A second-order method achieves local quadratic convergence on the Stiefel manifold without retractions by combining a modified Newton tangent step with Newton-Schulz normal steps for constraint satisfaction.
Hyv \"a rinen , Fast and robust fixed-point algorithms for independent component analysis , IEEE Transactions on Neural Networks, 10 (1999), pp
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Embedding model performance on MTEB tasks correlates strongly with nearest-neighbor overlap and ICA magnitude differences in their embedding spaces.
CDSP uses an effect-size asymmetry assumption and statistical power to estimate causal directions from bivariate data with uncertainty, reducing false discoveries by 18% on 100 benchmark pairs.
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A second-order method landing on the Stiefel manifold via Newton$\unicode{x2013}$Schulz iteration
A second-order method achieves local quadratic convergence on the Stiefel manifold without retractions by combining a modified Newton tangent step with Newton-Schulz normal steps for constraint satisfaction.
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Structure Retention in Embedding Spaces as a Predictor of Benchmark Performance
Embedding model performance on MTEB tasks correlates strongly with nearest-neighbor overlap and ICA magnitude differences in their embedding spaces.
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Causal Discovery via Statistical Power (CDSP)
CDSP uses an effect-size asymmetry assumption and statistical power to estimate causal directions from bivariate data with uncertainty, reducing false discoveries by 18% on 100 benchmark pairs.