publications 

Francisco Acosta, Sophia Sanborn, Khanh Dao Duc, Manu Madhav, Nina Miolane

Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition

2023/06

The neural manifold hypothesis postulates that the activity of a neural population forms a low-dimensional manifold whose structure reflects that of the encoded task variables. In this work, we combine topological deep generative models and extrinsic Riemannian geometry to introduce a novel approach for studying the structure of neural manifolds. This approach (i) computes an explicit parameterization of the manifolds and (ii) estimates their local extrinsic curvature--hence quantifying their shape within the neural state space. Importantly, we prove that our methodology is invariant with respect to transformations that do not bear meaningful neuroscience information, such as permutation of the order in which neurons are recorded. We show empirically that we correctly estimate the geometry of synthetic manifolds generated from smooth deformations of circles, spheres, and tori, using realistic noise levels. We additionally validate our methodology on simulated and real neural data, and show that we recover geometric structure known to exist in hippocampal place cells. We expect this approach to open new avenues of inquiry into geometric neural correlates of perception and behavior, while providing a new means to compare representations in biological and artificial neural systems.

Thibault Niederhauser, Adam Lester, Nina Miolane, Khanh Dao Duc, Manu S. Madhav

NeurIPS 2022 Workshop on Symmetry and Geometry in Neural Representations

2022/12

Hippocampal place cells can encode spatial locations of an animal in physical or task-relevant spaces. We simulated place cell populations that encoded either Euclidean- or graph-based positions of a rat navigating to goal nodes in a maze with a graph topology, and used manifold learning methods such as UMAP and Autoencoders (AE) to analyze these neural population activities. The structure of the latent spaces learned by the AE reflects their true geometric structure, while PCA fails to do so and UMAP is less robust to noise. Our results support future applications of AE architectures to decipher the geometry of spatial encoding in the brain.

Manu S. Madhav, Ravikrishnan P. Jayakumar, Brian Li, Francesco Savelli, James J. Knierim, Noah J. Cowan

BioRxiv Preprint

2022/6/15

In the absence of landmarks, path integration of self-motion inputs can accumulate error and cause the hippocampal representation of position to drift. In the presence of pure optic flow in our VR dome, place fields drift. Speeding up or slowing down optic flow can predictably influence the rate of this drift. We decoded the drift rate, the hippocampal gain, in real time and controlled this internal variable directly by manipulating optic flow. Using this novel 'cognitive clamp' experiment, the value to which the hippocampal gain was clamped predicts its value once optic flow was turned off. This shows that much like visual landmarks, optic flow can serve as a teaching signal to recalibrate the gain of path integration.

Vagvolgyi, Balazs P., Ravikrishnan P. Jayakumar, Manu S. Madhav, James J. Knierim, and Noah J. Cowan

Journal of Neuroscience Methods

2022/2/15

Camera images can encode large amounts of visual information of an animal and its environment, enabling high fidelity 3D reconstruction of the animal and its environment using computer vision methods. Most systems, both markerless (e.g. deep learning based) and marker-based, require multiple cameras to track features across multiple points of view to enable such 3D reconstruction. However, such systems can be expensive and are challenging to set up in small animal research apparatuses.

Madhav, Manu S., Ravikrishnan P. Jayakumar, Shahin G. Lashkari, Francesco Savelli, Hugh T. Blair, James J. Knierim, and Noah J. Cowan

Journal of Neuroscience Methods

2021/8/26

The cognitive map in the hippocampal formation of rodents and other mammals integrates multiple classes of sensory and motor information into a coherent representation of space. Here, we describe the Dome, a virtual reality apparatus for freely locomoting rats, designed to examine the relative contributions of various spatial inputs to an animal’s spatial representation. The Dome was designed to preserve the range of spatial inputs typically available to an animal in free, untethered locomotion while providing the ability to perturb specific sensory cues. We present the design rationale and corresponding specifications of the Dome, along with a variety of engineering and biological analyses to validate the efficacy of the Dome as an experimental tool to examine the interaction between visual information and path integration in place cells in rodents.

Madhav, Manu S., and Noah J. Cowan

Annual Review of Control, Robotics, and Autonomous Systems 3

2020/5/3

Here, we review the role of control theory in modeling neural control systems through a top-down analysis approach. Specifically, we examine the role of the brain and central nervous system as the controller in the organism, connected to but isolated from the rest of the animal through insulated interfaces. Though biological and engineering control systems operate on similar principles, they differ in several critical features, which makes drawing inspiration from biology for engineering controllers challenging but worthwhile.

Fortune, Eric S., Nicole Andanar, Manu Madhav, Ravikrishnan P. Jayakumar, Noah J. Cowan, Maria Elina Bichuette, and Daphne Soares

Frontiers in Integrative Neuroscience

2020/10/22

Glass knifefish (Eigenmannia) are a group of weakly electric fishes found throughout the Amazon basin. Their electric organ discharges (EODs) are energetically costly adaptations used in social communication and for localizing conspecifics and other objects including prey at night and in turbid water. Interestingly, a troglobitic population of blind cavefish Eigenmannia vicentespelea survives in complete darkness in a cave system in central Brazil. We examined the effects of troglobitic conditions, which includes a complete loss of visual cues and potentially reduced food sources, by comparing the behavior and movement of freely behaving cavefish to a nearby epigean (surface) population (Eigenmannia trilineata).

Jayakumar, Ravikrishnan P., Manu S. Madhav, Francesco Savelli, Hugh T. Blair, Noah J. Cowan, and James J. Knierim

Nature

2019/2/11

Hippocampal place cells are spatially tuned neurons that serve as elements of a ‘cognitive map’ in the mammalian brain. To detect the animal’s location, place cells are thought to rely upon two interacting mechanisms: sensing the position of the animal relative to familiar landmarks and measuring the distance and direction that the animal has travelled from previously occupied locations. The latter mechanism—known as path integration—requires a finely tuned gain factor that relates the animal’s self-movement to the updating of position on the internal cognitive map, as well as external landmarks to correct the positional error that accumulates.

Stamper, Sarah A., Manu S. Madhav, Noah J. Cowan, and Eric S. Fortune

Electroreception: Fundamental Insights from Comparative Approaches

2019/11/14

Animals routinely use their own motor outputs to modulate the sensory information they perceive, a process termed “active sensing.” This chapter highlights the use of control theoretic approaches to reveal the functional relationships between active sensing, task-related behaviors, sensing, and motor control. Specifically, recently developed experimental systems use artificially controlled feedback loops to perturb natural reafferent feedback in freely behaving animals. Such perturbations allow quantitative and systematic descriptions of control strategies for active sensing.

Madhav, Manu S., Ravikrishnan P. Jayakumar, Alican Demir, Sarah A. Stamper, Eric S. Fortune, and Noah J. Cowan

Scientific Reports

2018/4/11

The study of animal behavior has been revolutionized by sophisticated methodologies that identify and track individuals in video recordings. Video recording of behavior, however, is challenging for many species and habitats including fishes that live in turbid water. Here we present a methodology for identifying and localizing weakly electric fishes on the centimeter scale with subsecond temporal resolution based solely on the electric signals generated by each individual. These signals are recorded with a grid of electrodes and analyzed using a two-part algorithm that identifies the signals from each individual fish and then estimates the position and orientation of each fish using Bayesian inference.