Physicists used an acoustic metamaterial platform to experimentally demonstrate a 'critical topological phase transition,' a phenomenon where topological invariants remain well-defined even at the gapless critical point of a phase transition. They observed topological edge states along critical phase boundaries and confirmed criticality through logarithmic scaling of entanglement entropy, including an additive scaling pattern at a special multicritical point where distinct critical boundaries intersect.
nature.com
· 2026-10-07
A technical post outlines a statistical challenge in machine learning: estimating log-sum-exp functions, which are widely used for normalizing probabilistic models and in reinforcement learning, becomes highly unreliable when the underlying potential function takes large values, causing estimation variance to grow exponentially. The author proposes using least-squares techniques to address this exploding variance problem, offering a way to stabilize these estimates even as the scale of the values involved increases.
francisbach.com
· 2026-09-25
In their book Time's Second Arrow, Robert Hazen and Michael Wong argue that alongside thermodynamics' entropy-driven decay, there exists a complementary natural principle that consistently pushes matter and systems toward greater order and complexity. They cite phenomena from element formation via nuclear fusion to biological evolution as recurring evidence of this ordering tendency across both living and non-living systems.
nature.com
· 2026-08-31
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