Empirical studies of trained models often report a transient regime in which signal is detectable in a finite gradient descent time window before overfitting dominates. We provide an analytically tractable random-matrix model that reproduces this phenomenon for gradient flow in a linear teacher--student setting. In this framework, learning occurs when an isolated eigenvalue separates from a noisy bulk, before eventually disappearing in the overfitting regime. The key ingredient is anisotropy in the input covariance, which induces fast and slow directions in the learning dynamics. In a two-block covariance model, we derive the full time-dependent bulk spectrum of the symmetrized weight matrix through a $2\times 2$ Dyson equation, and we obtain an explicit outlier condition for a rank-one teacher via a rank-two determinant formula. This yields a transient Baik-Ben Arous-Péché (BBP) transition: depending on signal strength and covariance anisotropy, the teacher spike may never emerge, emerge and persist, or emerge only during an intermediate time interval before being reabsorbed into the bulk. We map the corresponding phase diagrams and validate the theory against finite-size simulations. Our results provide a minimal solvable mechanism for early stopping as a transient spectral effect driven by anisotropy and noise.

The massive scale of pretrained models has made efficient compression essential for practical deployment. Low-rank decomposition based on the singular value decomposition (SVD) provides a principled approach for model reduction, but its exact computation is expensive for large weight matrices. Randomized alternatives such as randomized SVD (RSVD) improve efficiency, yet they can suffer from poor approximation quality when the singular value spectrum decays slowly, a regime commonly observed in modern pretrained models. In this work, we address this limitation from both theoretical and empirical perspectives. First, we establish a connection between low-rank approximation error and predictive performance by analyzing softmax perturbations, showing that deviations in class probabilities are controlled by the spectral error of the compressed weights. Second, we demonstrate that RSVD is inadequate, and we propose randomized subspace iteration (RSI) as a more effective alternative. By incorporating multiple power iterations, RSI improves spectral separation and provides a controllable mechanism for enhancing approximation quality. We evaluate our approach on both convolutional networks and transformer-based architectures. Our results show that RSI achieves near-optimal approximation quality while outperforming RSVD in predictive accuracy under aggressive compression, enabling efficient model compression.

Objective. We establish a principled method for inferring mental health related psychometric variables from neural and behavioral data using the Implicit Association Test (IAT) as the data generation engine, aiming to overcome the limited predictive performance (typically under 0.7 AUC) of the gold-standard D-score method, which relies solely on reaction times. Approach. We propose a sparse hierarchical Bayesian model that leverages multi-modal data to predict experiences related to mental illness symptoms in new participants. The model is a multivariate generalization of the D-score with trainable parameters, engineered for parameter efficiency in the small-cohort regime typical of IAT studies. Data from two IAT variants were analyzed: a suicidality-related E-IAT ($n=39$) and a psychosis-related PSY-IAT ($n=34$). Main Results. Our approach overcomes a high inter-individual variability and low within-session effect size in the dataset, reaching AUCs of 0.73 (E-IAT) and 0.76 (PSY-IAT) in the best modality configurations, though corrected 95% confidence intervals are wide ($\pm 0.18$) and results are marginally significant after FDR correction ($q=0.10$). Restricting the E-IAT to MDD participants improves AUC to 0.79 $[0.62, 0.97]$ (significant at $q=0.05$). Performance is on par with the best reference methods (shrinkage LDA and EEGNet) for each task, even when the latter were adapted to the task, while the proposed method was not. Accuracy was substantially above near-chance D-scores (0.50-0.53 AUC) in both tasks, with more consistent cross-task performance than any single reference method. Significance. Our framework shows promise for enhancing IAT-based assessment of experiences related to entrapment and psychosis, and potentially other mental health conditions, though further validation on larger and independent cohorts will be needed to establish clinical utility.

We propose a fast approximation method of a softmax function with a very large vocabulary using singular value decomposition (SVD).

Conventional models prepare a large embedding matrix whose size depends on the vocabulary size. Therefore, storing these models in memory and disk storage is costly.

We show that it provides significant benefits to RL agents on a suite of gridworld, CARL and MetaWorld tasks.

HR-based orthogonal fine-tuning is equivalent to an adaptive low-rank adaptation.

Homomorphic encryption (HE)-based deep neural network (DNN) inference protects data and model privacy but suffers from significant computation overhead. We observe transforming the DNN weights into circulant matrices converts general matrix-vector multiplications into HE-friendly 1-dimensional convolutions, drastically reducing the HE computation cost.

The following proof is from Daniely and V ardi [15], and we give it here for completeness. By Lemma A.1, there exists a DNF formula We construct such an affine layer in Lemma A.2. At least one of the k size-n slices in z contains 0 more than once. We define the outputs of our affine layer as follows. Pr [z represents a hyperedge ] = n (n 1) ... (n k + 1) null 1 n null Pr null z Z null 1 2 log(n) .