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Nicolas Brunel

Publications and source records attributed to Nicolas Brunel.

At least 19 recordsLinked to original sources
arXiv2025

Weighted Conformal Prediction Provides Adaptive and Valid Mask-Conditional Coverage for General Missing Data Mechanisms

Conformal prediction (CP) offers a principled framework for uncertainty quantification, but it fails to guarantee coverage when faced with missing covariates. In addressing the heterogeneity induced by various missing patterns, Mask-Conditional Valid (MCV) Coverage has emerged as a more desirable property than Marginal Coverage. In this work, we adapt split CP to handle missing values by proposing a preimpute-mask-then-correct framework that can offer valid coverage. We show that our method provides guaranteed Marginal Coverage and Mask-Conditional Validity for general missing data mechanisms. A key component of our approach is a reweighted conformal prediction procedure that corrects the prediction sets after distributional imputation (multiple imputation) of the calibration dataset, making our method compatible with standard imputation pipelines. We derive two algorithms, and we show that they are approximately marginally valid and MCV. We evaluate them on synthetic and real-world datasets. It reduces significantly the width of prediction intervals w.r.t standard MCV methods, while maintaining the target guarantees.

stat.ML↗
arXiv2025

Shape Analysis of Euclidean Curves under Frenet-Serret Framework

Geometric frameworks for analyzing curves are common in applications as they focus on invariant features and provide visually satisfying solutions to standard problems such as computing invariant distances, averaging curves, or registering curves. We show that for any smooth curve in R^d, d>1, the generalized curvatures associated with the Frenet-Serret equation can be used to define a Riemannian geometry that takes into account all the geometric features of the shape. This geometry is based on a Square Root Curvature Transform that extends the square root-velocity transform for Euclidean curves (in any dimensions) and provides likely geodesics that avoid artefacts encountered by representations using only first-order geometric information. Our analysis is supported by simulated data and is especially relevant for analyzing human motions. We consider trajectories acquired from sign language, and show the interest of considering curvature and also torsion in their analysis, both being physically meaningful.

stat.ME↗
arXiv2025

PSM: Prompt Sensitivity Minimization via LLM-Guided Black-Box Optimization

System prompts are critical for guiding the behavior of Large Language Models (LLMs), yet they often contain proprietary logic or sensitive information, making them a prime target for extraction attacks. Adversarial queries can successfully elicit these hidden instructions, posing significant security and privacy risks. Existing defense mechanisms frequently rely on heuristics, incur substantial computational overhead, or are inapplicable to models accessed via black-box APIs. This paper introduces a novel framework for hardening system prompts through shield appending, a lightweight approach that adds a protective textual layer to the original prompt. Our core contribution is the formalization of prompt hardening as a utility-constrained optimization problem. We leverage an LLM-as-optimizer to search the space of possible SHIELDs, seeking to minimize a leakage metric derived from a suite of adversarial attacks, while simultaneously preserving task utility above a specified threshold, measured by semantic fidelity to baseline outputs. This black-box, optimization-driven methodology is lightweight and practical, requiring only API access to the target and optimizer LLMs. We demonstrate empirically that our optimized SHIELDs significantly reduce prompt leakage against a comprehensive set of extraction attacks, outperforming established baseline defenses without compromising the model's intended functionality. Our work presents a paradigm for developing robust, utility-aware defenses in the escalating landscape of LLM security. The code is made public on the following link: https://github.com/psm-defense/psm

cs.CR↗
arXiv2025

Paradoxical increase of capacity due to spurious overlaps in attractor networks

In Hopfield-type associative memory models, memories are stored in the connectivity matrix and can be retrieved subsequently thanks to the collective dynamics of the network. In these models, the retrieval of a particular memory can be hampered by overlaps between the network state and other memories, termed spurious overlaps since these overlaps collectively introduce noise in the retrieval process. In classic models, spurious overlaps increase the variance of synaptic inputs but do not affect the mean. We show here that in models equipped with a learning rule inferred from neurobiological data, spurious overlaps collectively reduce the mean synaptic inputs to neurons, and that this mean reduction causes in turn an increase in storage capacity through a sparsening of network activity. Our paper demonstrates a link between a specific feature of experimentally inferred plasticity rules and network storage capacity.

