相关论文: Convexity of Neural Codes with Four Maximal Codewo…
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…
Convolutional Neural Networks (CNNs) have recently emerged as the dominant model in computer vision. If provided with enough training data, they predict almost any visual quantity. In a discrete setting, such as classification, CNNs are not…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
The neural coding is yet to be discovered. The neuronal operational modes that arise with fixed inputs but with varying degrees of stimulation help to elucidate their coding properties. In neurons receiving {\it in vivo} stimulation, we…
Neural circuits exhibit remarkable computational flexibility, enabling adaptive responses to noisy and ever-changing environmental cues. A fundamental question in neuroscience concerns how a wide range of behaviors can emerge from a…
Place recognition is one of the most challenging problems in computer vision, and has become a key part in mobile robotics and autonomous driving applications for performing loop closure in visual SLAM systems. Moreover, the difficulty of…
This study introduces a novel approach to ensure the existence and uniqueness of optimal parameters in neural networks. The paper details how a recurrent neural networks (RNN) can be transformed into a contraction in a domain where its…
The high computational complexity and increasing parameter counts of deep neural networks pose significant challenges for deployment in resource-constrained environments, such as edge devices or real-time systems. To address this, we…
Cells actively probe and respond to the stiffness of their surroundings. Since mechanosensory cells in connective tissue are surrounded by a disordered network of biopolymers, their in vivo mechanical environment can be extremely…
Statistical language modeling techniques have successfully been applied to source code, yielding a variety of new software development tools, such as tools for code suggestion and improving readability. A major issue with these techniques…
The energy landscape of high-dimensional non-convex optimization problems is crucial to understanding the effectiveness of modern deep neural network architectures. Recent works have experimentally shown that two different solutions found…
Convolutional codes are error-correcting linear codes that utilize shift registers to encode. These codes have an arbitrary block size and they can incorporate both past and current information bits. DNA codes represent DNA sequences and…
Non-overlapping codes are block codes that have arisen in diverse contexts of computer science and biology. Applications typically require finding non-overlapping codes with large cardinalities, but the maximum size of non-overlapping codes…
Optimization results are one method for understanding neural computation from Nature's perspective and for defining the physical limits on neuron-like engineering. Earlier work looks at individual properties or performance criteria and…
Precise behavioral control of large language models (LLMs) is critical for complex applications. However, existing methods often incur high training costs, lack natural language controllability, or compromise semantic coherence. To bridge…
To evaluate the nature of the neural code in the cerebral cortex, we have used a combination of theory and experiment to assess how information is represented in a realistic cortical population response. We have shown how a sensory stimulus…
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…
Sparse tensor networks are commonly used to represent contractions over sparse tensors. Tensor contractions are higher-order analogs of matrix multiplication. Tensor networks arise commonly in many domains of scientific computing and data…
Metric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes…
The brain is composed of billions of neurons with virtually endless morphologies and ion channel compositions, resulting in unique extracellular waveforms. Nevertheless, almost all neuronal morphologies can be reduced to a simple…