arXiv:2511.12760v2 Announce Type: replace-cross Abstract: We introduce Conformal Online Learning of Koopman embeddings (COLoKe), a novel framework for adaptively updating Koopman-invariant representations of nonlinear dynamical systems from streaming data. Our modeling approach combines deep feature learning with multistep prediction consistency in the lifted space, where the dynamics evolve linearly. To prevent overfitting, COLoKe employs a conformal-style mechanism that shifts the focus from evaluating the conformity of new states to assessing the consistency of the current Koopman model. Updates […]

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An information-theoretic framework is introduced to analyze last-layer embedding, focusing on learned representations for regression tasks. We define representation-rate and derive limits on the reliability with which input-output information can be represented as is inherently determined by the input-source entropy. We further define representation capacity in a perturbed setting, and representation rate-distortion for a compressed output. We derive the achievable capacity, the achievable representation-rate, and their converse. Finally, we combine the results in a unified setting.

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Table of Links Abstract and 1. Introduction Some recent trends in theoretical ML 2.1 Deep Learning via continuous-time controlled dynamical system 2.2 Probabilistic modeling and inference in DL 2.3 Deep Learning in non-Euclidean spaces 2.4 Physics Informed ML Kuramoto model 3.1 Kuramoto models from the geometric point of view 3.2 Hyperbolic geometry of Kuramoto ensembles 3.3 Kuramoto models with several globally coupled sub-ensembles Kuramoto models on higher-dimensional manifolds 4.1 Non-Abelian Kuramoto models on Lie groups 4.2 Kuramoto models […]

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A new wave of work on covariance cleaning and nonlinear shrinkage has delivered asymptotically optimal analytical solutions for large covariance matrices. Building on this progress, these ideas have been generalized to empirical cross-covariance matrices, whose singular-value shrinkage characterizes comovements between one set of assets and another. Existing analytical cross-covariance cleaners are derived under strong stationarity and large-sample assumptions, and they typically rely on mesoscopic regularity conditions such as bounded spectra; macroscopic common modes (e.g., a global market factor) […]

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I am a Computer Vision and ML engineer with over five years of experience and a research based Masters degree. A few months ago I left a well paying remote role because the work environment and micromanagement were seriously affecting my mental health. At the time I believed stepping away was the right decision for my sanity. It has now been around three months and I am barely getting any recruiter screens let alone technical interviews. The lack […]

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We demonstrate deterministic localization of cryptographic hash preimages within specific layers of deep neural networks trained on information-geometric principles. Using a modified Spin-Glass architecture, MD5 and SHA-256 password preimages are consistently identified in layers ES15-ES20 with >90% accuracy for passwords and >85% for hash values. Analysis reveals linear scaling where longer passwords occupy proportionally expanded layer space, with systematic replication in higher-dimensional layers showing exact topological correspondence.Critically, independent network runs with fresh initialization maintain 41.8% information persistence across […]

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The crypto market is no longer driven purely by hype. As investors look ahead to 2026, the focus has shifted toward timing, utility, and long-term sustainability. In this article, we take a closer look at Dogecoin (DOGE) and Mutuum Finance (MUTM)—two very different cryptocurrencies at very different stages—to assess which may offer the stronger investment opportunity in today’s market environment. Dogecoin (DOGE) Dogecoin remains one of the most recognizable cryptocurrencies in the market, largely due to its meme-driven […]

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A founder recently asked me how to stop caring what other people think. I didn’t have an answer, and after reflecting on it more, I think it’s the wrong question. Almost everyone cares what someone thinks (though caring what everyone thinks is definitely a mistake), and it’s probably important. Caring too much makes you a sheep. But you need to be at least a little in tune with others to do something useful for them. It seems like […]

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