arXiv subjects

Jean-Pascal Pfister

Publications and source records attributed to Jean-Pascal Pfister.

At least 19 recordsLinked to original sources

arXiv2026

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↗

arXiv2025

On the stability of event-based control with neuronal dynamics

Event-based control, unlike analogue control, poses significant analytical challenges due to its hybrid dynamics. This work investigates the stability and inter-event time properties of a control-affine system under event-based impulsive control. The controller consists of multiple neuronal units with leaky integrate-and-fire dynamics acting on a time-invariant, multivariable plant in closed loop. Both the plant state and the neuronal units exhibit discontinuities that cancel if combined linearly, enabling a direct correspondence between the event-based impulsive controller and a corresponding analogue controller. Leveraging this observation, we prove global practical stability of the event-based impulsive control system. In the general nonlinear case, we show that the event-based impulsive controller ensures global practical asymptotic stability if the analogue system is input-to-state stable (ISS) with respect to specific disturbances. In the linear case, we further show global practical exponential stability if the analogue system is stable. We illustrate our results with numerical simulations. The findings reveal a fundamental link between analogue and event-based impulsive control, providing new insights for the design of neuromorphic controllers.

eess.SY↗

arXiv2025

Phase Transitions of the Additive Uniform Noise Channel with Peak Amplitude and Cost Constraint

Under which condition is quantization optimal? We address this question in the context of the additive uniform noise channel under peak amplitude and cost constraints. We compute analytically the capacity-achieving input distribution as a function of the noise level, the average cost constraint, and the curvature of the cost function. We find that when the cost function is concave, the capacity-achieving input distribution is discrete, whereas when the cost function is convex and the cost constraint is active, the support of the capacity-achieving input distribution spans the entire interval. For the cases of a discrete capacity-achieving input distribution, we derive the analytical expressions for the capacity of the channel.

cs.IT↗

arXiv2025

Capacity-Achieving Input Distribution of the Additive Uniform Noise Channel With Peak Amplitude and Cost Constraint

Under which condition is quantization optimal? We address this question in the context of the additive uniform noise channel under peak amplitude and power constraints. We compute analytically the capacity-achieving input distribution as a function of the noise level, the average power constraint and the exponent of the power constraint. We found that when the cost constraint is tight and the cost function is concave, the capacity-achieving input distribution is discrete, whereas when the cost function is convex, the support of the capacity-achieving input distribution spans the entire interval.

cs.IT↗

arXiv2024

On gauge freedom, conservativity and intrinsic dimensionality estimation in diffusion models

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward continuous denoising process, which can be described by a time-dependent vector field and is used as a generative model. In the original formulation of the diffusion model, this vector field is assumed to be the score function (i.e. it is the gradient of the log-probability at a given time in the diffusion process). Curiously, on the practical side, most studies on diffusion models implement this vector field as a neural network function and do not constrain it be the gradient of some energy function (that is, most studies do not constrain the vector field to be conservative). Even though some studies investigated empirically whether such a constraint will lead to a performance gain, they lead to contradicting results and failed to provide analytical results. Here, we provide three analytical results regarding the extent of the modeling freedom of this vector field. {Firstly, we propose a novel decomposition of vector fields into a conservative component and an orthogonal component which satisfies a given (gauge) freedom. Secondly, from this orthogonal decomposition, we show that exact density estimation and exact sampling is achieved when the conservative component is exactly equals to the true score and therefore conservativity is neither necessary nor sufficient to obtain exact density estimation and exact sampling. Finally, we show that when it comes to inferring local information of the data manifold, constraining the vector field to be conservative is desirable.

cs.LG↗

arXiv2022

Rate-Distortion Problems of the Poisson Process based on a Group-Theoretic Approach

We study rate-distortion problems of a Poisson process using a group theoretic approach. By describing a realization of a Poisson point process with either point timings or inter-event (inter-point) intervals and by choosing appropriate distortion measures, we establish rate-distortion problems of a homogeneous Poisson process as ball- or sphere-covering problems for realizations of the hyperoctahedral group in $\mathbb{R}^n$. Specifically, the realizations we investigate are a hypercube and a hyperoctahedron. Thereby we unify three known rate-distortion problems of a Poisson process (with different distortion measures, but resulting in the same rate-distortion function) with the Laplacian-$\ell_1$ rate-distortion problem.

