We investigate a reduction of supervised learning to game playing that reveals new connections and learning methods. For convex one-layer problems, we demonstrate an equivalence between global minimizers of the training problem and Nash equilibria in a simple game. We then show how the game can be extended to general acyclic neural networks with differentiable convex gates, establishing a bijection between the Nash equilibria and critical (or KKT) points of the deep learning problem. Based on these connections we investigate alternative learning methods, and find that regret matching can achieve competitive training performance while producing sparser models than current deep learning approaches.

To ensure large language models (LLMs) are used safely, one must reduce their propensity to hallucinate or to generate unacceptable answers. A simple and often used strategy is to first let the LLM generate multiple hypotheses and then employ a reranker to choose the best one.

That is, letusregardHk = Cq.

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We propose in this paper a general framework for deriving loss functions for structured prediction. Inourframework,theuserchooses aconvexsetincluding the output space and provides an oracle forprojectingonto that set.

Roland Martin defends Rep. Jasmine Crockett against white progressive critics of her Texas Senate bid, telling them to "sit their a-- down" on Tuesday's episode of "At Our Table."

Is Cognitive Dissonance Actually a Thing? In 1934, an 8.0-magnitude earthquake hit eastern India, killing thousands and devastating several cities. Curiously, in areas that were spared the worst destruction, stories soon spread that an even bigger disaster was on its way. Leon Festinger, a young American psychologist at the University of Minnesota, read about these rumors in the early nineteen-fifties and was puzzled. Festinger didn't think people would voluntarily adopt anxiety-inducing ideas. Instead, he reasoned, the rumors could better be described as "anxiety justifying." Some had felt the earth shake and were overwhelmed with fear. When the outcome--they were spared--didn't match their emotions, they embraced predictions that affirmed their fright.

An Garda Síochána (Irish police force) has launched an investigation after drones were detected in Irish skies on the night the Ukrainian president arrived in Ireland. Volodymyr Zelensky flew into Dublin late on Monday night for a one-day official visit with his wife, First Lady Olena Zelenska. Senior Irish government figures, including Taoiseach (Irish Prime Minister) Micheál Martin, have been briefed on the issue. Martin confirmed it would be discussed at a National Security Council meeting later this month. In a statement, gardaí said its Special Detective Unit (SDU) is investigating the matter and will be liaising with the Defence Forces and international security partners.

We present the first systematic investigation of Martin's Law - the empirical relationship between word frequency and polysemy - in text generated by neural language models during training. Using DBSCAN clustering of contextualized embeddings as an operationalization of word senses, we analyze four Pythia models (70M-1B parameters) across 30 training checkpoints. Our results reveal a non-monotonic developmental trajectory: Martin's Law emerges around checkpoint 100, reaches peak correlation (r > 0.6) at checkpoint 104, then degrades by checkpoint 105. Smaller models (70M, 160M) experience catastrophic semantic collapse at late checkpoints, while larger models (410M, 1B) show graceful degradation. The frequency-specificity trade-off remains stable (r $\approx$ -0.3) across all models. These findings suggest that compliance with linguistic regularities in LLM-generated text is not monotonically increasing with training, but instead follows a balanced trajectory with an optimal semantic window. This work establishes a novel methodology for evaluating emergent linguistic structure in neural language models.