相关论文: Obstructions to convexity in neural codes
In this paper, we investigate a constrained formulation of neural networks where the output is a convex function of the input. We show that the convexity constraints can be enforced on both fully connected and convolutional layers, making…
We posit that hippocampal place cells encode information about future locations under a transition distribution observed as an agent explores a given (physical or conceptual) space. The encoding of information about the current location,…
A biologically plausible computational model for color representation is introduced. We present a mechanistic hierarchical model of neurons that not only successfully encodes local hue, but also explicitly reveals how the contributions of…
Grid cells in the entorhinal cortex, together with head direction, place, speed and border cells, are major contributors to the organization of spatial representations in the brain. In this work we introduce a novel theoretical and…
Grid cells in the brain respond when an animal occupies a periodic lattice of "grid fields" during spatial navigation. The grid scale varies along the dorso-ventral axis of the entorhinal cortex. We propose that the grid system minimizes…
The adaptation of neural codes to the statistics of their environment is well captured by efficient coding approaches. Here we solve an inverse problem: characterizing the objective and constraint functions that efficient codes appear to be…
In the mammalian brain, many neuronal ensembles are involved in representing spatial structure of the environment. In particular, there exist cells that encode the animal's location and cells that encode head direction. A number of studies…
The hippocampus supports spatial navigation by encoding cognitive maps through collective place cell activity. We model the place cell population as non-negative spatial embeddings derived from the spectral decomposition of multi-step…
Neural coding is a field of study that concerns how sensory information is represented in the brain by networks of neurons. The link between external stimulus and neural response can be studied from two parallel points of view. The first,…
Codifying memories is one of the fundamental problems of modern Neuroscience. The functional mechanisms behind this phenomenon remain largely unknown. Experimental evidence suggests that some of the memory functions are performed by…
Neuroscientists classify neurons into different types that perform similar computations at different locations in the visual field. Traditional methods for neural system identification do not capitalize on this separation of 'what' and…
Deep learning researchers commonly suggest that converged models are stuck in local minima. More recently, some researchers observed that under reasonable assumptions, the vast majority of critical points are saddle points, not true minima.…
Neural codes are collections of binary vectors that represent the firing patterns of neurons. The information given by a neural code $C$ can be represented by its neural ideal $J_C$. In turn, the polynomials in $J_C$ can be used to…
Convolutional networks are ubiquitous in deep learning. They are particularly useful for images, as they reduce the number of parameters, reduce training time, and increase accuracy. However, as a model of the brain they are seriously…
We describe the combinatorics of equilibria and steady states of neurons in threshold-linear networks that satisfy Dale's law. The combinatorial code of a Dale network is characterized in terms of two conditions: (i) a condition on the…
Neural network (connectionist) models are designed to encode image features and provide the building blocks for object and shape recognition. These models generally call for: a) initial diffuse connections from one neuron population to…
The hippocampus is often attributed to episodic memory formation and storage in the mammalian brain; in particular, Alme et al. showed that hippocampal area CA3 forms statistically independent representations across a large number of…
Soft-thresholding has been widely used in neural networks. Its basic network structure is a two-layer convolution neural network with soft-thresholding. Due to the network's nature of nonlinearity and nonconvexity, the training process…
Encoding information about continuous variables using noisy computational units is a challenge; nonetheless, asymptotic theory shows that combining multiple periodic scales for coding can be highly precise despite the corrupting influence…
The hippocampal formation is thought to learn spatial maps of environments, and in many models this learning process consists of forming a sensory association for each location in the environment. This is inefficient, akin to learning a…