cs.IT↗

arXiv2022

Efficient Sampling-Based Bayesian Active Learning for synaptic characterization

Bayesian Active Learning (BAL) is an efficient framework for learning the parameters of a model, in which input stimuli are selected to maximize the mutual information between the observations and the unknown parameters. However, the applicability of BAL to experiments is limited as it requires performing high-dimensional integrations and optimizations in real time: current methods are either too time consuming, or only applicable to specific models. Here, we propose an Efficient Sampling-Based Bayesian Active Learning (ESB-BAL) framework, which is efficient enough to be used in real-time biological experiments. We apply our method to the problem of estimating the parameters of a chemical synapse from the postsynaptic responses to evoked presynaptic action potentials. Using synthetic data and synaptic whole-cell patch-clamp recordings, we show that our method can improve the precision of model-based inferences, thereby paving the way towards more systematic and efficient experimental designs in physiology.

q-bio.QM↗

arXiv2021

Density estimation on low-dimensional manifolds: an inflation-deflation approach

Normalizing Flows (NFs) are universal density estimators based on Neural Networks. However, this universality is limited: the density's support needs to be diffeomorphic to a Euclidean space. In this paper, we propose a novel method to overcome this limitation without sacrificing universality. The proposed method inflates the data manifold by adding noise in the normal space, trains an NF on this inflated manifold, and, finally, deflates the learned density. Our main result provides sufficient conditions on the manifold and the specific choice of noise under which the corresponding estimator is exact. Our method has the same computational complexity as NFs and does not require computing an inverse flow. We also show that, if the embedding dimension is much larger than the manifold dimension, noise in the normal space can be well approximated by Gaussian noise. This allows using our method for approximating arbitrary densities on unknown manifolds provided that the manifold dimension is known.

cs.LG↗

arXiv2020

A Unification of Weighted and Unweighted Particle Filters

Particle filters (PFs), which are successful methods for approximating the solution of the filtering problem, can be divided into two types: weighted and unweighted PFs. It is well known that weighted PFs suffer from the weight degeneracy and curse of dimensionality. To sidestep these issues, unweighted PFs have been gaining attention, though they have their own challenges. The existing literature on these types of PFs is based on distinct approaches. In order to establish a connection, we put forward a framework that unifies weighted and unweighted PFs in the continuous-time filtering problem. We show that the stochastic dynamics of a particle system described by a pair process, representing particles and their importance weights, should satisfy two necessary conditions in order for its distribution to match the solution of the Kushner--Stratonovich equation. In particular, we demonstrate that the bootstrap particle filter (BPF), which relies on importance sampling, and the feedback particle filter (FPF), which is an unweighted PF based on optimal control, arise as special cases from a broad class and that there is a smooth transition between the two. The freedom in designing the PF dynamics opens up potential ways to address the existing issues in the aforementioned algorithms, namely weight degeneracy in the BPF and gain estimation in the FPF.

math.OC↗

arXiv2020

Learning as filtering: implications for spike-based plasticity

Most normative models in computational neuroscience describe the task of learning as the optimisation of a cost function with respect to a set of parameters. However, learning as optimisation fails to account for a time varying environment during the learning process; and the resulting point estimate in parameter space does not account for uncertainty. Here, we frame learning as filtering, i.e., a principled method for including time and parameter uncertainty. We derive the filtering-based learning rule for a spiking neuronal network - the Synaptic Filter - and show its computational and biological relevance. For the computational relevance, we show that filtering in combination with Bayesian regression improves performance compared to a gradient learning rule with optimal learning rate in terms of weight estimation. Furthermore, the filtering-based rule outperforms gradient-based rules in the presence of model mismatch, indicating a better generalisation performance. The dynamics of the mean of the Synaptic Filter is consistent with the spike-timing dependent plasticity (STDP) while the dynamics of the variance makes novel predictions regarding spike-timing dependent changes of EPSP variability. Moreover, the Synaptic Filter explains experimentally observed negative correlations between homo- and heterosynaptic plasticity.