q-bio.NC↗
arXiv2025

From the perceptron to the cerebellum

The perceptron has served as a prototypical neuronal learning machine in the physics community interested in neural networks and artificial intelligence, which included G\'erard Toulouse as one of its prominent figures. It has also been used as a model of Purkinje cells of the cerebellum, a brain structure involved in motor learning, in the early influential theories of David Marr and James Albus. We review these theories, more recent developments in the field, and highlight questions of current interest.

q-bio.NC↗
arXiv2024

Impact of dendritic non-linearities on the computational capabilities of neurons

How neurons integrate the myriad synaptic inputs scattered across their dendrites is a fundamental question in neuroscience. Multiple neurophysiological experiments have shown that dendritic non-linearities can have a strong influence on synaptic input integration. These non-linearities have motivated mathematical descriptions of single neuron as a two-layer computational units, which have been shown to increase substantially the computational abilities of neurons, compared to linear dendritic integration. However, current analytical studies are restricted to neurons with unconstrained synaptic weights and unplausible dendritic non-linearities. Here, we introduce a two-layer model with sign-constrained synaptic weights and a biologically plausible form of dendritic non-linearity, and investigate its properties using both statistical physics methods and numerical simulations. We find that the dendritic non-linearity enhances both the number of possible learned input-output associations and the learning velocity. We characterize how capacity and learning speed depend on the implemented non-linearity and the levels of dendritic and somatic inhibition. We calculate analytically the distribution of synaptic weights in networks close to maximal capacity, and find that a large fraction of zero-weight ('silent' or 'potential') synapses naturally emerge in neurons with sign-constrained synapses, as a consequence of non-linear dendritic integration. Non-linearly induced sparsity comes with a second central advantage for neuronal information processing, i.e. input and synaptic noise robustness. We test our model on standard real-world benchmark datasets and observe empirically that the non-linearity provides an enhancement in generalization performance, showing that it enables to capture more complex input/output relations.

q-bio.NC↗
arXiv2024

Conformal Approach To Gaussian Process Surrogate Evaluation With Coverage Guarantees

Gaussian processes (GPs) are a Bayesian machine learning approach widely used to construct surrogate models for the uncertainty quantification of computer simulation codes in industrial applications. It provides both a mean predictor and an estimate of the posterior prediction variance, the latter being used to produce Bayesian credibility intervals. Interpreting these intervals relies on the Gaussianity of the simulation model as well as the well-specification of the priors which are not always appropriate. We propose to address this issue with the help of conformal prediction. In the present work, a method for building adaptive cross-conformal prediction intervals is proposed by weighting the non-conformity score with the posterior standard deviation of the GP. The resulting conformal prediction intervals exhibit a level of adaptivity akin to Bayesian credibility sets and display a significant correlation with the surrogate model local approximation error, while being free from the underlying model assumptions and having frequentist coverage guarantees. These estimators can thus be used for evaluating the quality of a GP surrogate model and can assist a decision-maker in the choice of the best prior for the specific application of the GP. The performance of the method is illustrated through a panel of numerical examples based on various reference databases. Moreover, the potential applicability of the method is demonstrated in the context of surrogate modeling of an expensive-to-evaluate simulator of the clogging phenomenon in steam generators of nuclear reactors.

stat.ML↗
arXiv2022

Robust PCA for Anomaly Detection and Data Imputation in Seasonal Time Series

We propose a robust principal component analysis (RPCA) framework to recover low-rank and sparse matrices from temporal observations. We develop an online version of the batch temporal algorithm in order to process larger datasets or streaming data. We empirically compare the proposed approaches with different RPCA frameworks and show their effectiveness in practical situations.

stat.ML↗
arXiv2022

MAPIE: an open-source library for distribution-free uncertainty quantification

Estimating uncertainties associated with the predictions of Machine Learning (ML) models is of crucial importance to assess their robustness and predictive power. In this submission, we introduce MAPIE (Model Agnostic Prediction Interval Estimator), an open-source Python library that quantifies the uncertainties of ML models for single-output regression and multi-class classification tasks. MAPIE implements conformal prediction methods, allowing the user to easily compute uncertainties with strong theoretical guarantees on the marginal coverages and with mild assumptions on the model or on the underlying data distribution. MAPIE is hosted on scikit-learn-contrib and is fully "scikit-learn-compatible". As such, it accepts any type of regressor or classifier coming with a scikit-learn API. The library is available at: https://github.com/scikit-learn-contrib/MAPIE/.

