Nonlinear independent component analysis (ICA) provides an appealing framework for unsupervised feature learning, but the models proposed so far are not identifiable. Here, we first propose a new intuitive principle of unsupervised deep learning from time series which uses the nonstationary structure of the data. Our learning principle, time-contrastive learning (TCL), finds a representation which allows optimal discrimination of time segments (windows). Surprisingly, we show how TCL can be related to a nonlinear ICA model, when ICA is redefined to include temporal nonstationarities. In particular, we show that TCL combined with linear ICA estimates the nonlinear ICA model up to point-wise transformations of the sources, and this solution is unique --- thus providing the first identifiability result for nonlinear ICA which is rigorous, constructive, as well as very general.

This story appears in the April 2026 print edition. While some stories from this issue are not yet available to read online, you can explore more from the magazine . Get our editors' guide to what matters in the world, delivered to your inbox every weekday. The race to power AI is already remaking the physical world. Three Mile Island's cooling towers have until recently served as grave markers for America's nuclear-power industry. A s we drove through southwest Memphis, KeShaun Pearson told me to keep my window down--our destination was best tasted, not viewed. Along the way, we passed an abandoned coal plant to our right, then an active power plant to our left, equipped with enormous natural-gas turbines. Pearson, who directs the nonprofit Memphis Community Against Pollution, was bringing me to his hometown's latest industrial megaproject.

ROTC students at Old Dominion subdued and killed ISIS-linked gunman who left one dead, two wounded after shouting'Allahu Akbar' and opened fire Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Hollywood icon who starred in Psycho after Hitchcock dubbed her'my new Grace Kelly' looks incredible at 95 Kylie Jenner's total humiliation in Hollywood: Derogatory rumor leaves her boyfriend's peers'laughing at her' behind her back Tucker Carlson erupts at Trump adviser as she hurls'SLANDER' claim linking him to synagogue shooting Ben Affleck'scores $600m deal' with Netflix to sell his AI film start-up Long hair over 45 is ageing and try-hard. I've finally cut mine off. Alexander brothers' alleged HIGH SCHOOL rape video: Classmates speak out on sickening footage... as creepy unseen photos are exposed Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' Rare 30-foot'Doomsday fish' sighting by US tourists sparks ancient fears of imminent disaster A pair of American tourists had a'one-in-a-billion chance' encounter with a rare sea creature, said to be a sign of imminent disaster. Monica Pittenger and her sister, Katie, were on a beach in Mexico's Cabo San Lucas last month when they spotted two massive oarfish washing ashore, to the shock of everyone in the area. Oarfish, also known as sea serpents, have been referred to in Japanese folklore as'Doomsday fish' because they are said to be the messengers from the sea god's palace .

Minamitorishima is nearly 1,250 miles east of Tokyo. The island is surrounded by a coral atoll and is only 0.6 miles wide. Breakthroughs, discoveries, and DIY tips sent six days a week. Nuclear power is on the rise around the world, but with it comes an extremely pressing question: where will all of the radioactive waste be stored? For Japan, one answer may lie in literally the most remote location at their disposal.

Spatio-temporal forecasting is fundamental to intelligent systems in transportation, climate science, and urban planning. However, training deep learning models on the massive, often redundant, datasets from these domains presents a significant computational bottleneck. Existing solutions typically focus on optimizing model architectures or optimizers, while overlooking the inherent inefficiency of the training data itself. This conventional approach of iterating over the entire static dataset each epoch wastes considerable resources on easy-to-learn or repetitive samples. In this paper, we explore a novel training-efficiency techniques, namely learning from complexity with dynamic sample pruning, ST-Prune, for spatio-temporal forecasting. Through dynamic sample pruning, we aim to intelligently identify the most informative samples based on the model's real-time learning state, thereby accelerating convergence and improving training efficiency. Extensive experiments conducted on real-world spatio-temporal datasets show that ST-Prune significantly accelerates the training speed while maintaining or even improving the model performance, and it also has scalability and universality.

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, $ρ_x$) identify a failure mode in our top-$n$ setting: stronger injection increases IER but crowds out passthrough energy ($ρ_x: 1.00\!\rightarrow\!0.77$), degrading SI-SDR by up to $2.2$\,dB. A guarded RSI controller preserves passthrough retention and recovers mean performance to within $0.1$\,dB of baseline $1/N$ scaling. With passthrough preserved, RE-OICA improves over vanilla online ICA by $+1.7$\,dB under nonlinear mixing and achieves positive SI-SDR$_{\mathrm{sc}}$ on the tested super-Gaussian benchmark ($+0.6$\,dB).

Abstract--Kurtosis-based Independent Component Analysis (ICA) weakens in wide, balanced mixtures. We also show that purification--selecting m R sign-consistent sources--restores R-independent contrast Ω(1/m), with a simple data-driven heuristic. Synthetic experiments validate the predicted decay, the T crossover, and contrast recovery. Independent Component Analysis (ICA) recovers statistically independent latent sources from linear mixtures and is identifiable whenever at most one source is Gaussian [1]. Excess kurtosis--the standardized fourth cumulant--is a central contrast function [9], and kurtosis-type nonlinearities remain standard in FastICA.

The government plans to submit a bill to revise the economic security promotion law during the current session of parliament that began on Wednesday. The Japanese government plans to revise the economic security promotion law to support companies with economic security-linked projects overseas. This will be the first revision of the law, established in 2022. The move comes amid a rapidly changing international environment, as the Ukraine-Russia war drags on and China continues to flex its economic muscle. Competition is also intensifying in the development of artificial intelligence and other cutting-edge technologies.

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