SMART: A Spectral Transfer Approach to Multi-Task Learning

Multi-task learning is effective for related applications, but its performance can deteriorate when the target sample size is small. Transfer learning can borrow strength from related studies; yet, many existing methods rely on restrictive bounded-difference assumptions between the source and target models. We propose SMART, a spectral transfer method for multi-task linear regression that instead assumes spectral similarity: the target left and right singular subspaces lie within the corresponding source subspaces and are sparsely aligned with the source singular bases. Such an assumption is natural when studies share latent structures and enables transfer beyond the bounded-difference settings. SMART estimates the target coefficient matrix through structured regularization that incorporates spectral information from a source study. Importantly, it requires only a fitted source model rather than the raw source data, making it useful when data sharing is limited. Although the optimization problem is nonconvex, we develop a practical ADMM-based algorithm. We establish general, non-asymptotic error bounds and a minimax lower bound in the noiseless-source regime. Under additional regularity conditions, these results yield near-minimax Frobenius error rates up to logarithmic factors. Simulations confirm improved estimation accuracy and robustness to negative transfer, and analysis of multi-modal single-cell data demonstrates better predictive performance. The Python implementation of SMART, along with the code to reproduce all experiments in this paper, is publicly available at https://github.com/boxinz17/smart.

Cell-Based Representation of Relational Binding in Language Models

Understanding a discourse requires tracking entities and the relations that hold between them. While Large Language Models (LLMs) perform well on relational reasoning, the mechanism by which they bind entities, relations, and attributes remains unclear. We study discourse-level relational binding and show that LLMs encode it via a Cell-based Binding Representation (CBR): a low-dimensional linear subspace in which each ``cell'' corresponds to an entity--relation index pair, and bound attributes are retrieved from the corresponding cell during inference. Using controlled multi-sentence data annotated with entity and relation indices, we identify the CBR subspace by decoding these indices from attribute-token activations with Partial Least Squares regression. Across domains and two model families, the indices are linearly decodable and form a grid-like geometry in the projected space. We further find that context-specific CBR representations are related by translation vectors in activation space, enabling cross-context transfer. Finally, activation patching shows that manipulating this subspace systematically changes relational predictions and that perturbing it disrupts performance, providing causal evidence that LLMs rely on CBR for relational binding.

An `Inverse' Experimental Framework to Estimate Market Efficiency

Digital marketplaces processing billions of dollars annually represent critical infrastructure in sociotechnical ecosystems, yet their performance optimization lacks principled measurement frameworks that can inform algorithmic governance decisions regarding market efficiency and fairness from complex market data. By looking at orderbook data from double auction markets alone, because bids and asks do not represent true maximum willingnesses to buy and true minimum willingnesses to sell, there is little an economist can say about the market's actual performance in terms of allocative efficiency. We turn to experimental data to address this issue, `inverting' the standard induced value approach of double auction experiments. Our aim is to predict key market features relevant to market efficiency, particularly allocative efficiency, using orderbook data only -- specifically bids, asks and price realizations, but not the induced reservation values -- as early as possible. Since there is no established model of strategically optimal behavior in these markets, and because orderbook data is highly unstructured, non-stationary and non-linear, we propose quantile-based normalization techniques that help us build general predictive models. We develop and train several models, including linear regressions and gradient boosting trees, leveraging quantile-based input from the underlying supply-demand model. Our models can predict allocative efficiency with reasonable accuracy from the earliest bids and asks, and these predictions improve with additional realized price data. The performance of the prediction techniques varies by target and market type. Our framework holds significant potential for application to real-world market data, offering valuable insights into market efficiency and performance, even prior to any trade realizations.

Probing for Reading Times

Probing has shown that language model representations encode rich linguistic information, but it remains unclear whether they also capture cognitive signals about human processing. In this work, we probe language model representations for human reading times. Using regularized linear regression on two eye-tracking corpora spanning five languages (English, Greek, Hebrew, Russian, and Turkish), we compare the representations from every model layer against scalar predictors -- surprisal, information value, and logit-lens surprisal. We find that the representations from early layers outperform surprisal in predicting early-pass measures such as first fixation and gaze duration. The concentration of predictive power in the early layers suggests that human-like processing signatures are captured by low-level structural or lexical representations, pointing to a functional alignment between model depth and the temporal stages of human reading. In contrast, for late-pass measures such as total reading time, scalar surprisal remains superior, despite its being a much more compressed representation. We also observe performance gains when using both surprisal and early-layer representations. Overall, we find that the best-performing predictor varies strongly depending on the language and eye-tracking measure.

SOLIS: Physics-Informed Learning of Interpretable Neural Surrogates for Nonlinear Systems

Nonlinear system identification must balance physical interpretability with model flexibility. Classical methods yield structured, control-relevant models but rely on rigid parametric forms that often miss complex nonlinearities, whereas Neural ODEs are expressive yet largely black-box. Physics-Informed Neural Networks (PINNs) sit between these extremes, but inverse PINNs typically assume a known governing equation with fixed coefficients, leading to identifiability failures when the true dynamics are unknown or state-dependent. We propose \textbf{SOLIS}, which models unknown dynamics via a \emph{state-conditioned second-order surrogate model} and recasts identification as learning a Quasi-Linear Parameter-Varying (Quasi-LPV) representation, recovering interpretable natural frequency, damping, and gain without presupposing a global equation. SOLIS decouples trajectory reconstruction from parameter estimation and stabilizes training with a cyclic curriculum and \textbf{Local Physics Hints} windowed ridge-regression anchors that mitigate optimization collapse. Experiments on benchmarks show accurate parameter-manifold recovery and coherent physical rollouts from sparse data, including regimes where standard inverse methods fail.

