Statistical Physics and Representations in Real and Artificial Neural Networks

This document presents the material of two lectures on statistical physics and neural representations, delivered by one of us (R.M.) at the Fundamental Problems in Statistical Physics XIV summer school in July 2017. In a first part, we consider the neural representations of space (maps) in the hippocampus. We introduce an extension of the Hopfield model, able to store multiple spatial maps as continuous, finite-dimensional attractors. The phase diagram and dynamical properties of the model are analyzed. We then show how spatial representations can be dynamically decoded using an effective Ising model capturing the correlation structure in the neural data, and compare applications to data obtained from hippocampal multi-electrode recordings and by (sub)sampling our attractor model. In a second part, we focus on the problem of learning data representations in machine learning, in particular with artificial neural networks. We start by introducing data representations through some illustrations. We then analyze two important algorithms, Principal Component Analysis and Restricted Boltzmann Machines, with tools from statistical physics

Uncovering representations of sleep-associated hippocampal ensemble spike activity

Pyramidal neurons in the rodent hippocampus exhibit spatial tuning during spatial navigation, and they are reactivated in specific temporal order during sharp-wave ripples observed in quiet wakefulness or slow wave sleep. However, analyzing representations of sleep-associated hippocampal ensemble spike activity remains a great challenge. In contrast to wake, during sleep there is a complete absence of animal behavior, and the ensemble spike activity is sparse (low occurrence) and fragmental in time. To examine important issues encountered in sleep data analysis, we constructed synthetic sleep-like hippocampal spike data (short epochs, sparse and sporadic firing, compressed timescale) for detailed investigations. Based upon two Bayesian population-decoding methods (one receptive field-based, and the other not), we systematically investigated their representation power and detection reliability. Notably, the receptive-field-free decoding method was found to be well-tuned for hippocampal ensemble spike data in slow wave sleep (SWS), even in the absence of prior behavioral measure or ground truth. Our results showed that in addition to the sample length, bin size, and firing rate, number of active hippocampal pyramidal neurons are critical for reliable representation of the space as well as for detection of spatiotemporal reactivated patterns in SWS or quiet wakefulness.Collaborative Research in Computational Neuroscience (Award IIS-1307645)United States. Office of Naval Research. Multidisciplinary University Research Initiative (Grant N00014-10-1-0936)National Institutes of Health (U.S.) (Grant TR01-GM10498

