients, training these networks is a challenge. Learning via error propagation confers models such as FORCE, RTRL or BPTT a significant functional advantage, but at the expense of biological plausibility. While reservoir computing circumvents this issue by learning only the readout weights, it does not scale well with problem complexity. We propose that two prominent structural features of cortical networks can alleviate these issues: the presence of a certain network scaffold at the onset of learning and the existence of dendritic compartments for enhancing neuronal information storage and computation. Our resulting model for Efficient Learning of Sequences (ELiSe) builds on these features to acquire and replay complex non-Markovian spatio-temporal patterns using only local, always-on and phase-free synaptic plasticity. We showcase the capabilities of ELiSe in a mock-up of birdsong learning, and demonstrate its flexibility with respect to parametrization, as well as its robustness to external disturbances.

q-bio.NC

Prospective and retrospective coding in cortical neurons

Brains can process sensory information from different modalities at astonishing speed; this is surprising as the integration of inputs through the membrane of each individual neuron already causes a delayed response. Neuronal recordings {\em in vitro} reveal a possible explanation for this fast processing, in terms of individual neurons advancing their output firing rates with respect to the input, a concept which we refer to as prospective coding. The underlying mechanisms of prospective coding, however, are not completely understood. We propose a mechanistic explanation for individual neurons advancing their output on the level of single action potentials and instantaneous firing rates. We show that the spike generation mechanism can be the source for prospective (advanced) or retrospective (delayed) responses. A simplified Hodgkin-Huxley model identifies sodium inactivation as a source for prospective firing, controlling the timing of the neuron's output as a function of the voltage and its temporal derivative. We further show that slow adaptation processes, such as spike-frequency adaptation or deactivating dendritic currents, represent mechanisms generating prospective firing for inputs that undergo slow temporal modulations. In general, we show that adaptation processes at different time scales can cause advanced neuronal responses to time-varying inputs that are modulated on the corresponding time scales.

q-bio.NC

Primordial Earth mantle heterogeneity caused by the Moon-forming giant impact

The giant impact hypothesis for Moon formation successfully explains the dynamic properties of the Earth-Moon system but remains challenged by the similarity of isotopic fingerprints of the terrestrial and lunar mantles. Moreover, recent geochemical evidence suggests that the Earth's mantle preserves ancient (or "primordial") heterogeneity that predates the Moon-forming giant impact. Using a new hydrodynamical method, we here show that Moon-forming giant impacts lead to a stratified starting condition for the evolution of the terrestrial mantle. The upper layer of the Earth is compositionally similar to the disk, out of which the Moon evolves, whereas the lower layer preserves proto-Earth characteristics. As long as this predicted compositional stratification can at least partially be preserved over the subsequent billions of years of Earth mantle convection, the compositional similarity between the Moon and the accessible Earth's mantle is a natural outcome of realistic and high-probability Moon-forming impact scenarios. The preservation of primordial heterogeneity in the modern Earth not only reconciles geochemical constraints but is also consistent with recent geophysical observations. Furthermore, for significant preservation of a proto-Earth reservoir, the bulk composition of the Earth-Moon system may be systematically shifted towards chondritic values.

astro-ph.EP

Enhanced mixing in giant impact simulations with a new Lagrangian method

Giant impacts (GIs) are common in the late stage of planet formation. The Smoothed Particle Hydrodynamics (SPH) method is widely used for simulating the outcome of such violent collisions, one prominent example being the formation of the Moon. However, a decade of numerical studies in various areas of computational astrophysics has shown that the standard formulation of SPH suffers from several shortcomings such as artificial surface tension and its tendency to promptly damp turbulent motions on scales much larger than the physical dissipation scale, both resulting in the suppression of mixing. In order to quantify how severe these limitations are when modeling GIs we carried out a comparison of simulations with identical initial conditions performed with the standard SPH as well as with the novel Lagrangian Meshless Finite Mass (MFM) method in the GIZMO code. We confirm the lack of mixing between the impactor and target when SPH is employed, while MFM is capable of driving vigorous sub-sonic turbulence and leads to significant mixing between the two bodies. Modern SPH variants with artificial conductivity, a different formulation of the hydro force or reduced artificial viscosity, do not improve mixing as significantly. Angular momentum is conserved similarly well in both methods, but MFM does not suffer from spurious transport induced by artificial viscosity, resulting in a slightly higher angular momentum of the proto-lunar disk. Furthermore, SPH initial conditions exhibit an unphysical density discontinuity at the core-mantle boundary which is easily removed in MFM.