Mechanistic Decoding of Cognitive Constructs in LLMs

While Large Language Models (LLMs) demonstrate increasingly sophisticated affective capabilities, the internal mechanisms by which they process complex emotions remain unclear. Existing interpretability approaches often treat models as black boxes or focus on coarse-grained basic emotions, leaving the cognitive structure of more complex affective states underexplored. To bridge this gap, we propose a Cognitive Reverse-Engineering framework based on Representation Engineering (RepE) to analyze social-comparison jealousy. By combining appraisal theory with subspace orthogonalization, regression-based weighting, and bidirectional causal steering, we isolate and quantify two psychological antecedents of jealousy, Superiority of Comparison Person and Domain Self-Definitional Relevance, and examine their causal effects on model judgments. Experiments on eight LLMs from the Llama, Qwen, and Gemma families suggest that models natively encode jealousy as a structured linear combination of these constituent factors. Their internal representations are broadly consistent with the human psychological construct, treating Superiority as the foundational trigger and Relevance as the ultimate intensity multiplier. Our framework also demonstrates that toxic emotional states can be mechanically detected and surgically suppressed, suggesting a possible route toward representational monitoring and intervention for AI safety in multi-agent environments.

Classical Machine Learning Baselines for Deepfake Audio Detection on the Fake-or-Real Dataset

Deep learning has enabled highly realistic synthetic speech, raising concerns about fraud, impersonation, and disinformation. Despite rapid progress in neural detectors, transparent baselines are needed to reveal which acoustic cues reliably separate real from synthetic speech. This paper presents an interpretable classical machine learning baseline for deepfake audio detection using the Fake-or-Real (FoR) dataset. We extract prosodic, voice-quality, and spectral features from two-second clips at 44.1 kHz (high-fidelity) and 16 kHz (telephone-quality) sampling rates. Statistical analysis (ANOVA, correlation heatmaps) identifies features that differ significantly between real and fake speech. We then train multiple classifiers -- Logistic Regression, LDA, QDA, Gaussian Naive Bayes, SVMs, and GMMs -- and evaluate performance using accuracy, ROC-AUC, EER, and DET curves. Pairwise McNemar's tests confirm statistically significant differences between models. The best model, an RBF SVM, achieves ~93% test accuracy and ~7% EER on both sampling rates, while linear models reach ~75% accuracy. Feature analysis reveals that pitch variability and spectral richness (spectral centroid, bandwidth) are key discriminative cues. These results provide a strong, interpretable baseline for future deepfake audio detectors.

From Order to Distribution: A Spectral Characterization of Forgetting in Continual Learning

A central challenge in continual learning is forgetting, the loss of performance on previously learned tasks induced by sequential adaptation to new ones. While forgetting has been extensively studied empirically, rigorous theoretical characterizations remain limited. A notable step in this direction is \citet{evron2022catastrophic}, which analyzes forgetting under random orderings of a fixed task collection in overparameterized linear regression. We shift the perspective from order to distribution. Rather than asking how a fixed task collection behaves under random orderings, we study an exact-fit linear regime in which tasks are sampled i.i.d.\ from a task distribution~$Π$, and ask how the generating distribution itself governs forgetting. In this setting, we derive an exact operator identity for the forgetting quantity, revealing a recursive spectral structure. Building on this identity, we establish an unconditional upper bound, identify the leading asymptotic term, and, in generic nondegenerate cases, characterize the convergence rate up to constants. We further relate this rate to geometric properties of the task distribution, clarifying what drives slow or fast forgetting in this model.

Inferring Change Points in Regression via Sample Weighting

We study the problem of identifying change points in high-dimensional generalized linear models, and propose an approach based on sample-weighted empirical risk minimization. Our method, Weighted ERM, encodes priors on the change points via weights assigned to each sample, to obtain weighted versions of standard estimators such as M-estimators and maximum-likelihood estimators. Under mild assumptions on the data, we obtain a precise asymptotic characterization of the performance of our method for general Gaussian designs, in the high-dimensional limit where the number of samples and covariate dimension grow proportionally. We show how this characterization can be used to efficiently construct a posterior distribution over change points. Numerical experiments on both simulated and real data illustrate the efficacy of Weighted ERM compared to existing approaches, demonstrating that sample weights constructed with weakly informative priors can yield accurate change point estimators. Our method is implemented as an open-source package, weightederm, available in Python and R.

Refined Differentially Private Linear Regression via Extension of a Free Lunch Result

As data-privacy regulations tighten and statistical models are increasingly deployed on sensitive human-sourced data, privacy-preserving linear regression has become a critical necessity. For the add-remove DP model, Kulesza et al. (2024) and Fitzsimons et al. (2024) have independently shown that the size of the dataset -- an important statistic for linear regression -- can be privately estimated for "free", via a simplex transformation of bounded variables and private sum queries on the transformed variables. In this work, we extend this free lunch result via carefully crafted multidimensional simplex transformations to variables and functions that are bounded in the interval [0,1]. We show that these transformations can be applied to refine the estimates of sufficient statistics needed for private simple linear regression based on ordinary least squares. We provide both analytical and numerical results to demonstrate the superiority of our approach. Our proposed transformations have general applicability and can be readily adapted for differentially private polynomial regression.