arXiv subjects

Andrew Campbell

Publications and source records attributed to Andrew Campbell.

At least 37 records · Page 2Linked to original sources

arXiv2026

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↗

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 $(\varepsilon,δ)$-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

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

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

Free infinite divisibility, fractional convolution powers, and Appell polynomials

Initiated by a result of Gorin and Marcus [Int. Math. Res. Not., (3):883--913, 2020] and an observation of Steinerberger [Proc. Amer. Math. Soc., 147(11):4733--4744, 2019], there has been a recent growing body of literature connecting repeated differentiation of polynomials to free additive convolution semigroups in free probability. Roughly, this connection states that in the large degree limit the empirical measure of the roots after many derivatives is, up to a rescaling, the original empirical measure of the roots raised to a free additive convolution power. If the original real roots satisfy some bounds and the number of derivatives is such that the remaining degree is fixed, then these high derivatives converge to the Hermite polynomials. In the context of convolution semigroups and finite free probability these results have a natural interpretation as a central limit theorem for repeated differentiation. We consider the case when these root bounds are removed and identify the potential limits of repeated differentiation as the real rooted Appell sequences. We prove that a sequence of polynomials is in the domain of attraction of an Appell sequence exactly when the empirical measures of the roots are, up to a rescaling, in the domain of attraction of a free infinitely divisible distribution naturally associated to the Appell sequence. We additionally extend these notions of infinite divisibility and fractional convolution semigroups to rectangular finite free probability. Our approach is based on the finite free R-transform of the polynomials, providing a step towards an analytic theory of finite free probability. These transforms provide a clear connection between Appell polynomials and free infinitely divisible distributions, where the finite free R-transform of a real rooted Appell polynomial is a truncated version of the R-transform of an infinitely divisible distribution.

math.PR↗

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 $(ε,δ)$-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 $(ε,δ)$-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 $(ε,δ)$-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 ($ε\in[2, 5]$). 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

On the spectral edge of non-Hermitian random matrices

For general non-Hermitian random matrices $X$ and deterministic deformation matrices $A$, we prove that the local eigenvalue statistics of $A+X$ close to the typical edge points of its spectrum are universal. Furthermore, we show that under natural assumptions on $A$ the spectrum of $A+X$ does not have outliers at a distance larger than the natural fluctuation scale of the eigenvalues. As a consequence, the number of eigenvalues in each component of $\mathrm{Spec}(A+X)$ is deterministic.

math.PR↗

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↗

arXiv2025

Think While You Generate: Discrete Diffusion with Planned Denoising

Discrete diffusion has achieved state-of-the-art performance, outperforming or approaching autoregressive models on standard benchmarks. In this work, we introduce Discrete Diffusion with Planned Denoising (DDPD), a novel framework that separates the generation process into two models: a planner and a denoiser. At inference time, the planner selects which positions to denoise next by identifying the most corrupted positions in need of denoising, including both initially corrupted and those requiring additional refinement. This plan-and-denoise approach enables more efficient reconstruction during generation by iteratively identifying and denoising corruptions in the optimal order. DDPD outperforms traditional denoiser-only mask diffusion methods, achieving superior results on language modeling benchmarks such as text8, OpenWebText, and token-based image generation on ImageNet $256 \times 256$. Notably, in language modeling, DDPD significantly reduces the performance gap between diffusion-based and autoregressive methods in terms of generative perplexity. Code is available at https://github.com/liusulin/DDPD.

cs.LG↗

arXiv2024

Score-Optimal Diffusion Schedules

Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data distribution by incrementally injecting noise into the data. To numerically simulate the sampling process, a discretisation schedule from the reference back towards clean data must be chosen. An appropriate discretisation schedule is crucial to obtain high quality samples. However, beyond hand crafted heuristics, a general method for choosing this schedule remains elusive. This paper presents a novel algorithm for adaptively selecting an optimal discretisation schedule with respect to a cost that we derive. Our cost measures the work done by the simulation procedure to transport samples from one point in the diffusion path to the next. Our method does not require hyperparameter tuning and adapts to the dynamics and geometry of the diffusion path. Our algorithm only involves the evaluation of the estimated Stein score, making it scalable to existing pre-trained models at inference time and online during training. We find that our learned schedule recovers performant schedules previously only discovered through manual search and obtains competitive FID scores on image datasets.