Slow Inhibition and Inhibitory Recruitment in the Hippocampal Dentate Gyrus

L’hippocampe joue un rôle central dans la navigation spatiale, la mémoire et l’organisation spatio-temporelle des souvenirs. Ces fonctions sont maintenues par la capacité du gyrus denté (GD) de séparation des patrons d'activité neuronales. Le GD est situé à l’entrée de la formation hippocampique où il reconnaît la présence de nouveaux motifs parmi la densité de signaux afférant arrivant par la voie entorhinale (voie perforante). Le codage parcimonieux est la marque distinctive du GD. Ce type de codage est le résultat de la faible excitabilité intrinsèque des cellules granulaires (CGs) en combinaison avec une inhibition locale prédominante. En particulier, l’inhibition de type « feedforward » ou circuit inhibiteur antérograde, est engagée par la voie perforante en même temps que les CGs. Ainsi les interneurones du circuit antérograde fournissent des signaux GABAergique aux CGs de manière presque simultanée qu’elles reçoivent les signaux glutamatergiques. Cette thèse est centrée sur l’étude des interactions entre ces signaux excitateurs de la voie entorhinale et les signaux inhibiteurs provenant des interneurones résidant dans le GD et ceci dans le contexte du codage parcimonieux et le patron de décharge en rafale caractéristique des cellules granulaires. Nous avons adressé les relations entre les projections entorhinales et le réseau inhibitoire antérograde du GD en faisant des enregistrements électrophysiologiques des CG pendant que la voie perforante est stimulée de manière électrique ou optogénétique. Nous avons découvert un nouvel mécanisme d’inhibition qui apparait à délais dans les CGs suite à une stimulation dans les fréquences gamma. Ce mécanisme induit une hyperpolarisation de longue durée (HLD) et d’une amplitude prononce. Cette longue hyperpolarisation est particulièrement prolongée et dépasse la durée d’autres types d’inhibition transitoire lente décrits chez les CGs. L’induction de HLD crée une fenêtre temporaire de faible excitabilité suite à laquelle le patron de décharge des CGs et l’intégration d’autres signaux excitateurs sont altérés de manière transitoire. Nous avons donc conclu que l’activité inhibitrice antérograde joue un rôle central dans les processus de codage dans le GD. Cependant, alors qu’il existe une multitude d’études décrivant les interneurones qui font partie de ce circuit inhibiteur, la question de comment ces cellules sont recrutées par la voie entorhinale reste quelque peu explorée. Pour apprendre plus à ce sujet, nous avons enregistré des interneurones résidant iii dans la couche moléculaire du GD tout en stimulant la voie perforante de manière optogénétique. Cette méthode de stimulation nous a permis d’induire la libération de glutamate endogène des terminales entorhinales et ainsi d’observer le recrutement purement synaptique d’interneurones. De manière surprenante, les résultats de cette expérience démontrent un faible taux d’activation des interneurones, accompagné d’un tout aussi faible nombre total de potentiels d’action émis en réponse à la stimulation même à haute fréquence. Ce constat semble contre-intuitif étant donné qu’en générale on assume qu’une forte activité inhibitrice est requise pour le maintien du codage parcimonieux. Tout de même, l’analyse des patrons de décharge des interneurones qui ont été activés a fait ressortir la prééminence de trois grands types: décharge précoce, retardée ou régulière par rapport le début des pulses lumineux. Les résultats obtenus durant cette thèse mettent la lumière sur l’important conséquences fonctionnelles des interactions synaptique et polysynaptique de nature transitoire dans les réseaux neuronaux. Nous aimerions aussi souligner l’effet prononcé de l’inhibition à court terme du type prolongée sur l’excitabilité des neurones et leurs capacités d’émettre des potentiels d’action. De plus que cet effet est encore plus prononcé dans le cas de HLD dont la durée dépasse souvent la seconde et altère l’intégration d’autres signaux arrivants simultanément. Donc on croit que les effets de HLD se traduisent au niveau du réseaux neuronal du GD comme une composante cruciale pour le codage parcimonieux. En effet, ce type de codage semble être la marque distinctive de cette région étant donné que nous avons aussi observé un faible niveau d’activation chez les interneurones. Cependant, le manque d’activité accrue du réseau inhibiteur antérograde peut être compensé par le maintien d’un gradient GABAergique constant à travers le GD via l’alternance des trois modes de décharges des interneurones. En conclusion, il semble que le codage parcimonieux dans le GD peut être préservé même en absence d’activité soutenue du réseau inhibiteur antérograde et ceci grâce à des mécanismes alternatives d’inhibition prolongée à court terme.The hippocampus is implicated in spatial navigation, the generation and recall of memories, as well as their spatio-temporal organization. These functions are supported by the processes of pattern separation that occurs in the dentate gyrus (DG). Situated at the entry of the hippocampal formation, the DG is well placed to detect and sort novelty patterns amongst the high-density excitatory signals that arrive via the entorhinal cortex (EC). A hallmark of the DG is sparse encoding that is enabled by a combination of low intrinsic excitability of the principal cells and local inhibition. Feedforward inhibition (FFI) is recruited directly by the EC and simultaneously with the granule cells (GCs). Therefore, FFI provides fast GABA release and shapes input integration at the millisecond time scale. This thesis aimed to investigate the interplay of entorhinal excitatory signals with GCs and interneurons, from the FFI in the DG, in the framework of sparse encoding and GC’s characteristic burst firing. We addressed the long-range excitation – local inhibitory network interactions using electrophysiological recordings of GCs – while applying an electrical or optogenetic stimulation of the perforant path (PP) in the DG. We discovered and described a novel delayed-onset inhibitory post synaptic potential (IPSP) in GCs, following PP stimulation in the gamma frequency range. Most importantly, the IPSP was characterized by a large amplitude and prolonged decay, outlasting previously described slow inhibitory events in GCs. The long-lasting hyperpolarization (LLH) caused by the slow IPSPs generates a low excitability time window, alters the GCs firing pattern, and interferes with other stimuli that arrive simultaneously. FFI is therefore a key player in the computational processes that occurs in the DG. However, while many studies have been dedicated to the description of the various types of the interneurons from the FFI, the question of how these cells are synaptically recruited by the EC remains not entirely elucidated. We tackled this problem by recording from interneurons in the DG molecular layer during PP-specific optogenetic stimulation. Light-driven activation of the EC terminals enabled a purely synaptic recruitment of interneurons via endogenous glutamate release. We found that this method of stimulation recruits only a subset of interneurons. In addition, the total number of action potentials (AP) was surprisingly low even at high frequency stimulation. This result is counterintuitive, as strong and persistent inhibitory signals are assumed to restrict GC v activation and maintain sparseness. However, amongst the early firing interneurons, late and regular spiking patterns were clearly distinguishable. Interestingly, some interneurons expressed LLH similar to the GCs, arguing that it could be a commonly used mechanism for regulation of excitability across the hippocampal network. In summary, we show that slow inhibition can result in a prolonged hyperpolarization that significantly alters concurrent input’s integration. We believe that these interactions contribute to important computational processes such as sparse encoding. Interestingly, sparseness seems to be the hallmark of the DG, as we observed a rather low activation of the interneuron network as well. However, the alternating firing of ML-INs could compensate the lack of persistent activity by the continuous GABA release across the DG. Taken together these results offer an insight into a mechanism of feedforward inhibition serving as a sparse neural code generator in the DG