stat.ML↗
arXiv2022

Curvature and Torsion estimation of 3D functional data: A geometric approach to build the mean shape under the Frenet Serret framework

The analysis of curves has been routinely dealt with using tools from functional data analysis. However its extension to multi-dimensional curves poses a new challenge due to its inherent geometric features that are difficult to capture with the classical approaches that rely on linear approximations. We develop an alternative characterization of a mean that reflects shape variation of the curves. Based on a geometric representation of the curves through the Frenet-Serret ordinary differential equations, we introduce a new definition of mean curvature and mean torsion, as well as mean shape through the notion of mean vector field. This new formulation of the mean for multi-dimensional curves allows us to integrate the parameters for the shape features into the unified functional data modelling framework. We formulate the estimation problem of the functional parameters in a penalized regression and develop an efficient algorithm. We demonstrate our approach with both simulated data and real data examples.

stat.ME↗
arXiv2021

Storage capacity of networks with discrete synapses and sparsely encoded memories

Attractor neural networks (ANNs) are one of the leading theoretical frameworks for the formation and retrieval of memories in networks of biological neurons. In this framework, a pattern imposed by external inputs to the network is said to be learned when this pattern becomes a fixed point attractor of the network dynamics. The storage capacity is the maximum number of patterns that can be learned by the network. In this paper, we study the storage capacity of fully-connected and sparsely-connected networks with a binarized Hebbian rule, for arbitrary coding levels. Our results show that a network with discrete synapses has a similar storage capacity as the model with continuous synapses, and that this capacity tends asymptotically towards the optimal capacity, in the space of all possible binary connectivity matrices, in the sparse coding limit. We also derive finite coding level corrections for the asymptotic solution in the sparse coding limit. The result indicates the capacity of network with Hebbian learning rules converges to the optimal capacity extremely slowly when the coding level becomes small. Our results also show that in networks with sparse binary connectivity matrices, the information capacity per synapse is larger than in the fully connected case, and thus such networks store information more efficiently.

physics.bio-ph↗
arXiv2021

Forgetting leads to chaos in attractor networks

Attractor networks are an influential theory for memory storage in brain systems. This theory has recently been challenged by the observation of strong temporal variability in neuronal recordings during memory tasks. In this work, we study a sparsely connected attractor network where memories are learned according to a Hebbian synaptic plasticity rule. After recapitulating known results for the continuous, sparsely connected Hopfield model, we investigate a model in which new memories are learned continuously and old memories are forgotten, using an online synaptic plasticity rule. We show that for a forgetting time scale that optimizes storage capacity, the qualitative features of the network's memory retrieval dynamics are age-dependent: most recent memories are retrieved as fixed-point attractors while older memories are retrieved as chaotic attractors characterized by strong heterogeneity and temporal fluctuations. Therefore, fixed-point and chaotic attractors co-exist in the network phase space. The network presents a continuum of statistically distinguishable memory states, where chaotic fluctuations appear abruptly above a critical age and then increase gradually until the memory disappears. We develop a dynamical mean field theory (DMFT) to analyze the age-dependent dynamics and compare the theory with simulations of large networks. Our numerical simulations show that a high-degree of sparsity is necessary for the DMFT to accurately predict the network capacity. Finally, our theory provides specific predictions for delay response tasks with aging memoranda. Our theory of attractor networks that continuously learn new information at the price of forgetting old memories can account for the observed diversity of retrieval states in the cortex, and in particular the strong temporal fluctuations of cortical activity.

q-bio.NC↗
arXiv2021

Bayesian reconstruction of memories stored in neural networks from their connectivity

The advent of comprehensive synaptic wiring diagrams of large neural circuits has created the field of connectomics and given rise to a number of open research questions. One such question is whether it is possible to reconstruct the information stored in a recurrent network of neurons, given its synaptic connectivity matrix. Here, we address this question by determining when solving such an inference problem is theoretically possible in specific attractor network models and by providing a practical algorithm to do so. The algorithm builds on ideas from statistical physics to perform approximate Bayesian inference and is amenable to exact analysis. We study its performance on three different models, compare the algorithm to standard algorithms such as PCA, and explore the limitations of reconstructing stored patterns from synaptic connectivity.

