arXiv subjects

Andrew Campbell

Publications and source records attributed to Andrew Campbell.

At least 19 recordsLinked to original sources

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

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 $\Theta(L^2\log L)$ 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

P\'olya--Schur problems and free probability

In this work, we build a bridge between the P\'olya--Schur program and Voiculescu's free probability theory. A cornerstone of the former is the P\'olya--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--P\'olya 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--P\'olya 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 L\'evy process. As corollaries, we identify free stable distributions by choosing $f_n$ to be a fixed rescaled Laguerre--P\'olya 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 $\Xi$-function is given by the Cauchy distribution.

math.PR↗

arXiv2026

Toward World Modeling of Physiological Signals with Chaos-Theoretic Balancing and Latent Dynamics

Physiological time series signals reflect complex, multi-scale dynamical processes of the human body. Existing modeling studies focus on static tasks such as classification, event forecasting, or short-horizon next step prediction, while long-horizon signal-level forecasting and predictive nature of physiological signals remain underexplored. We introduce NormWear-2, a world model that encodes both multivariate physiological signals and clinical intervention variables into a shared latent space and models their joint temporal evolution as a dynamical system. Our approach combines inference from prior pre-trained knowledge (intuition) with instant non-parametric latent state transition adaptation (insight), enabling coherent forecasting across multiple temporal scales, conditioned on heterogeneous clinical interventions. During the pretraining phase, we find that chaos-theoretic balancing of dynamical regime diversity yields more robust representations, with a smaller balanced corpus outperforming one twice its size and capturing bifurcation regimes. We evaluate the world model performance across diverse real-world physiological datasets spanning heterogeneous temporal resolutions and intervention regimes, covering daily life, point-of-care, and clinical settings, including fitness planning, hemodialysis, diabetes management, and surgical monitoring. These evaluation datasets comprise records from 8,026 subjects, spanning study durations from 3.2 hours for high-resolution signal data to 2.3 years for longitudinal clinical biomarker tracking. NormWear-2 achieves the best overall forecasting performance across time, frequency, and latent representation domains, with significant improvements over state-of-the-art time series foundation models, while maintaining competitive downstream representation quality, providing a step toward general-purpose world models for physiological signals.

cs.LG↗

arXiv2026

Differentially Private Synthetic Voltage Phasor Release for Distribution Grids

Training machine learning models, including Grid Foundation Models (GFMs), requires large volumes of realistic grid data, yet substantial privacy concerns discourage utilities and data providers from sharing load profiles and network parameters. We study the release of synthetic voltage phasor trajectories for distribution grids under differential privacy (DP). We first fit a DP generative model to historical customer loads, then propagate synthetic load trajectories through the AC power flow equations on the true admittance matrix to produce voltage phasors. The central question is whether the randomness already present in the DP synthetic loads is sufficient to protect not only the loads, but also the network topology encoded by the bus admittance matrix. We show that it is. The implication is that a corpus of voltage trajectories can be constructed from DP synthetic loads while preserving the statistics of AC power flow, which is critical for training GFMs. This preservation of the power flow statistics stands in contrast to approaches that perturb the admittance matrix directly or inject noise into the voltage outputs, both of which distort the underlying physics. Concretely, we derive $(\varepsilon,\delta)$-DP guarantees for the released voltage trajectories with respect to the admittance matrix, meaning privacy of the network parameters is obtained without any additional noise mechanism. Our bound depends on the adjacency assumption, the Jacobian of the AC power flow, and the covariance of the synthetic DP-loads. Finally, we present a synthetic voltage generation procedure and an empirical evaluation against Gaussian output-perturbation baselines, demonstrating that our approach provides a clear advantage for enabling GFM training.

eess.SY↗

arXiv2026

Learning Transferable Sensor Models via Language-Informed Pretraining

Modern sensing systems generate large volumes of unlabeled multivariate time-series data. This abundance of unlabeled data makes self-supervised learning (SSL) a natural approach for learning transferable representations. However, most existing approaches are optimized for reconstruction or forecasting objectives and often fail to capture the semantic structure required for downstream classification and reasoning tasks. While recent sensor-language alignment methods improve semantic generalization through captioning and zero-shot transfer, they are limited to fixed sensor configurations, such as predefined channel sets, signal lengths, or temporal resolutions, which hinders cross-domain applicability. To address these gaps, we introduce \textbf{SLIP} (\textbf{S}ensor \textbf{L}anguage-\textbf{I}nformed \textbf{P}retraining), 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 an elegant, flexible patch-embedder, SLIP supports different temporal resolutions and variable-length input at inference time without additional retraining. Across 11 datasets, SLIP demonstrates superior performance in zero-shot transfer, signal captioning, and question answering. It achieves a 77.14% average linear-probing accuracy, a 5.93% relative improvement over strong baselines, and reaches 64.83% accuracy in sensor-based question answering.

cs.AI↗

arXiv2025

LENS: LLM-Enabled Narrative Synthesis for Mental Health by Aligning Multimodal Sensing with Language Models

Multimodal health sensing offers rich behavioral signals for assessing mental health, yet translating these numerical time-series measurements into natural language remains challenging. Current LLMs cannot natively ingest long-duration sensor streams, and paired sensor-text datasets are scarce. To address these challenges, we introduce LENS, a framework that aligns multimodal sensing data with language models to generate clinically grounded mental-health narratives. LENS first constructs a large-scale dataset by transforming Ecological Momentary Assessment (EMA) responses related to depression and anxiety symptoms into natural-language descriptions, yielding over 100,000 sensor-text QA pairs from 258 participants. To enable native time-series integration, we train a patch-level encoder that projects raw sensor signals directly into an LLM's representation space. Our results show that LENS outperforms strong baselines on standard NLP metrics and task-specific measures of symptom-severity accuracy. A user study with 13 mental-health professionals further indicates that LENS-produced narratives are comprehensive and clinically meaningful. Ultimately, our approach advances LLMs as interfaces for health sensing, providing a scalable path toward models that can reason over raw behavioral signals and support downstream clinical decision-making.

cs.CL↗

arXiv2025

MotionTeller: Multi-modal Integration of Wearable Time-Series with LLMs for Health and Behavioral Understanding

As wearable sensing becomes increasingly pervasive, a key challenge remains: how can we generate natural language summaries from raw physiological signals such as actigraphy - minute-level movement data collected via accelerometers? In this work, we introduce MotionTeller, a generative framework that natively integrates minute-level wearable activity data with large language models (LLMs). MotionTeller combines a pretrained actigraphy encoder with a lightweight projection module that maps behavioral embeddings into the token space of a frozen decoder-only LLM, enabling free-text, autoregressive generation of daily behavioral summaries. We construct a novel dataset of 54383 (actigraphy, text) pairs derived from real-world NHANES recordings, and train the model using cross-entropy loss with supervision only on the language tokens. MotionTeller achieves high semantic fidelity (BERTScore-F1 = 0.924) and lexical accuracy (ROUGE-1 = 0.722), outperforming prompt-based baselines by 7 percent in ROUGE-1. The average training loss converges to 0.38 by epoch 15, indicating stable optimization. Qualitative analysis confirms that MotionTeller captures circadian structure and behavioral transitions, while PCA plots reveal enhanced cluster alignment in embedding space post-training. Together, these results position MotionTeller as a scalable, interpretable system for transforming wearable sensor data into fluent, human-centered descriptions, introducing new pathways for behavioral monitoring, clinical review, and personalized health interventions.

cs.LG↗

arXiv2025

Self-Speculative Masked Diffusions

We present self-speculative masked diffusions, a new class of masked diffusion generative models for discrete data that require significantly fewer function evaluations to generate samples. Standard masked diffusion models predict factorized logits over currently masked positions. A number of masked positions are then sampled, however, the factorization approximation means that sampling too many positions in one go leads to poor sample quality. As a result, many simulation steps and therefore neural network function evaluations are required to generate high-quality data. We reduce the computational burden by generating non-factorized predictions over masked positions. This is achieved by modifying the final transformer attention mask from non-causal to causal, enabling draft token generation and parallel validation via a novel, model-integrated speculative sampling mechanism. This results in a non-factorized predictive distribution over masked positions in a single forward pass. We apply our method to GPT2 scale text modelling and protein sequence generation, finding that we can achieve a ~2x reduction in the required number of network forward passes relative to standard masked diffusion models.

stat.ML↗

arXiv2025

Differential Privacy of Network Parameters from a System Identification Perspective