Deciphering the Firing Patterns of Hippocampal Neurons During Sharp-Wave Ripples

The hippocampus is essential for learning and memory. Neurons in the rat hippocampus selectively fire when the animal is at specific locations - place fields - within an environment. Place fields corresponding to such place cells tile the entire environment, forming a stable spatial map supporting navigation and planning. Remarkably, the same place cells reactivate together outside of their place fields and in coincidence with sharp-wave ripples (SWRs) - dominant electrical field oscillations (150-250 Hz) in the hippocampus. These offline SWR events frequently occur during quiet wake periods in the middle of exploration and the follow-up slow-wave sleep and are associated with spatial memory performance and stabilization of spatial maps. Therefore, deciphering the firing patterns during these events is essential to understanding offline memory processing.I provide two novel methods to analyze the SWRs firing patterns in this dissertation project. The first method uses hidden Markov models (HMM), in which I model the dynamics of neural activity during SWRs in terms of transitions between distinct states of neuronal ensemble activity. This method detects consistent temporal structures over many instances of SWRs and, in contrast to standard approaches, relaxes the dependence on positional data during the behavior to interpret temporal patterns during SWRs. To validate this method, I applied the method to quiet wake SWRs. In a simple spatial memory task in which the animal ran on a linear track or in an open arena, the individual states corresponded to the activation of distinct group of neurons with inter-state transitions that resembled the animal’s trajectories during the exploration. In other words, this method enabled us to identify the topology and spatial map of the explored environment by dissecting the firings occurring during the quiescence periods’ SWRs. This result indicated that downstream brain regions may rely only on SWRs to uncover hippocampal code as a substrate for memory processing. I developed a second analysis method based on the principles of Bayesian learning. This method enabled us to track the spatial tunings over the sleep following exploration of an environment by taking neurons’ place fields in the environment as the prior belief and updating it using dynamic ensemble firing patterns unfolding over time. This method introduces a neuronal-ensemble-based approach that calculates tunings to the position encoded by ensemble firings during sleep rather than the animal’s actual position during exploration. When I applied this method to several datasets, I found that during the early slow-wave sleep after an experience, but not during late hours of sleep or sleep before the exploration, the spatial tunings highly resembled the place fields on the track. Furthermore, the fidelity of the spatial tunings to the place fields predicted the place fields’ stability when the animal was re-exposed to the same environment after ~ 9h. Moreover, even for neurons with shifted place fields during re-exposure, the spatial tunings during early sleep were predictive of the place fields during the re-exposure. These results indicated that early sleep actively maintains or retunes the place fields of neurons, explaining the representational drift of place fields across multiple exposures

