Related papers: Invariants for neural automata
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
We describe a mathematical models of grounded symbols in the brain. It also serves as a computational foundations for Perceptual Symbol System (PSS). This development requires new mathematical methods of dynamic logic (DL), which have…
This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…
Neuro-encoded expression programming(NEEP) that aims to offer a novel continuous representation of combinatorial encoding for genetic programming methods is proposed in this paper. Genetic programming with linear representation uses…
In the wild, we often encounter collections of sequential data such as electrocardiograms, motion capture, genomes, and natural language, and sequences may be multichannel or symbolic with nonlinear dynamics. We introduce a new method to…
Neither deep neural networks nor symbolic AI alone has approached the kind of intelligence expressed in humans. This is mainly because neural networks are not able to decompose joint representations to obtain distinct objects (the so-called…
Dynamical systems are ubiquitous within science and engineering, from turbulent flow across aircraft wings to structural variability of proteins. Although some systems are well understood and simulated, scientific imaging often confronts…
Symbolic regression is a task aimed at identifying patterns in data and representing them through mathematical expressions, generally involving skeleton prediction and constant optimization. Many methods have achieved some success, however…
Neural networks posses the crucial ability to generate meaningful representations of task-dependent features. Indeed, with appropriate scaling, supervised learning in neural networks can result in strong, task-dependent feature learning.…
Robots that interact with humans in a physical space or application need to think about the person's posture, which typically comes from visual sensors like cameras and infra-red. Artificial intelligence and machine learning algorithms use…
Modern recording techniques enable neuroscientists to simultaneously study neural activity across large populations of neurons, with capturing predictor-dependent correlations being a fundamental challenge in neuroscience. Moreover, the…
The study of neural computation aims to understand the function of a neural system as an information processing machine. Neural systems are undoubtedly complex, necessitating principled and automated tools to abstract away details to…
Elements of a novel theory of quantum physics are developed, synthesising the role of symbolism in describing quantum measurement and in the topological representation of fractal invariant sets in nonlinear dynamical systems theory. In this…
Neural networks transform high-dimensional data into compact, structured representations, often modeled as elements of a lower dimensional latent space. In this paper, we present an alternative interpretation of neural models as dynamical…
The coding mechanism of sensory memory on the neuron scale is one of the most important questions in neuroscience. We have put forward a quantitative neural network model, which is self organized, self similar, and self adaptive, just like…
Neural population activity is theorized to reflect an underlying dynamical structure. This structure can be accurately captured using state space models with explicit dynamics, such as those based on recurrent neural networks (RNNs).…
Deep neural networks exhibit a fascinating spectrum of phenomena ranging from predictable scaling laws to the unpredictable emergence of new capabilities as a function of training time, dataset size and network size. Analysis of these…
The paper tackles four basic questions associated with human brain as a learning system. How can the brain learn to (1) mentally simulate different external memory aids, (2) perform, in principle, any mental computations using imaginary…
Handling static images that lack inherent temporal dynamics remains a fundamental challenge for spiking neural networks (SNNs). In directly trained SNNs, static inputs are typically repeated across time steps, causing the temporal dimension…
Classical deep learning typically operates on individual cases. Despite its success, real-world usage often requires repeated inference to estimate statistical quantities for complex decision-making tasks involving uncertainty or…