Related papers: Invariants for neural automata
Symbolic computer vision represents diagrams through explicit logical rules and structured representations, enabling interpretable understanding in machine vision. This requires fundamentally different learning paradigms from pixel-based…
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
What types of numeric representations emerge in neural systems, and what would a satisfying answer to this question look like? In this work, we interpret Neural Network (NN) solutions to sequence based number tasks using a variety of…
Recent experiments in neuroscience reveal that task-relevant variables are often encoded in approximately orthogonal subspaces of neural population activity. These disentangled, or abstract, representations have been observed in multiple…
The research area of Networked Control Systems (NCS) has been the topic of intensive study in the last decade. In this paper we give a contribution to this research line by addressing symbolic control design of (possibly unstable) nonlinear…
Patterns of microcircuitry suggest that the brain has an array of repeated canonical computational units. Yet neural representations are distributed, so the relevant computations may only be related indirectly to single-neuron…
Analysis and manipulation of trained neural networks is a challenging and important problem. We propose a symbolic representation for piecewise-linear neural networks and discuss its efficient computation. With this representation, one can…
We propose a symbolic generative task description language and a corresponding inference engine capable of representing arbitrary multimodal tasks as structured symbolic flows. Unlike conventional generative models that rely on large-scale…
Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography. Simulations evince a complex phase-space structure for these kinds of models;…
Neuro-symbolic artificial intelligence is a novel area of AI research which seeks to combine traditional rules-based AI approaches with modern deep learning techniques. Neuro-symbolic models have already demonstrated the capability to…
Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in…
Advancing our knowledge of how the brain processes information remains a key challenge in neuroscience. This thesis combines three different approaches to the study of the dynamics of neural networks and their encoding representations: a…
Neural networks that process the parameters of other neural networks find applications in domains as diverse as classifying implicit neural representations, generating neural network weights, and predicting generalization errors. However,…
Nervous systems are characterized by neurons displaying a diversity of morphological shapes. Traditionally, different shapes have been qualitatively described based on visual inspection and quantitatively described based on morphometric…
Perceptual learning enables humans to recognize and represent stimuli invariant to various transformations and build a consistent representation of the self and physical world. Such representations preserve the invariant physical relations…
An internal model of the own body can be assumed a fundamental and evolutionary-early representation as it is present throughout the animal kingdom. Such functional models are, on the one hand, required in motor control, for example solving…
The recent developments and growing interest in neural-symbolic models has shown that hybrid approaches can offer richer models for Artificial Intelligence. The integration of effective relational learning and reasoning methods is one of…
This work provides the first unifying theoretical framework for node (positional) embeddings and structural graph representations, bridging methods like matrix factorization and graph neural networks. Using invariant theory, we show that…
Symbolic regression is a technique that can automatically derive analytic models from data. Traditionally, symbolic regression has been implemented primarily through genetic programming that evolves populations of candidate solutions…
The computational capabilities of a neural network are widely assumed to be determined by its static architecture. Here we challenge this view by establishing that a fixed neural structure can operate in fundamentally different…