Related papers: Obstructions to convexity in neural codes

Sensory neuroscience seeks to understand how the brain encodes natural environments. However, neural coding has largely been studied using simplified stimuli. In order to assess whether the brain's coding strategy depend on the stimulus…

Mammalian spatial navigation relies on specialized neurons, such as place and grid cells, which encode position based on self-motion and environmental cues. While extensive research has explored the computational role of grid cells, the…

Artificial neural networks have realized incredible successes at image recognition, but the underlying mechanism of visual space representation remains a huge mystery. Grid cells (2014 Nobel Prize) in the entorhinal cortex support a…

Convolutional neural nets (convnets) trained from massive labeled datasets have substantially improved the state-of-the-art in image classification and object detection. However, visual understanding requires establishing correspondence on…

For 20 years the beautiful structure in the grid cell code has presented an attractive puzzle: what computation do these representations subserve, and why does it manifest so curiously in neurons. The first question quickly attracted an…

Learning the underlying equation from data is a fundamental problem in many disciplines. Recent advances rely on Neural Networks (NNs) but do not provide theoretical guarantees in obtaining the exact equations owing to the non-convexity of…

In this paper, we consider networks of deterministic spiking neurons, firing synchronously at discrete times; such spiking neural networks are inspired by networks of neurons and synapses that occur in brains. We consider the problem of…

Spatial navigation in mammals is based on building a mental representation of their environment---a cognitive map. However, both the nature of this cognitive map and its underpinning in neural structures and activity remains vague. A key…

In contrast to fully connected networks, Convolutional Neural Networks (CNNs) achieve efficiency by learning weights associated with local filters with a finite spatial extent. An implication of this is that a filter may know what it is…

Understanding functional representations within higher visual cortex is a fundamental question in computational neuroscience. While artificial neural networks pretrained on large-scale datasets exhibit striking representational alignment…

The human brain cortical layer has a convoluted morphology that is unique to each individual. Characterization of the cortical morphology is necessary in longitudinal studies of structural brain change, as well as in discriminating…

Traditionally, most complex intelligence architectures are extremely non-convex, which could not be well performed by convex optimization. However, this paper decomposes complex structures into three types of nodes: operators, algorithms…

Sequences of neuronal activation have long been implicated in a variety of brain functions. In particular, these sequences have been tied to memory formation and spatial navigation in the hippocampus, a region of mammalian brains.…

Inverse problems in imaging such as denoising, deblurring, superresolution (SR) have been addressed for many decades. In recent years, convolutional neural networks (CNNs) have been widely used for many inverse problem areas. Although their…

A key question in neuroscience is at which level functional meaning emerges from biophysical phenomena. In most vertebrate systems, precise functions are assigned at the level of neural populations, while single-neurons are deemed…

How does the mind organize thoughts? The hippocampal-entorhinal complex is thought to support domain-general representation and processing of structural knowledge of arbitrary state, feature and concept spaces. In particular, it enables the…

Decades of psychological research have been aimed at modeling how people learn features and categories. The empirical validation of these theories is often based on artificial stimuli with simple representations. Recently, deep neural…

Brain encoding models aim to predict brain voxel-wise responses to stimuli images, replicating brain signals captured by neuroimaging techniques. There is a large volume of publicly available data, but training a comprehensive brain…

Computational models of cortical activity provide insight into the mechanisms of higher-order processing in the human brain including planning, perception and the control of movement. Activity in the cortex is ongoing even in the absence of…

Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…