arXiv subjects

André Longtin

Publications and source records attributed to André Longtin.

7 recordsLinked to original sources

arXiv2025

Selecting fitted models under epistemic uncertainty using a stochastic process on quantile functions

Fitting models to data is an important part of the practice of science. Advances in machine learning have made it possible to fit more -- and more complex -- models, but have also exacerbated a problem: when multiple models fit the data equally well, which one(s) should we pick? The answer depends entirely on the modelling goal. In the scientific context, the essential goal is _replicability_: if a model works well to describe one experiment, it should continue to do so when that experiment is replicated tomorrow, or in another laboratory. The selection criterion must therefore be robust to the variations inherent to the replication process. In this work we develop a nonparametric method for estimating uncertainty on a model's empirical risk when replications are non-stationary, thus ensuring that a model is only rejected when another is _reproducibly_ better. We illustrate the method with two examples: one a more classical setting, where the models are structurally distinct, and a machine learning-inspired setting, where they differ only in the value of their parameters. We show how, in this context of replicability or "epistemic uncertainty", it compares favourably to existing model selection criteria, and has more satisfactory behaviour with large experimental datasets.

stat.ME↗

arXiv2025

Optimal rate-variance coding due to firing threshold adaptation near criticality

Recurrently connected neuron populations play key roles in sensory perception and memory storage across various brain regions. While these populations are often assumed to encode information through firing rates, this method becomes unreliable with weak stimuli. We propose that in such cases, information can be transmitted via spatial spike patterns, employing a sparse or combinatorial coding based on firing rate variance. Around the critical point of a stochastic recurrent excitable network, we uncover a synergistic dual-coding scheme, enabled by single-cell threshold adaptation. This scheme optimizes variance coding for weak signals without compromising rate coding for stronger inputs, thus maximizing input/output mutual information. These optimizations are robust across adaptation rules and coupling strengths through self-suppression of internal noise, particularly around the network's phase transition, and are linked to threshold recovery times observed in hippocampal memory circuits (~$10^2$-$10^3$ms). In contrast, nonadaptive networks perform similarly only at criticality, suggesting that threshold adaptation is essential for reliable encoding of weak signals into diverse spatial patterns. Our results imply a fundamental role for near-critical latent adaptive dynamics enabled by dual coding in biological and artificial neural networks.

q-bio.NC↗

arXiv2025

Neural Heterogeneity Enables Adaptive Encoding of Time Sequences

Biological systems represent time from microseconds to years. An important gap in our knowledge concerns the mechanisms for encoding time intervals of hundreds of milliseconds to minutes that matter for tasks like navigation, communication, storage, recall, and prediction of stimulus patterns. A recently identified mechanism in fish thalamic neurons addresses this gap. Representation of intervals between events uses the ubiquitous property of neural fatigue, where firing adaptation sets in quickly during an event. The recovery from fatigue by the next stimulus is a monotonous function of time elapsed. Here we develop a full theory for the representation of intervals, allowing for recovery time scales and sensitivity to past stimuli to vary across cells. Our Bayesian framework combines parametrically heterogeneous stochastic dynamical modeling with interval priors to predict available timing information independent of actual decoding mechanism. A compromise is found between optimally encoding the latest time interval and previous ones, crucial for spatial navigation. Cellular heterogeneity is actually necessary to represent interval sequences, a novel computational role for experimentally observed heterogeneity. This biophysical adaptation-based timing memory shapes spatiotemporal information for efficient storage and recall in target recurrent networks.

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arXiv2023

Connecting levels of analysis in the computational era

Neuroscience and artificial intelligence are closely intertwined, but so are the physics of dynamical system, philosophy and psychology. Each of these fields try in their own way to relate observations at the level of molecules, synapses, neurons or behavior, to a function. An influential conceptual approach to this end was popularized by David Marr, which focused on the interaction between three theoretical 'levels of analysis'. With the convergence of simulation-based approaches, algorithm-oriented Neuro-AI and high-throughput data, we currently see much research organized around four levels of analysis: observations, models, algorithms and functions. Bidirectional interaction between these levels influences how we undertake interdisciplinary science.

q-bio.NC↗

arXiv2020

Inference of a mesoscopic population model from population spike trains

To understand how rich dynamics emerge in neural populations, we require models exhibiting a wide range of activity patterns while remaining interpretable in terms of connectivity and single-neuron dynamics. However, it has been challenging to fit such mechanistic spiking networks at the single neuron scale to empirical population data. To close this gap, we propose to fit such data at a meso scale, using a mechanistic but low-dimensional and hence statistically tractable model. The mesoscopic representation is obtained by approximating a population of neurons as multiple homogeneous `pools' of neurons, and modelling the dynamics of the aggregate population activity within each pool. We derive the likelihood of both single-neuron and connectivity parameters given this activity, which can then be used to either optimize parameters by gradient ascent on the log-likelihood, or to perform Bayesian inference using Markov Chain Monte Carlo (MCMC) sampling. We illustrate this approach using a model of generalized integrate-and-fire neurons for which mesoscopic dynamics have been previously derived, and show that both single-neuron and connectivity parameters can be recovered from simulated data. In particular, our inference method extracts posterior correlations between model parameters, which define parameter subsets able to reproduce the data. We compute the Bayesian posterior for combinations of parameters using MCMC sampling and investigate how the approximations inherent to a mesoscopic population model impact the accuracy of the inferred single-neuron parameters.

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arXiv2019

Interspike interval correlations in networks of inhibitory integrate-and-fire neurons

We study temporal correlations of interspike intervals (ISIs), quantified by the network-averaged serial correlation coefficient (SCC), in networks of both current- and conductance-based purely inhibitory integrate-and-fire neurons. Numerical simulations reveal transitions to negative SCCs at intermediate values of bias current drive and network size. As bias drive and network size are increased past these values, the SCC returns to zero. The SCC is maximally negative at an intermediate value of the network oscillation strength. The dependence of the SCC on two canonical schemes for synaptic connectivity is studied, and it is shown that the results occur robustly in both schemes. For conductance-based synapses, the SCC becomes negative at the onset of both a fast and slow coherent network oscillation. Finally, we devise a noise-reduced diffusion approximation for current-based networks that accounts for the observed temporal correlation transitions.

q-bio.NC↗

arXiv2017

Evolution of moments and correlations in non-renewal escape-time processes

The theoretical description of non-renewal stochastic systems is a challenge. Analytical results are often not available or can only be obtained under strong conditions, limiting their applicability. Also, numerical results have mostly been obtained by ad-hoc Monte--Carlo simulations, which are usually computationally expensive when a high degree of accuracy is needed. To gain quantitative insight into these systems under general conditions, we here introduce a numerical iterated first-passage time approach based on solving the time-dependent Fokker-Planck equation (FPE) to describe the statistics of non-renewal stochastic systems. We illustrate the approach using spike-triggered neuronal adaptation in the leaky and perfect integrate-and-fire model, respectively. The transition to stationarity of first-passage time moments and their sequential correlations occur on a non-trivial timescale that depends on all system parameters. Surprisingly this is so for both single exponential and scale-free power-law adaptation. The method works beyond the small noise and timescale separation approximations. It shows excellent agreement with direct Monte Carlo simulations, which allows for the computation of transient and stationary distributions. We compare different methods to compute the evolution of the moments and serial correlation coefficients (SCC), and discuss the challenge of reliably computing the SCC which we find to be very sensitive to numerical inaccuracies for both the leaky and perfect integrate-and-fire models. In conclusion, our methods provide a general picture of non-renewal dynamics in a wide range of stochastic systems exhibiting short and long-range correlations.

q-bio.NC↗