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As the demand to integrate Artificial Intelligence into high-stakes environments continues to grow, explaining the reasoning behind neural-network predictions has shifted from a theoretical curiosity to a strict operational requirement. Our…
This paper gives an overview of a theory for modelling the interaction between geometric image transformations and receptive field responses for a visual observer that views objects and spatio-temporal events in the environment. This…
We rigorously study the relation between the training dynamics via stochastic gradient descent (SGD) and the spectra of empirical Hessian and gradient matrices. We prove that in two canonical classification tasks for multi-class…
We propose a method of aligning a source image to a target image, where the transform is specified by a dense vector field. The two images are encoded as feature hierarchies by siamese convolutional nets. Then a hierarchy of aligner modules…
In this paper, we propose a harmonized rotational gradient method, termed HRGrad, for simultaneously tackling multiscale time-dependent kinetic problems with varying small parameters. These parameters exhibit asymptotic transitions from…
A grand challenge in modern neuroscience is to bridge the gap between the detailed mapping of microscale neural circuits and mechanistic understanding of cognitive functions. While extensive knowledge exists about neuronal connectivity and…
Brains learn to represent information from a large set of stimuli, typically by weak supervision. Unsupervised learning is therefore a natural approach for exploring the design of biological neural networks and their computations.…
The brain's spatial orientation system uses different neuron ensembles to aid in environment-based navigation. Two of the ways brains encode spatial information is through head direction cells and grid cells. Brains use head direction cells…
Goal-conditioned hierarchical reinforcement learning (HRL) decomposes complex reaching tasks into a sequence of simple subgoal-conditioned tasks, showing significant promise for addressing long-horizon planning in large-scale environments.…
Neural approximations of scalar and vector fields, such as signed distance functions and radiance fields, have emerged as accurate, high-quality representations. State-of-the-art results are obtained by conditioning a neural approximation…
Protein structure prediction has reached revolutionary levels of accuracy on single structures, yet distributional modeling paradigms are needed to capture the conformational ensembles and flexibility that underlie biological function.…
Many contemporary studies utilize grid-based models for neural field representation, but a systematic analysis of grid-based models is still missing, hindering the improvement of those models. Therefore, this paper introduces a theoretical…
Continuous neural field models with inhomogeneous synaptic connectivities are known to support traveling fronts as well as stable bumps of localized activity. We analyze stationary localized structures in a neural field model with periodic…
Hypergraphs offer a generalized framework for capturing high-order relationships between entities and have been widely applied in various domains, including healthcare, social networks, and bioinformatics. Hypergraph neural networks, which…
A central idea in understanding brains and building artificial intelligence is that structure determines function. Yet, how the brain's complex structure arises from a limited set of genetic instructions remains a key question. The ultra…
We introduce a novel approach to endowing neural networks with emergent, long-term, large-scale memory. Distinct from strategies that connect neural networks to external memory banks via intricately crafted controllers and hand-designed…
Spectral gradient methods, such as the Muon optimizer, modify gradient updates by preserving directional information while discarding scale, and have shown strong empirical performance in deep learning. We investigate the mechanisms…
Hopfield models, originally developed to study memory retrieval in neural networks, have become versatile tools for modeling diverse biological systems in which function emerges from collective dynamics. In this review, we provide a…
Hopfield neural networks are a possible basis for modelling associative memory in living organisms. After summarising previous studies in the field, we take a new look at learning rules, exhibiting them as descent-type algorithms for…
We present a Hopfield-like autoassociative network for memories representing examples of concepts. Each memory is encoded by two activity patterns with complementary properties. The first is dense and correlated across examples within…