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Solving Coupled Tensor Equation $\mathcal{A} \ltimes \mathcal{X} =\mathcal{B}, \ \mathcal{X}\ltimes \mathcal{C}=\mathcal{D}$ using Semi-Tensor Products in the t-product
arXiv:2605.31122v1 Announce Type: new Abstract: This paper investigates the solution of coupled third-order tensor equation $\mathcal{A} \ltimes \mathcal{X} = \mathcal{B},\ \mathcal{X} \ltimes \mathcal{C} = \mathcal{D},$ of arbitrary dimensions by incorporating semi-tensor product (STP) within t-product framework, where the unknown $\mathcal{X}$ can take form of vector, matrix, or tensor. For the unknown $\mathcal{X}$, we establish a necessary and sufficient condition that provides an...
Emergent Ordinal Geometry in Transformers Trained on Local Comparisons
arXiv:2606.01269v1 Announce Type: new Abstract: Transitive inference is the challenge of inferring that A < C from knowing only adjacent relations (A < B, B < C). It is solved by humans and animals not through logical chaining but via an analogue mental number line, whose signature is the symbolic distance effect: distant comparisons are easier than nearby ones. We ask whether Transformers acquire the same primitive, training small models exclusively on adjacent comparisons from a hidden...
Emergent Ordinal Geometry in Transformers Trained on Local Comparisons
arXiv:2606.01269v2 Announce Type: replace Abstract: Transitive inference is the challenge of inferring that A < C from knowing only adjacent relations (A < B, B < C). It is solved by humans and animals not through logical chaining but via an analogue mental number line, whose signature is the symbolic distance effect: distant comparisons are easier than nearby ones. We ask whether Transformers acquire the same primitive, training small models exclusively on adjacent comparisons from a hidden...
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Ultrafast machine learning on FPGAs via Kolmogorov-Arnold Networks This post is a high-level explainer for my Master’s thesis, which involves designing hardware architectures for ultrafast inference and online learning using the Kolmogorov-Arnold Network (KAN) architecture. I’ll assume familiarity with standard machine learning concepts, as well as some understanding of hardware and digital circuits; read my previous post here for the latter. Please read the two papers below for more...
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