相关论文: Non-monotonicity of closed convexity in neural cod…

Constant dimension codes, with a prescribed minimum distance, have found recently an application in network coding. All the codewords in such a code are subspaces of $\F_q^n$ with a given dimension. A computer search for large constant…

Scalar variables, e.g., the orientation of a shape in an image, are commonly predicted using a single output neuron in a neural network. In contrast, the mammalian cortex represents variables with a population of neurons. In this population…

Understanding how neural networks align with human cognitive processes is a crucial step toward developing more interpretable and reliable AI systems. Motivated by theories of human cognition, this study examines the relationship between…

It has been studied by Curto et al. (SIAM J. on App. Alg. and Geom., 1(1) : 222 $\unicode{x2013}$ 238, 2017) that a neural code that has an open convex realization does not have any local obstruction relative to the neural code. Further, a…

A neural code on $ n $ neurons is a collection of subsets of the set $ [n]=\{1,2,\dots,n\} $. Curto et al. \cite{curto2013neural} associated a ring $\mathcal{R}_{\mathcal{C}}$ (neural ring) to a neural code $\mathcal{C}$. A special class of…

Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than $ 1 $ are derived. An application in coding theory is illustrated by showing that multispace…

We consider neural networks with a single hidden layer and non-decreasing homogeneous activa-tion functions like the rectified linear units. By letting the number of hidden units grow unbounded and using classical non-Euclidean…

Understanding neural networks is challenging in part because of the dense, continuous nature of their hidden states. We explore whether we can train neural networks to have hidden states that are sparse, discrete, and more interpretable by…

Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random linear network coding. What the maximal cardinality of any constant-dimension code with finite dimension and minimum…

Evolution and its intelligence element present thrill and challenges in its exploration. Yet, how species have memory, retrieve them and maintain continuity are the fundamental questions. Most of the phenomenon can only be hypothesised by…

In general, approximating classes of functions defined over high-dimensional input spaces by linear combinations of a fixed set of basis functions or ``features'' is known to be hard. Typically, the worst-case error of the best basis set…

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…

Neurons in the brain represent external stimuli via neural codes. These codes often arise from stereotyped stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer…

Neurons in the brain represent external stimuli via neural codes. These codes often arise from stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties…

A class of one-dimensional convolutional codes will be presented. They are all MDS codes, i. e., have the largest distance among all one-dimensional codes of the same length n and overall constraint length delta. Furthermore, their extended…

Continuous attractor networks (CANs) are widely used to model how the brain temporarily retains continuous behavioural variables via persistent recurrent activity, such as an animal's position in an environment. However, this memory…

This paper concerns non-overlapping codes, block codes motivated by synchronisation and DNA-based storage applications. Most existing constructions of these codes do not account for the restrictions posed by the physical properties of…

How do we imagine visual objects and combine them to create new forms? To answer this question, we need to explore the cognitive, computational and neural mechanisms underlying imagery and creativity. The body of research on deep learning…

Connected decision boundaries are useful in several tasks like image segmentation, clustering, alpha-shape or defining a region in nD-space. However, the machine learning literature lacks methods for generating connected decision boundaries…

We introduce the factor complex of a neural code, and show how intervals and maximal codewords are captured by the combinatorics of factor complexes. We use these results to obtain algebraic and combinatorial characterizations of…