q-bio.NC↗
arXiv2020

Emergence of irregular activity in networks of strongly coupled conductance-based neurons

Cortical neurons are characterized by irregular firing and a broad distribution of rates. The balanced state model explains these observations with a cancellation of mean excitatory and inhibitory currents, which makes fluctuations drive firing. In networks of neurons with current-based synapses, the balanced state emerges dynamically if coupling is strong, i.e. if the mean number of synapses per neuron $K$ is large and synaptic efficacy is of order $1/\sqrt{K}$. When synapses are conductance-based, current fluctuations are suppressed when coupling is strong, questioning the applicability of the balanced state idea to biological neural networks. We analyze networks of strongly coupled conductance-based neurons and show that asynchronous irregular activity and broad distributions of rates emerge if synapses are of order $1/\log(K)$. In such networks, unlike in the standard balanced state model, current fluctuations are small and firing is maintained by a drift-diffusion balance. This balance emerges dynamically, without fine tuning, if inputs are smaller than a critical value, which depends on synaptic time constants and coupling strength, and is significantly more robust to connection heterogeneities than the classical balanced state model. Our analysis makes experimentally testable predictions of how the network response properties should evolve as input increases.

q-bio.NC↗
arXiv2018

Correlations between synapses in pairs of neurons slow down dynamics in randomly connected neural networks

Networks of randomly connected neurons are among the most popular models in theoretical neuroscience. The connectivity between neurons in the cortex is however not fully random, the simplest and most prominent deviation from randomness found in experimental data being the overrepresentation of bidirectional connections among pyramidal cells. Using numerical and analytical methods, we investigated the effects of partially symmetric connectivity on dynamics in networks of rate units. We considered the two dynamical regimes exhibited by random neural networks: the weak-coupling regime, where the firing activity decays to a single fixed point unless the network is stimulated, and the strong-coupling or chaotic regime, characterized by internally generated fluctuating firing rates. In the weak-coupling regime, we computed analytically for an arbitrary degree of symmetry the auto-correlation of network activity in presence of external noise. In the chaotic regime, we performed simulations to determine the timescale of the intrinsic fluctuations. In both cases, symmetry increases the characteristic asymptotic decay time of the autocorrelation function and therefore slows down the dynamics in the network.

q-bio.NC↗
arXiv2016

Modulation of synaptic plasticity by glutamatergic gliotransmission: A modeling study

Glutamatergic gliotransmission, that is the release of glutamate from perisynaptic astrocyte processes in an activity-dependent manner, has emerged as a potentially crucial signaling pathway for regulation of synaptic plasticity, yet its modes of expression and function in vivo remain unclear. Here, we focus on two experimentally well-identified gliotransmitter patwhays: (i)~modulations of synaptic release and (ii)~postynaptic slow inward currents mediated by glutamate released from astrocytes, and investigate their possible functional relevance on synaptic plasticity in a biophysical model of an astrocyte-regulated synapse. Our model predicts that both pathways could profoundly affect both short- and long-term plasticity. In particular, activity-dependent glutamate release from astrocytes, could dramatically change spike-timing--dependent plasticity, turning potentiation into depression (and vice versa) for the same protocol.

q-bio.NC↗
arXiv2016

Constrained Nonlinear and Mixed Effects Differential Equation Models for Dynamic Cell Polarity Signaling

The key of tip growth in eukaryotes is the polarized distribution on plasma membrane of a particle named ROP1. This distribution is the result of a positive feedback loop, whose mechanism can be described by a Differential Equation parametrized by two meaningful parameters kpf and knf . We introduce a mechanistic Integro-Differential Equation (IDE) derived from a spatiotemporal model of cell polarity and we show how this model can be fitted to real data, i.e., ROP1 intensities measured on pollen tubes. At first, we provide an existence and uniqueness result for the solution of our IDE model under certain conditions. Interestingly, this analysis gives a tractable expression for the likelihood, and our approach can be seen as the estimation of a constrained nonlinear model. Moreover, we introduce a population variability by a constrained nonlinear mixed model. We then propose a constrained Least Squares method to fit the model for the single pollen tube case, and two methods, constrained Methods of Moments and constrained Restricted Maximum Likelihood (REML) to fit the model for the multiple pollen tubes case. The performances of all three methods are studied through simulations and are used on an in-house multiple pollen tubes dataset generated at UC Riverside.

stat.ME↗