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Topological signal processing and learning: Recent advances and future challenges
Develo** methods to process irregularly structured data is crucial in applications like gene-
regulatory, brain, power, and socioeconomic networks. Graphs have been the go-to …
regulatory, brain, power, and socioeconomic networks. Graphs have been the go-to …
[HTML][HTML] What ChatGPT Has to Say About Its Topological Structure: The Anyon Hypothesis
Large language models (LLMs) achieve remarkable predictive capabilities but remain
opaque in their internal reasoning, creating a pressing need for more interpretable artificial …
opaque in their internal reasoning, creating a pressing need for more interpretable artificial …
Integrable Matrix Probabilistic Diffusions and the Matrix Stochastic Heat Equation
We introduce a matrix version of the stochastic heat equation, the MSHE, and obtain its
explicit invariant measure in spatial dimension $ D= 1$. We show that it is classically …
explicit invariant measure in spatial dimension $ D= 1$. We show that it is classically …
Wrapped Gaussian on the manifold of Symmetric Positive Definite Matrices
Circular and non-flat data distributions are prevalent across diverse domains of data
science, yet their specific geometric structures often remain underutilized in machine …
science, yet their specific geometric structures often remain underutilized in machine …