These challenges are exacerbated by dynamics influenced not only by the environment but also by strategies of opponents.

We introduce a novel paradigm of emergent local memory. It is a continuous-learning completely-parallel content-addressable memory encoding global order. It demonstrates how local constraints on uncoordinated learning can produce topologically protected memories realizing emergent symbolic order. It is therefore a neuro-symbolic bridge. It further has the ability to produce human language without data, by exploiting its own self-organizing dynamics. It teaches us that words arise as a side-effect of emergent symbolic order, and that human language patterns at all structural levels reflect a universal mechanism of word formation (which is subregular). This work answers essential questions about the existence \& origin of all the human language data.

Analyzing our model using maximally activating stimuli and saliency maps, we reveal new insights into cortical function, including the prevalence of mixed selectivity for behavioral variables in mouse V1.

Devoid of some assumption, aPU learning is impossible [6].

We develop a framework for analyzing the training and learning rate dynamics on a variety of high- dimensional optimization problems trained using one-pass stochastic gradient descent (SGD) with data generated from multiple anisotropic classes. We give exact expressions for a large class of functions of the limiting dynamics, including the risk and the overlap with the true signal, in terms of a deterministic solution to a system of ODEs. We extend the existing theory of high-dimensional SGD dynamics to Gaussian-mixture data and a large (growing with the parameter size) number of classes. We then investigate in detail the effect of the anisotropic structure of the covariance of the data in the problems of binary logistic regression and least square loss. We study three cases: isotropic covariances, data covariance matrices with a large fraction of zero eigenvalues (denoted as the zero-one model), and covariance matrices with spectra following a power-law distribution. We show that there exists a structural phase transition. In particular, we demonstrate that, for the zero-one model and the power-law model with sufficiently large power, SGD tends to align more closely with values of the class mean that are projected onto the "clean directions" (i.e., directions of smaller variance). This is supported by both numerical simulations and analytical studies, which show the exact asymptotic behavior of the loss in the high-dimensional limit.

Argument structure constructions (ASCs) offer a theoretically grounded lens for analyzing second language (L2) proficiency, yet scalable and systematic tools for measuring their usage remain limited. This paper introduces the ASC analyzer, a publicly available Python package designed to address this gap. The analyzer automatically tags ASCs and computes 50 indices that capture diversity, proportion, frequency, and ASC-verb lemma association strength. To demonstrate its utility, we conduct both bivariate and multivariate analyses that examine the relationship between ASC-based indices and L2 writing scores.

We propose an unsupervised adaptation framework, Self-T Aught Recognizer (ST AR), which leverages unlabeled data to enhance the robustness of automatic speech recognition (ASR) systems in diverse target domains, such as noise and accents. ST AR is developed for prevalent speech foundation models based on Transformer-related architecture with auto-regressive decoding (e.g., Whisper, Canary; SeamlessM4T).