A Neural Signal Processor for Low-Latency Spike Inference

This thesis describes the development of a system that can assign identities to a population of single-units, in multi-electrode recordings, at single-spike resolution with low-latency. The system has two parts. The first is a Field-Programmable Gate Array (FPGA)-based Neural Signal Processor (NSP) that receives raw input and generates labelled spikes as output, a process referred to as real-time spike inference. The second is a piece of software (Spiketag) that runs on a PC, communicates with the NSP, and generates a spike-sorted model to guide the real-time spike inference. The NSP provides clocks and control signals to five 32-channel INTAN RHD2132 chips to manage the acquisition of 160 channels of raw neural data. In parallel, the NSP further filters, detects and extracts extracellular spike waveforms from the raw neural data recorded by tetrodes or silicon probes and assigns single-unit identity to each detected spike. A set of Python application programming interfaces (APIs) was developed in Spiketag to enable the communication between the NSP and the PC. These APIs allow the NSP to obtain a model from the PC, which holds parameters such as reference channels, spike detection thresholds, spike feature transformation matrix and vector quantized clusters generated by spike sorting a short recording session. Using the spike-sorted model, the NSP performs data acquisition and real-time spike inference simultaneously. Algorithmic modules were implemented in the FPGA and pipelined to compute during 40 ms acquisition intervals. At the output end of the FPGA NSP, the real-time assigned single-unit identity (spike-id) is packaged with the timestamp, the electrode group, and the spike features as a spike-id packet. Spike-id packets are asynchronously transmitted through a low-latency Peripheral Component Interconnect Express (PCIe) interface to the PC, producing the real-time spike trains. The real-time spike trains can be used for further processing, such as real-time decoding. Several types of ground-truth data, including intracellular/extracellular paired recordings, synthesized tetrode extracellular waveforms with ground-truth spike timing and high-channel-count silicon probe recordings with ground-truth animal positions during navigation were used to validate the low-latency (1 ms) and high-accuracy (as high as state-of-the-art offline sorting and decoding algorithms) of the NSP’s real-time spike inference and the NSP-based real-time population decoding performance

Micro-, Meso- and Macro-Dynamics of the Brain

Neurosciences, Neurology, Psychiatr

On memories, neural ensembles and mental flexibility

Memories are assumed to be represented by groups of co-activated neurons, called neural ensembles. Describing ensembles is a challenge: complexity of the underlying micro-circuitry is immense. Current approaches use a piecemeal fashion, focusing on single neurons and employing local measures like pairwise correlations. We introduce an alternative approach that identifies ensembles and describes the effective connectivity between them in a holistic fashion. It also links the oscillatory frequencies observed in ensembles with the spatial scales at which activity is expressed. Using unsupervised learning, biophysical modeling and graph theory, we analyze multi-electrode LFPs from frontal cortex during a spatial delayed response task. We find distinct ensembles for different cues and more parsimonious connectivity for cues on the horizontal axis, which may explain the oblique effect in psychophysics. Our approach paves the way for biophysical models with learned parameters that can guide future Brain Computer Interface development