astro-ph.EP

Non-Perturbative Renormalization Group for the Diffusive Epidemic Process

We consider the Diffusive Epidemic Process (DEP), a two-species reaction-diffusion process originally proposed to model disease spread within a population. This model exhibits a phase transition from an active epidemic to an absorbing state without sick individuals. Field-theoretic analyses suggest that this transition belongs to the universality class of Directed Percolation with a Conserved quantity (DP-C). However, some exact predictions derived from the symmetries of DP-C seem to be in contradiction with lattice simulations. Here we revisit the field theory of both DP-C and DEP. We discuss in detail the symmetries present in the various formulations of both models, some of which had not been identified previously. We then investigate the DP-C model using the derivative expansion of the non-perturbative renormalization group formalism. We recover previous results for DP-C near its upper critical dimension $d_c=4$, but show how the corresponding fixed point seems to no longer exist below $d \lesssim 3$. Consequences for the DEP universality class are considered.

cond-mat.stat-mech

Quantum wetting transitions in two dimensions: an alternative path to non-universal interfacial singularities

We consider two-dimensional ($d=2$) systems with short-ranged microscopic interactions, where interface unbinding (wetting) transitions occur in the limit of vanishing temperature $T$. For $T=0$ the transition is characterized by non-universal critical properties analogous to those established for thermal wetting transitions in $d=3$, albeit with a redefined capillary parameter $\tildeω$. Within a functional renormalization-group treatment of an effective interfacial model, we compute the finite temperature phase diagram, exhibiting a line of interface unbinding transitions, terminating at $T=0$ with an interfacial quantum critical point. At finite $T$ we identify distinct scaling regimes, reflecting the interplay between quantum and thermal interfacial fluctuations. A crossover line marking the onset of the quantum critical regime is described by the $d=3$ interfacial correlation-length exponent $ν_{||}$. This opens a new way to investigate the non-universal character of $ν_{||}$ without penetrating the true critical regime. On the other hand, the emergent interfacial quantum critical regime shows no signatures of non-universality.

cond-mat.stat-mech

Some exact results in branching and annihilating random walks

We present some exact results on the behavior of Branching and Annihilating Random Walks, both in the Directed Percolation and Parity Conserving universality classes. Contrary to usual perturbation theory, we perform an expansion in the branching rate around the non trivial Pure Annihilation model, whose correlation and response function we compute exactly. With this, the non-universal threshold value for having a phase transition in the simplest system belonging to the Directed Percolation universality class is found to coincide with previous Non Perturbative Renormalization Group approximate results. We also show that the Parity Conserving universality class has an unexpected RG fixed point structure, with a PA fixed point which is unstable in all dimensions of physical interest.

cond-mat.stat-mech

Branching rate expansion around annihilating random walks

We present some exact results for branching and annihilating random walks. We compute the nonuniversal threshold value of the annihilation rate for having a phase transition in the simplest reaction-diffusion system belonging to the directed percolation universality class. Also, we show that the accepted scenario for the appearance of a phase transition in the parity conserving universality class must be improved. In order to obtain these results we perform an expansion in the branching rate around pure annihilation, a theory without branching. This expansion is possible because we manage to solve pure annihilation exactly in any dimension.

cond-mat.stat-mech

The Relativistic Factor in the Orbital Dynamics of Point Masses

There is a growing population of relativistically relevant minor bodies in the Solar System and a growing population of massive extrasolar planets with orbits very close to the central star where relativistic effects should have some signature. Our purpose is to review how general relativity affects the orbital dynamics of the planetary systems and to define a suitable relativistic correction for Solar System orbital studies when only point masses are considered. Using relativistic formulae for the N body problem suited for a planetary system given in the literature we present a series of numerical orbital integrations designed to test the relevance of the effects due to the general theory of relativity in the case of our Solar System. Comparison between different algorithms for accounting for the relativistic corrections are performed. Relativistic effects generated by the Sun or by the central star are the most relevant ones and produce evident modifications in the secular dynamics of the inner Solar System. The Kozai mechanism, for example, is modified due to the relativistic effects on the argument of the perihelion. Relativistic effects generated by planets instead are of very low relevance but detectable in numerical simulations.

astro-ph

On the 2-point function of the O(N) model

The self-energy of the critical 3-dimensional O(N) model is calculated. The analysis is performed in the context of the Non-Perturbative Renormalization Group, by exploiting an approximation which takes into account contributions of an infinite number of vertices. A very simple calculation yields the 2-point function in the whole range of momenta, from the UV Gaussian regime to the scaling one. Results are in good agreement with best estimates in the literature for any value of N in all momenta regimes. This encourages the use of this simple approximation procedure to calculate correlation functions at finite momenta in other physical situations.

cond-mat.stat-mech