Related papers: Invariants for neural automata
The traditional view of neural computation in the cerebral cortex holds that sensory neurons are specialized, i.e., selective for certain dimensions of sensory stimuli. This view was challenged by evidence of contextual interactions between…
Characterizing precisely the asymptotic generalization error of neural networks using parameters that can be estimated efficiently is a crucial problem in machine learning, which relies heavily on heuristics and practitioners' intuition to…
Representations in the auditory cortex might be based on mechanisms similar to the visual ventral stream; modules for building invariance to transformations and multiple layers for compositionality and selectivity. In this paper we propose…
Recent advances in physics-augmented neural networks have enabled thermodynamically consistent data-driven constitutive modeling of complex inelastic materials. Most existing approaches, however, implicitly adopt a specific thermodynamic…
This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…
Given a natural language instruction and an input scene, our goal is to train a model to output a manipulation program that can be executed by the robot. Prior approaches for this task possess one of the following limitations: (i) rely on…
Sensory perception (e.g. vision) relies on a hierarchy of cortical areas, in which neural activity propagates in both directions, to convey information not only about sensory inputs but also about cognitive states, expectations and…
Traveling waves of neural activity are widely observed in the brain, but their precise computational function remains unclear. One prominent hypothesis is that they enable the transfer and integration of spatial information across neural…
Neuro-symbolic methods integrate neural architectures, knowledge representation and reasoning. However, they have been struggling at both dealing with the intrinsic uncertainty of the observations and scaling to real-world applications.…
Symmetric functions, which take as input an unordered, fixed-size set, are known to be universally representable by neural networks that enforce permutation invariance. These architectures only give guarantees for fixed input sizes, yet in…
Statistical mechanics determines the abundance of different arrangements of matter depending on cost-benefit balances. Its formalism and phenomenology percolate throughout biological processes and set limits to effective computation. Under…
We present a neural-symbolic framework for observing the environment and continuously learning visual semantics and intuitive physics to reproduce them in an interactive simulation. The framework consists of five parts, a neural-symbolic…
We present a formal and constructive theory showing that probabilistic finite automata (PFAs) can be exactly simulated using symbolic feedforward neural networks. Our architecture represents state distributions as vectors and transitions as…
Gradient Symbolic Computation is proposed as a means of solving discrete global optimization problems using a neurally plausible continuous stochastic dynamical system. Gradient symbolic dynamics involves two free parameters that must be…
Deep learning architectures based on convolutional neural networks tend to rely on continuous, smooth features. While this characteristics provides significant robustness and proves useful in many real-world tasks, it is strikingly…
Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering. Traditional stability and receptivity…
Neurosymbolic (NeSy) AI has emerged as a promising direction to integrate neural and symbolic reasoning. Unfortunately, little effort has been given to developing NeSy systems tailored to sequential/temporal problems. We identify symbolic…
Neuromechanics aims to understand the link between an animal's neural activity and its physical behaviors. Recent advances in experimental and machine learning techniques enable simultaneous recordings of neural and locomotion dynamics over…