arXiv:2601.13776v1 Announce Type: cross Abstract: Orthogonal and 1-Lipschitz neural network layers are essential building blocks in robust deep learning architectures, crucial for certified adversarial robustness, stable generative models, and reliable recurrent networks. Despite significant advancements, existing implementations remain fragmented, limited, and computationally demanding. To address these issues, we introduce Orthogonium , a unified, efficient, and comprehensive PyTorch library providing orthogonal and 1-Lipschitz layers. Orthogonium provides access to standard convolution features-including support for strides, dilation, grouping, and transposed-while maintaining […]

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arXiv:2603.02178v1 Announce Type: cross Abstract: Reservoir expansion can improve online independent component analysis (ICA) under nonlinear mixing, yet top-$n$ whitening may discard injected features. We formalize this bottleneck as emph{reservoir subspace injection} (RSI): injected features help only if they enter the retained eigenspace without displacing passthrough directions. RSI diagnostics (IER, SSO, $rho_x$) identify a failure mode in our top-$n$ setting: stronger injection increases IER but crowds out passthrough energy ($rho_x: 1.00!rightarrow!0.77$), degrading SI-SDR by up to $2.2$,dB. A […]

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arXiv:2601.10775v1 Announce Type: new Abstract: We propose a novel LLM-based framework for reasoning in discrete, game-theoretic tasks, illustrated with emph{Tic-Tac-Toe}. The method integrates in-context learning with entropy-guided chain-of-thought (CoT) reasoning and adaptive context retrieval. The model dynamically adjusts both the number of retrieved examples and reasoning paths according to token-level uncertainty: concise reasoning with minimal context is used when uncertainty is low, whereas higher uncertainty triggers expanded multi-path CoT exploration. Experimental evaluation against a sub-optimal algorithmic opponent shows […]

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Learning from structured multi-way data, represented as higher-order tensors, requires capturing complex interactions across tensor modes while remaining computationally efficient. We introduce Uncertainty-driven Kernel Tensor Learning (UKTL), a novel kernel framework for $M$-mode tensors that compares mode-wise subspaces derived from tensor unfoldings, enabling expressive and robust similarity measure. To handle large-scale tensor data, we propose a scalable Nyström kernel linearization with dynamically learned pivot tensors obtained via soft $k$-means clustering. A key innovation of UKTL is its uncertainty-aware […]

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Artificial Intelligence (AI) has developed over the years from rudimentary systems of symbolic reasoning in the middle of the twentieth century to sophisticated data-driven and generative architectures, which give rise to modern society. The acceleration of machine learning, deep neural networks and large-scale computational infrastructures has turned AI into a basic technology in the economic, social, and societal sectors. This paper investigates the history of the development of AI and critically discusses its influence on society in the […]

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