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To a significant extent, the rich physical properties of photonic crystals are determined by the underlying geometry, in which the composed symmetry operators and their combinations contribute to the unique topological invariant to…
A standard way of approximating or discretizing a metric space is by taking its Rips complexes. These approximations for all parameters are often bound together into a filtration, to which we apply the fundamental group or the first…
The transport on top of a periodic two-dimensional hexagonal magnetic pattern of (i) a single macroscopic steel sphere, (ii) a doublet of wax/magnetite composite spheres, and (iii) an immiscible mixture of ferrofluid droplets with a…
We solve the dynamics of Hopfield-type neural networks which store sequences of patterns, close to saturation. The asymmetry of the interaction matrix in such models leads to violation of detailed balance, ruling out an equilibrium…
Scale does not uniformly improve reasoning - it restructures it. Analyzing 25,000+ chain-of-thought trajectories across four domains (Law, Science, Code, Math) and two scales (8B, 70B parameters), we discover that neural scaling laws…
We propose a normative model for spatial representation in the hippocampal formation that combines optimality principles, such as maximizing coding range and spatial information per neuron, with an algebraic framework for computing in…
The space of possible behaviors complex biological systems may exhibit is unimaginably vast, and these systems often appear to be stochastic, whether due to variable noisy environmental inputs or intrinsically generated chaos. The brain is…
Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…
Topological techniques have become a popular tool for studying information flows in neural networks. In particular, simplicial homology theory is used to analyze how cognitive representations of space emerge from large conglomerates of…
Decomposition is a proven way to shrink deep networks without changing input-output dimensionality or interface semantics. We bring this idea to hyperdimensional computing (HDC), where footprint cuts usually shrink the feature axis and…
The general stable quantum memory unit is a hybrid consisting of a classical digit with a quantum digit (qudit) assigned to each classical state. The shape of the memory is the vector of sizes of these qudits, which may differ. We determine…
Functional brain connectivity changes dynamically over time, making its representation challenging for learning on non-Euclidean data. We present a framework that encodes dynamic functional connectivity as an image representation of…
Effective analysis in neuroscience benefits significantly from robust conceptual frameworks. Traditional metrics of interbrain synchrony in social neuroscience typically depend on fixed, correlation-based approaches, restricting their…
Disordered and amorphous materials often retain memories of perturbations they have experienced since preparation. Studying such memories is a gateway to understanding this challenging class of systems, yet it often requires the ability to…
Transition graphs capture the memory and sequential response of multistable media, by specifying their evolution under external driving. Microscopically, collections of bistable elements, or hysterons, provide a powerful model for these…
We propose a novel topological photonic memory that encodes information through dynamically controllable Chern numbers in a two-band topological photonic system. Utilizing a honeycomb lattice photonic crystal, the memory leverages…
In this report we discuss the concepts of geometric memory align- ment, geometric memory allocation and geometric memory mapping. We introduce block trees as an efficient data structure for representing geo- metrically aligned block…
Hierarchical temporal memory (HTM) tries to mimic the computing in cerebral-neocortex. It identifies spatial and temporal patterns in the input for making inferences. This may require large number of computationally expensive tasks like,…
A memristor is a nonlinear two-terminal electrical element that incorporates memory features and nanoscale properties, enabling us to design very high-density artificial neural networks. To enhance the memory property, we should use…
Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase…