arXiv subjects

Andrew Campbell

Publications and source records attributed to Andrew Campbell.

At least 19 recordsLinked to original sources

arXiv2026

Scaling Therapy Supervision: Assessing Psychotherapy Fidelity Using Large Language Models

Psychotherapy fidelity assessment measures how faithfully a therapist adheres to a treatment protocol, a critical determinant of positive patient outcomes. However, fidelity assessment is bottlenecked by manual expert review, rendering the process labor-intensive and unscalable. To scale therapy supervision and support clinician self-learning, we present an integrated application of large language models (LLMs) that automates psychotherapy fidelity workflows and generates actionable supervisory feedback from authentic, long-form clinical transcripts. We evaluate three open-weight models across multiple task decomposition configurations and reasoning strategies, demonstrating that evidence-first reasoning improves fidelity estimation. Furthermore, we establish the framework's external construct validity on an independent randomized controlled trial (RCT), where it reliably distinguishes Cognitive Behavioral Therapy (CBT) from non-CBT sessions across core therapeutic skills. Through a user study that evaluates the generated feedback, mental health experts indicate that the pipeline synthesizes actionable clinical feedback. Ultimately, our work offers a practical, scalable solution toward bridging the community mental health supervision gap.

cs.CL↗

arXiv2026

MontageFlow: Physically Valid High Fidelity EEG Generation

Generative modeling offers a promising solution to the scarcity of labeled clinical electroencephalography (EEG) data under strict privacy constraints. Although recent generative models report substantial improvements in generation fidelity, we show that these gains conceal a categorical failure. EEG is not an arbitrary multichannel signal: each channel records the voltage difference between two scalp electrodes. So, real recordings satisfy exact linear identities among their channels. Current generators invariably violate these identities, yet this has gone unnoticed. We therefore propose MontageFlow, a flow-matching model that enforces these identities by restricting its output to signals that satisfy them. We find that ensuring validity improves fidelity too. Furthermore, to retain the EEG characteristics that oversmoothing washes out, we also condition the model on a physiological state vector encoded from the whole EEG window. For generation, this vector is drawn from a prior fitted in latent space. Across 3 large-scale benchmarks, our model improves TS-FID by 1.6-3.6$\times$ over the closest rival while ensuring validity.

cs.AI↗

arXiv2026

Lapras: Latent Reasoning for Time Series Language Models

Time Series Language Models (TSLMs) offer a promising path toward time series understanding by reasoning over temporal signals and producing natural language answers and explanations. A common approach is Chain-of-Thought (CoT), which generates step-by-step rationales linking relevant signal patterns to final answers. Although these models learn from reference CoT traces during post-training, generating faithful descriptions of input time series at inference remains challenging. Expressing high-dimensional, continuous temporal representations in discrete language tokens may cause the model to neglect task-relevant patterns or describe them inaccurately. Because later reasoning steps build on these descriptions, early errors propagate, leading to incorrect answers with plausible explanations that are inconsistent with the input signal. We propose Lapras (Latent Post-trained Reasoning Across Series), a post-training framework that equips TSLMs with latent reasoning. A model trained with Lapras reasons through a sequence of continuous thoughts in the joint time series-language space, producing text only for the final answer. It learns this through teacher-student self-distillation, where a teacher trained on CoT reference traces reasons explicitly through text. The student aligns its hidden states with the teacher's at the answer stage, transferring the teacher's reasoning ability into its latent computation. We evaluate Lapras across four TSLM backbones on five time series question answering benchmarks. Lapras improves average F1 by up to 10.79% over explicit CoT while generating 23.9x fewer tokens. Lapras's continuous thoughts can also be decoded into readable reasoning traces via standard language decoding, preserving textual explanations. Together, these results highlight Lapras as a promising post-training paradigm for efficient, effective, and interpretable TSLM reasoning.

cs.CL↗

arXiv2026

Universality for the extreme eigenvalues of Laplacian random matrices

We study the eigenvalues of the random Laplacian matrix $D - A$, where $A$ is a Wigner matrix with sub-Gaussian entries and the diagonal matrix $D$ contains the row sums of $A$. Our main results show that the extreme eigenvalues of this model exhibit Poisson statistics; in particular, after the appropriate centering and scaling, the largest eigenvalue converges to the Gumbel distribution as the dimension of the matrix tends to infinity. This confirms, for general sub-Gaussian entries, a phenomenon the authors previously established only in the Gaussian case [Electron. J. Probab. 30 (2025), Paper No. 104], resolving a conjecture raised there. As a corollary, for an Erdős--Rényi random graph, we show the asymptotic fluctuations of the algebraic connectivity (Fiedler value) can be described in terms of the Gumbel distribution.

math.PR↗

arXiv2026

Gumbel Straight Flow: Distilling Autoregressive Models into One-step Flow Maps

We present Gumbel Straight Flow (GSF), a continuous flow map language model that leverages the noise-data coupling of a pretrained autoregressive language (AR) model. We theoretically demonstrate that the coupling between Gumbel noise and one-hot token sequences induced by an autoregressive model yields non-intersecting linear paths connecting the noise to the sequence representations. To further enhance high-quality few-step path sampling, we use a flow map semigroup objective where the tangent (velocity) condition is guided directly by the AR teacher. Across various benchmarks, including pretraining and downstream tasks, GSF can outperform current few-step language generation baselines.

cs.LG↗

arXiv2026

Simplex Diffusion Models

Diffusion models have revolutionized generative modeling for continuous data through the gradual refinement of a belief state. This iterative refinement has not yet carried over to discrete diffusion models, which discard uncertainty at intermediate steps through categorical sampling (information collapse). We propose Simplex Diffusion Models (SDMs), a framework that lifts the diffusion process to the probability simplex to represent beliefs over categories. SDMs admit probability paths with closed-form reverse transitions and can be trained with a simple cross-entropy loss. Contrary to earlier proposals such as Dirichlet Flow Matching which requires integrating an ordinary differential equation, we introduce a DDIM-like sampler with a tunable level of stochasticity. Because SDMs operate on samples on the simplex, they can carry uncertainty across denoising steps, which mitigates information collapse. On OpenWebText, SDMs are competitive with strong Discrete Diffusion baselines, achieving $17.0$ GenPPL at $5.46$ unigram entropy in 64 sampling steps, close to real validation data. Even without Self-Conditioning (SC), SDMs outperform masked and uniform diffusion (with SC or predictor-corrector sampling) on code generation (TinyGSM, $T=0.1$; $49.0\%$ vs. $45.8\%$). Distilled down to 8 steps, SDMs solve $32.1\%$ of GSM8K problems, more than distilled Discrete Diffusion models with 128 steps ($21.4\%$).

cs.LG↗

arXiv2026

Learning Transferable Sensor Models via Language-Informed Pretraining

Multimodal language models have demonstrated strong semantic understanding and reasoning over physiological and behavioral signals captured from diverse healthcare sensors. However, existing sensor-language models can only process a fixed number of sensor channels at a fixed sampling rate, making them difficult to adapt to new or different sensor configurations. This inflexibility prevents models from generalizing across heterogeneous health sensing ecosystems, where data spans high-frequency wearable streams to sparse, day-scale clinical signals. To bridge this gap, we introduce SLIP (Sensor Language-Informed Pretraining), an open-source framework for learning language-aligned representations that generalize across diverse sensor setups. SLIP integrates contrastive alignment with sensor-conditioned captioning, facilitating both discriminative understanding and generative reasoning. By repurposing a pretrained decoder-only language model via cross-attention and introducing a flexible patch embedder, SLIP transfers to new sensor configurations at inference without retraining, regardless of their native sampling rate or input length. Across 11 datasets, SLIP demonstrates superior performance in retrieval, signal captioning, and question answering. It achieves a 77.14% average linear-probing accuracy, a 3.56% improvement over the strongest baseline (SensorLM). Beyond classification, SLIP supports open-vocabulary sensor captioning and question answering without any architectural modifications. Our work offers broad implications for the development of sensor-language models, utilizing cross-modal supervision to ensure more robust generalizability in health sensing applications.

cs.AI↗

arXiv2026

When Do Differentially Private Inputs Protect Graph Shift Operators?

We study the differential privacy (DP) of a graph shift operator (GSO) when an analyst observes the output of a graph filter. In particular, we study the setting in which the input signals to the graph filter are drawn from a differentially private distribution. Unlike approaches that perturb the GSO or the filter output, we use the randomness already present in the inputs to protect the GSO. This yields an equivalent level of privacy protection to that of the perturbation methods without adding noise, and thus a better privacy-utility trade-off. We provide an explicit characterization of the privacy loss and its certificate in terms of the zeros of the graph filter. In doing so, we show that the log-likelihood ratio between the releases of two adjacent topologies is governed by the distances from each zero to the graph frequencies of the two GSOs. Then, by uniformly bounding the log-likelihood ratio over the adjacent topologies, we obtain an explicit $(\varepsilon,δ)$-DP guarantee for Gaussian inputs. We further show, via a Cramér--Rao bound, that the zero placement that limits the privacy loss also raises the floor on the adversary's reconstruction error. Finally, empirical validation is performed on a synthetic network of financial exposures, where the largest position a pair can conceal and the accuracy with which it can be sized are collinear across pairs. Both are set by the graph-frequency content of the pair, and the full network becomes recoverable only as the certified budget grows.

cs.CR↗

arXiv2026

TimeThink: Eliciting Compositional Reasoning in Timeseries Large Language Models

Timeseries multimodal large language models (TS-MLLMs) have recently begun leveraging the reasoning capabilities of large language models (LLMs) for question-answering tasks. However, these models often fail to capture dynamic temporal patterns, providing only implicit reasoning that lacks the underlying explanations critical for high-stakes applications like healthcare. While reinforcement learning (RL)-based timeseries language models aim to address this, they often fall short because they are trained on narrow, in-distribution data and struggle with out-of-distribution compositional questions. To address these challenges, we present TimeThink, a synthetic framework for eliciting compositional timeseries reasoning. Core timeseries primitives (e.g., trend, seasonality) are domain-independent and can be deterministically generated. Guided by this premise, TimeThink first designs a synthetic data generator that produces atomic and composite question-answer pairs, providing objective ground truth with reasoning traces. Building on this framework, TimeThink employs a reinforcement learning with verifiable rewards (RLVR) training strategy that encourages explicit reasoning. Unlike template-reliant methods, this approach enables the model to learn the underlying logic of composition rather than simply imitating traces. Extensive experiments show that TimeThink, trained only on synthetic data, significantly outperforms strong baselines on both synthetic and real-world benchmarks.

cs.AI↗

arXiv2026

BALMS: Benchmarking Agentic LLMs for Longitudinal Mental Health Sensing

Mental health assessment relies on episodic self-report scales, which convert subjective states such as stress into numerical scores but provide only sparse snapshots of wellbeing. Wearable devices offer longitudinal behavioral and physiological signals for continuous, low-burden monitoring. Recent LLM-driven personal-health agents enable natural language queries over wearable signals, but mainly handle short-term, retrieval-based lookups (e.g., highest step count over a week). They do not evaluate whether agents can reason over long-term signals to predict wellbeing scores paired with evidence-grounded rationales. To address this gap, we introduce BALMS, the first systematic benchmark of LLM-based agentic systems for longitudinal mental health sensing. BALMS spans 3 real-world longitudinal datasets, 2 task families (closed-form wellbeing-score prediction and rationale generation auto-graded by an LLM-as-Judge), 3 agentic paradigms evaluated across 5 open- and closed-source LLM backbones. We find that zero-shot agents rarely outperform a simple mean baseline, except with stronger backbones or compact, semantically meaningful features. Chain-of-thought prompting improves reasoning-oriented backbones, but does not guarantee temporal grounding or numerical correctness. Together with more analysis on efficiency and temporal scaling, BALMS highlights the need for longitudinal mental health agents that selectively retrieve history, ground temporal evidence, and reason over interpretable behavioral features.

cs.CL↗

arXiv2026

ReliaGate: Reliability Routing for Low-Stakes Wearable Stress Prediction

We study when a wearable stress system should surface a prediction rather than change it. In low-stakes reflection and summary settings, aggregate accuracy is insufficient because withholding can reduce error while leaving some people with little or no information. We formulate fixed-label reliability routing: after a locked classifier emits a protocol-defined stress/non-stress label, a post-hoc gate surfaces that unchanged label or withholds it as unavailable. ReliaGate assembles established confidence, signal-quality/trust, agreement, train-standardized atypicality, and train-fitted geometry cues into a post-hoc correctness score. We evaluate four wearable datasets using subject-disjoint folds, validation-selected routing, paired held-out-subject intervals, and pooled and per-subject analyses. WESAD point estimates favored ReliaGate, UBFC-Phys primary coverage/risk intervals favored ReliaGate, and E4 checks were mixed. ReliaGate provides an operational framework for studying surfaced-label error, output availability, and accepted-output distribution across subjects, without revising labels or providing clinical or finite-sample risk guarantees.