This paper addresses the problem of protecting network information from privacy system identification (SI) attacks when sharing cyber-physical system simulations. We model analyst observations of networked states as time-series outputs of a graph filter driven by differentially private (DP) nodal excitations, with the analyst aiming to infer the underlying graph shift operator (GSO). Unlike traditional SI, which estimates system parameters, we study the inverse problem: what assumptions prevent adversaries from identifying the GSO while preserving utility for legitimate analysis. We show that applying DP mechanisms to inputs provides formal privacy guarantees for the GSO, linking the $(\epsilon,\delta)$-DP bound to the spectral properties of the graph filter and noise covariance. More precisely, for DP Gaussian signals, the spectral characteristics of both the filter and noise covariance determine the privacy bound, with smooth filters and low-condition-number covariance yielding greater privacy.

cs.CR↗

arXiv2025

Decentralized Differentially Private Power Method

We propose a novel Decentralized Differentially Private Power Method (D-DP-PM) for performing Principal Component Analysis (PCA) in networked multi-agent settings. Unlike conventional decentralized PCA approaches where each agent accesses the full n-dimensional sample space, we address the challenging scenario where each agent observes only a subset of dimensions through row-wise data partitioning. Our method ensures $(\epsilon,\delta)$-Differential Privacy (DP) while enabling collaborative estimation of global eigenvectors across the network without requiring a central aggregator. We achieve this by having agents share only local embeddings of the current eigenvector iterate, leveraging both the inherent privacy from random initialization and carefully calibrated Gaussian noise additions. We prove that our algorithm satisfies the prescribed $(\epsilon,\delta)$-DP guarantee and establish convergence rates that explicitly characterize the impact of the network topology. Our theoretical analysis, based on linear dynamics and high-dimensional probability theory, provides tight bounds on both privacy and utility. Experiments on real-world datasets demonstrate that D-DP-PM achieves superior privacy-utility tradeoffs compared to naive local DP approaches, with particularly strong performance in moderate privacy regimes ($\epsilon\in[2, 5]$). The method converges rapidly, allowing practitioners to trade iterations for enhanced privacy while maintaining competitive utility.

cs.LG↗

arXiv2025

Critical points of random polynomials and finite free cumulants

A result of Hoskins and Steinerberger [Int. Math. Res. Not., (13):9784-9809, 2022] states that repeatedly differentiating a random polynomials with independent and identically distributed mean zero and variance one roots will result, after an appropriate rescaling, in a Hermite polynomial. We use the theory of finite free probability to extend this result in two natural directions: (1) We prove central limit theorems for the fluctuations around these deterministic limits for the polynomials and their roots. (2) We consider a generalized version of the Hoskins and Steinerberger result by removing the finite second moment assumption from the roots. In this case the Hermite polynomials are replaced by a random Appell sequence conveniently described through finite free probability and an infinitely divisible distribution. We use finite free cumulants to provide compact proofs of our main results with little prerequisite knowledge of free probability required.

math.PR↗

arXiv2025

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↗

arXiv2025

Time2Lang: Bridging Time-Series Foundation Models and Large Language Models for Health Sensing Beyond Prompting

Large language models (LLMs) show promise for health applications when combined with behavioral sensing data. Traditional approaches convert sensor data into text prompts, but this process is prone to errors, computationally expensive, and requires domain expertise. These challenges are particularly acute when processing extended time series data. While time series foundation models (TFMs) have recently emerged as powerful tools for learning representations from temporal data, bridging TFMs and LLMs remains challenging. Here, we present Time2Lang, a framework that directly maps TFM outputs to LLM representations without intermediate text conversion. Our approach first trains on synthetic data using periodicity prediction as a pretext task, followed by evaluation on mental health classification tasks. We validate Time2Lang on two longitudinal wearable and mobile sensing datasets: daily depression prediction using step count data (17,251 days from 256 participants) and flourishing classification based on conversation duration (46 participants over 10 weeks). Time2Lang maintains near constant inference times regardless of input length, unlike traditional prompting methods. The generated embeddings preserve essential time-series characteristics such as auto-correlation. Our results demonstrate that TFMs and LLMs can be effectively integrated while minimizing information loss and enabling performance transfer across these distinct modeling paradigms. To our knowledge, we are the first to integrate a TFM and an LLM for health, thus establishing a foundation for future research combining general-purpose large models for complex healthcare tasks.

cs.LG↗