q-bio.NC↗

arXiv2019

Asymptotically exact unweighted particle filter for manifold-valued hidden states and point process observations

The filtering of a Markov diffusion process on a manifold from counting process observations leads to `large' changes in the conditional distribution upon an observed event, corresponding to a multiplication of the density by the intensity function of the observation process. If that distribution is represented by unweighted samples or particles, they need to be jointly transformed such that they sample from the modified distribution. In previous work, this transformation has been approximated by a translation of all the particles by a common vector. However, such an operation is ill-defined on a manifold, and on a vector space, a constant gain can lead to a wrong estimate of the uncertainty over the hidden state. Here, taking inspiration from the feedback particle filter (FPF), we derive an asymptotically exact filter (called ppFPF) for point process observations, whose particles evolve according to intrinsic (i.e. parametrization-invariant) dynamics that are composed of the dynamics of the hidden state plus additional control terms. While not sharing the gain-times-error structure of the FPF, the optimal control terms are expressed as solutions to partial differential equations analogous to the weighted Poisson equation for the gain of the FPF. The proposed filter can therefore make use of existing approximation algorithms for solutions of weighted Poisson equations.

math.OC↗

arXiv2019

The Hitchhiker's Guide to Nonlinear Filtering

Nonlinear filtering is the problem of online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We start our review of the theory on nonlinear filtering from the simplest `filtering' task we can think of, namely static Bayesian inference. From there we continue our journey through discrete-time models, which is usually encountered in machine learning, and generalize to and further emphasize continuous-time filtering theory. The idea of changing the probability measure connects and elucidates several aspects of the theory, such as the parallels between the discrete- and continuous-time problems and between different observation models. Furthermore, it gives insight into the construction of particle filtering algorithms. This tutorial is targeted at scientists and engineers and should serve as an introduction to the main ideas of nonlinear filtering, and as a segway to more advanced and specialized literature.

stat.ME↗

arXiv2019

Bayesian regression explains how human participants handle parameter uncertainty

The human brain copes with sensory uncertainty in accordance with Bayes' rule. However, it is unknown how the brain makes predictions in the presence of parameter uncertainty. Here, we tested whether and how humans take parameter uncertainty into account in a regression task. Participants extrapolated a parabola from a limited number of noisy points, shown on a computer screen. The quadratic parameter was drawn from a prior distribution, unknown to the observers. We tested whether human observers take full advantage of the given information, including the likelihood function of the observed points and the prior distribution of the quadratic parameter. We compared human performance with Bayesian regression, which is the (Bayes) optimal solution to this problem, and three sub-optimal models, namely maximum likelihood regression, prior regression and maximum a posteriori regression, which are simpler to compute. Our results clearly show that humans use Bayesian regression. We further investigated several variants of Bayesian regression models depending on how the generative noise is treated and found that participants act in line with the more sophisticated version.

q-bio.NC↗

arXiv2018

Propagation of spiking moments in linear Hawkes networks

The present paper provides exact mathematical expressions for the high-order moments of spiking activity in a recurrently-connected network of linear Hawkes processes. It extends previous studies that have explored the case of a (linear) Hawkes network driven by deterministic intensity functions to the case of a stimulation by external inputs (rate functions or spike trains) with arbitrary correlation structure. Our approach describes the spatio-temporal filtering induced by the afferent and recurrent connectivities (with arbitrary synaptic response kernels) using operators acting on the input moments. This algebraic viewpoint provides intuition about how the network ingredients shape the input-output mapping for moments, as well as cumulants. We also show using numerical simulation that our results hold for neurons with refractoriness implemented by self-inhibition, provided the corresponding negative feedback for each neuron only mildly alters its mean firing probability.

q-bio.NC↗

arXiv2018

On the choice of metric in gradient-based theories of brain function

The idea that the brain functions so as to minimize certain costs pervades theoretical neuroscience. Since a cost function by itself does not predict how the brain finds its minima, additional assumptions about the optimization method need to be made to predict the dynamics of physiological quantities. In this context, steepest descent (also called gradient descent) is often suggested as an algorithmic principle of optimization potentially implemented by the brain. In practice, researchers often consider the vector of partial derivatives as the gradient. However, the definition of the gradient and the notion of a steepest direction depend on the choice of a metric. Since the choice of the metric involves a large number of degrees of freedom, the predictive power of models that are based on gradient descent must be called into question, unless there are strong constraints on the choice of the metric. Here we provide a didactic review of the mathematics of gradient descent, illustrate common pitfalls of using gradient descent as a principle of brain function with examples from the literature and propose ways forward to constrain the metric.