cs.LG↗

arXiv2026

DiffusionGemma Technical Report

We introduce DiffusionGemma, an experimental open-weight language model that uses discrete diffusion to generate text at exceptionally high speed. Rather than decoding one token at a time, DiffusionGemma iteratively refines blocks of 256 tokens in parallel, avoiding the sequential decoding bottleneck of conventional autoregressive (AR) large language models. Instead of training from scratch, we obtain DiffusionGemma by fine-tuning the mixture-of-experts Gemma 4 model with 3.8B activated and 25.2B total parameters. Our compute-efficient two-stage training pipeline uses fewer than 10% of the starting AR model's total training token budget. The first stage uses supervised fine-tuning to teach bidirectional denoising, while the second stage combines reinforcement learning with sampler distillation to jointly improve generation quality and inference efficiency. DiffusionGemma establishes a new Pareto frontier for the trade-off between generation speed and model capability. Averaged across our full evaluation suite, it generates around 20 tokens per forward pass and achieves roughly 1,500 output tokens per second on a single NVIDIA H100 GPU, which is substantially faster than AR models even with state-of-the-art speculative decoding. DiffusionGemma also retains the starting model's support for thinking mode, multimodal inputs, and long contexts. Despite diffusion fine-tuning, it remains capable of AR generation with only minor performance degradation, suggesting a path toward hybrid diffusion-AR decoding.

cs.CL↗

arXiv2026

A Self-Supervised Framework for Space Object Behaviour Characterisation

Foundation Models, which leverage large neural networks pre-trained on unlabelled data before fine-tuning for specific tasks, are increasingly being applied to specialised domains. Recent examples include ClimaX for climate and Clay for satellite Earth observation, but a Foundation Model for Space Object Behavioural Analysis has not yet been developed. As orbital populations grow, automated methods for characterising space object behaviour are crucial for space safety. Here, we present a self-supervised framework for space object behavioural analysis, representing a first step towards a Foundation Model for SOBA. The backbone is a Perceiver-Variational Autoencoder (VAE) architecture, pre-trained with self-supervised reconstruction and masked reconstruction on ~227,000 light curves from the MMT-9 observatory. The VAE enables anomaly detection, motion prediction, and synthetic light curve generation. We fine-tuned the model using two independent light curve simulators (CASSANDRA and GRIAL), with CAD models of boxwing, Sentinel-3, SMOS, and Starlink platforms. Our pre-trained model achieved a reconstruction mean squared error of 0.0012, identifying potentially anomalous light curves through reconstruction difficulty. After fine-tuning, the model scored 85% and 82% accuracy, with 0.92 and 0.95 ROC AUC scores in anomaly detection and motion mode prediction (e.g., sun-pointing, spin, tumbling). Analysis of high-confidence predictions on real data revealed distinct patterns including characteristic object profiles and satellite glinting. Our work demonstrates how self-supervised learning can simultaneously enable anomaly detection, motion prediction, and synthetic data generation from rich pre-trained representations, supporting space safety and sustainability through automated monitoring and simulation.

cs.LG↗

arXiv2026

When Does Quality-Aware Multimodal Fusion Matter? A Leakage-Safe Diagnostic for Decision-Level Dependence

Many multimodal systems estimate the reliability of each modality and weight their contributions to the final prediction. However, it remains unclear whether these scores influence model decisions or merely correlate with performance. We propose a simple diagnostic to test whether reliability information is used during inference. After training, the model and inputs are fixed while reliability scores are permuted across test examples. If predictions depend on these scores, performance should degrade. Experiments on StressID for stress recognition and CMU-MOSEI for sentiment analysis show that permuting reliability scores leaves performance unchanged despite substantial potential gains from selecting the best modality per example. In positive controls where reliability signals identify the correct modality, the same frozen fusion rules yield significant improvements, indicating that reliability signals influence fused decisions only when they reliably predict unimodal correctness.

cs.LG↗

arXiv2026

Reconstruction Limits for Repeated Differentially Private Aggregates: A Cramer-Rao Perspective on Query Geometry

Repeated differentially private (DP) releases are often evaluated by transcript length or cumulative privacy accounting. We show that these quantities do not by themselves determine local reconstruction risk. For Gaussian-calibrated repeated statistical queries, the key object is the nuisance-profiled Fisher geometry of the release sequence: repetition helps only when new releases create identifiable directions after nuisance variables are removed. Thus, release geometry determines what can be locally identified, while the privacy accountant determines how precisely those directions can be estimated. We develop this principle in two settings. For labeled-target reconstruction with fixed-background IN/OUT averages, repeated copies collapse to a single target-versus-background contrast. The best linear unbiased estimator attains the Cramer-Rao bound, and additional copies provide only averaging gain; under Basic Composition this gain is dominated by the $Θ(L^2\log L)$ noise penalty, whereas zCDP/RDP-style Gaussian accounting makes the risk order-flat. For static permutation-invariant releases, labels remain unidentified, but feature diversity can make the sorted participating multiset locally identifiable. For polynomial moments and smooth thresholds, the useful number of releases is governed by the balance between newly exposed eigendirections and accountant-induced noise growth. These results provide a local, mechanism-specific benchmark for value leakage in repeated private sensing and analytics.