q-bio.NC↗

arXiv2018

Particle-filtering approaches for nonlinear Bayesian decoding of neuronal spike trains

The number of neurons that can be simultaneously recorded doubles every seven years. This ever increasing number of recorded neurons opens up the possibility to address new questions and extract higher dimensional stimuli from the recordings. Modeling neural spike trains as point processes, this task of extracting dynamical signals from spike trains is commonly set in the context of nonlinear filtering theory. Particle filter methods relying on importance weights are generic algorithms that solve the filtering task numerically, but exhibit a serious drawback when the problem dimensionality is high: they are known to suffer from the 'curse of dimensionality' (COD), i.e. the number of particles required for a certain performance scales exponentially with the observable dimensions. Here, we first briefly review the theory on filtering with point process observations in continuous time. Based on this theory, we investigate both analytically and numerically the reason for the COD of weighted particle filtering approaches: Similarly to particle filtering with continuous-time observations, the COD with point-process observations is due to the decay of effective number of particles, an effect that is stronger when the number of observable dimensions increases. Given the success of unweighted particle filtering approaches in overcoming the COD for continuous- time observations, we introduce an unweighted particle filter for point-process observations, the spike-based Neural Particle Filter (sNPF), and show that it exhibits a similar favorable scaling as the number of dimensions grows. Further, we derive rules for the parameters of the sNPF from a maximum likelihood approach learning. We finally employ a simple decoding task to illustrate the capabilities of the sNPF and to highlight one possible future application of our inference and learning algorithm.

q-bio.NC↗

arXiv2017

How to avoid the curse of dimensionality: scalability of particle filters with and without importance weights

Particle filters are a popular and flexible class of numerical algorithms to solve a large class of nonlinear filtering problems. However, standard particle filters with importance weights have been shown to require a sample size that increases exponentially with the dimension D of the state space in order to achieve a certain performance, which precludes their use in very high-dimensional filtering problems. Here, we focus on the dynamic aspect of this curse of dimensionality (COD) in continuous time filtering, which is caused by the degeneracy of importance weights over time. We show that the degeneracy occurs on a time-scale that decreases with increasing D. In order to soften the effects of weight degeneracy, most particle filters use particle resampling and improved proposal functions for the particle motion. We explain why neither of the two can prevent the COD in general. In order to address this fundamental problem, we investigate an existing filtering algorithm based on optimal feedback control that sidesteps the use of importance weights. We use numerical experiments to show that this Feedback Particle Filter (FPF) by Yang et al. (2013) does not exhibit a COD.

math.OC↗

arXiv2017

Optimised information gathering in smartphone users

Human activities from hunting to emailing are performed in a fractal-like scale invariant pattern. These patterns are considered efficient for hunting or foraging, but are they efficient for gathering information? Here we link the scale invariant pattern of inter-touch intervals on the smartphone to optimal strategies for information gathering. We recorded touchscreen touches in 65 individuals for a month and categorized the activity into checking for information vs. sharing content. For both categories, the inter-touch intervals were well described by power-law fits spanning 5 orders of magnitude, from 1 s to several hours. The power-law exponent typically found for checking was 1.5 and for generating it was 1.3. Next, by using computer simulations we addressed whether the checking pattern was efficient - in terms of minimizing futile attempts yielding no new information. We find that the best performing power law exponent depends on the duration of the assessment and the exponent of 1.5 was the most efficient in the short-term i.e. in the few minutes range. Finally, we addressed whether how people generated and shared content was in tune with the checking pattern. We assumed that the unchecked posts must be minimized for maximal efficiency and according to our analysis the most efficient temporal pattern to share content was the exponent of 1.3 - which was also the pattern displayed by the smartphone users. The behavioral organization for content generation is different from content consumption across time scales. We propose that this difference is a signature of optimal behavior and the short-term assessments used in modern human actions.

physics.soc-ph↗