cs.IT↗

arXiv2026

Graph Transfer Learning via Shared Latent Geometry: Theory and Applications

Inference and control in engineered physical systems pay a heavy physics cost at deployment: state estimators, inverse-problem solvers, model-predictive controllers, schedulers, and observers are often not closed-form and must re-solve a numerical optimization per instance, with the operator re-supplied each time. Physics-informed learning moves this cost to training, but uses a single encoder pathway whose latent geometry de-learns under fine-tuning and admits no quantitative transfer guarantee. We propose an asymmetric two-pathway architecture that resolves both issues. A teacher encoder consumes privileged dense states from a high-fidelity simulator and represents the system through operator-polynomial features stable under spectral perturbation; a student encoder learns the same latent geometry from sparse field data and operator descriptors. At deployment the teacher is discarded, and the frozen student runs in a single forward pass with a transfer certificate. The design connects to privileged-information learning, knowledge distillation, and cross-modal distillation, but targets cross-instance transfer rather than fixed-instance prediction: topology and operator may change, while the latent task does not. We establish sufficient and near-necessary transfer conditions via Wasserstein proximity between latent laws, yielding a zero-shot error bound, and develop a finite-sample certification protocol with active expansion when coverage is incomplete. The framework applies wherever a system admits an operator with reportable spectrum. On power-system estimation, it achieves zero-shot transfer to 100 unseen topologies, a 95% certificate pass rate, accuracy competitive with topology-aware Newton--Raphson, and sub-millisecond inference. These results suggest asymmetric pathways plus operator-anchored latent geometry provide a foundation for certified zero-shot inference and control.

cs.LG↗

arXiv2026

Pólya--Schur problems and free probability

In this work, we build a bridge between the Pólya--Schur program and Voiculescu's free probability theory. A cornerstone of the former is the Pólya--Benz Theorem, classifying a central family of real-root preserving operators on the space of polynomials, as those given by $f(\partial_z)$ for a Laguerre--Pólya function $f$ and the derivative operator $\partial_{z}$. We prove that any free (additive) infinitely divisible distribution can be attained as the weak limit of root distributions of Appell polynomials $f_n(\partial_z)z^n$ as $n\to\infty$, for a suitably chosen sequence $f_n$ of Laguerre--Pólya functions. Such questions on the (global) limiting distributions of real rooted polynomials belong to the active research area of finite free probability. In contrast to its standard tools, our approach allows for non-compactly supported limiting distributions, (barely) complex rooted polynomials and even provides the full microscopic description of the roots. Moreover, we extend our results to differential operators generating free multiplicative infinitely divisible distributions, to the rectangular free convolution, and to $f_n(\partial_z)p_n$ for real rooted polynomials $p_n$, implying a generalization of the recent connections between the heat flow and free Brownian motion to any free Lévy process. As corollaries, we identify free stable distributions by choosing $f_n$ to be a fixed rescaled Laguerre--Pólya function, and we prove various convergence results on the zero distributions of Jensen polynomials, e.g. the limiting root distribution of Jensen polynomial of the Riemann $Ξ$-function is given by the Cauchy distribution.

math.PR↗

arXiv2026

Universality for roots of derivatives of entire functions via finite free probability

A universality conjecture of Farmer and Rhoades [Trans. Amer. Math. Soc., 357(9):3789--3811, 2005] and Farmer [Adv. Math., 411:Paper No. 108781, 14, 2022] asserts that, under some natural conditions, the roots of an entire function should become perfectly spaced in the limit of repeated differentiation. This conjecture is known as Cosine Universality. We establish this conjecture for a class of even entire functions with only real roots which are real on the real line. Along the way, we establish a number of additional universality results for Jensen polynomials of entire functions, including the Hermite Universality conjecture of Farmer [Adv. Math., 411:Paper No. 108781, 14, 2022]. Our proofs are based on finite free probability theory. We establish finite free probability analogs of the law of large numbers, central limit theorem, and Poisson limit theorem for sequences of deterministic polynomials under repeated differentiation, under optimal moment conditions, which are of independent interest.

math.PR↗