stat.ML↗

arXiv2024

Extreme eigenvalues of Laplacian random matrices with Gaussian entries

A Laplacian matrix is a real symmetric matrix whose row and column sums are zero. We investigate the limiting distribution of the largest eigenvalues of a Laplacian random matrix with Gaussian entries. Unlike many classical matrix ensembles, this random matrix model contains dependent entries. Our main results show that the extreme eigenvalues of this model exhibit Poisson statistics. In particular, after properly shifting and scaling, we show that the largest eigenvalue converges to the Gumbel distribution as the dimension of the matrix tends to infinity. While the largest diagonal entry is also shown to have Gumbel fluctuations, there is a rather surprising difference between its deterministic centering term and the centering term required for the largest eigenvalues.

math.PR↗

arXiv2024

Improved motif-scaffolding with SE(3) flow matching

Protein design often begins with the knowledge of a desired function from a motif which motif-scaffolding aims to construct a functional protein around. Recently, generative models have achieved breakthrough success in designing scaffolds for a range of motifs. However, generated scaffolds tend to lack structural diversity, which can hinder success in wet-lab validation. In this work, we extend FrameFlow, an SE(3) flow matching model for protein backbone generation, to perform motif-scaffolding with two complementary approaches. The first is motif amortization, in which FrameFlow is trained with the motif as input using a data augmentation strategy. The second is motif guidance, which performs scaffolding using an estimate of the conditional score from FrameFlow without additional training. On a benchmark of 24 biologically meaningful motifs, we show our method achieves 2.5 times more designable and unique motif-scaffolds compared to state-of-the-art. Code: https://github.com/microsoft/protein-frame-flow

q-bio.QM↗

arXiv2024

Compressed and Sparse Models for Non-Convex Decentralized Learning

Recent research highlights frequent model communication as a significant bottleneck to the efficiency of decentralized machine learning (ML), especially for large-scale and over-parameterized neural networks (NNs). To address this, we present Malcom-PSGD, a novel decentralized ML algorithm that combines gradient compression techniques with model sparsification. We promote model sparsity by adding $\ell_1$ regularization to the objective and present a decentralized proximal SGD method for training. Our approach employs vector source coding and dithering-based quantization for the compressed gradient communication of sparsified models. Our analysis demonstrates that Malcom-PSGD achieves a convergence rate of $\mathcal{O}(1/\sqrt{t})$ with respect to the iterations $t$, assuming a constant consensus and learning rate. This result is supported by our proof for the convergence of non-convex compressed Proximal SGD methods. Additionally, we conduct a bit analysis, providing a closed-form expression for the communication costs associated with Malcom-PSGD. Numerical results verify our theoretical findings and demonstrate that our method reduces communication costs by approximately $75\%$ when compared to the state-of-the-art.

cs.LG↗

arXiv2024

Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design

Combining discrete and continuous data is an important capability for generative models. We present Discrete Flow Models (DFMs), a new flow-based model of discrete data that provides the missing link in enabling flow-based generative models to be applied to multimodal continuous and discrete data problems. Our key insight is that the discrete equivalent of continuous space flow matching can be realized using Continuous Time Markov Chains. DFMs benefit from a simple derivation that includes discrete diffusion models as a specific instance while allowing improved performance over existing diffusion-based approaches. We utilize our DFMs method to build a multimodal flow-based modeling framework. We apply this capability to the task of protein co-design, wherein we learn a model for jointly generating protein structure and sequence. Our approach achieves state-of-the-art co-design performance while allowing the same multimodal model to be used for flexible generation of the sequence or structure.

stat.ML↗

arXiv2024

The fractional free convolution of $R$-diagonal elements and random polynomials under repeated differentiation

We extend the free convolution of Brown measures of $R$-diagonal elements introduced by Kösters and Tikhomirov [Probab. Math. Statist. 38 (2018), no. 2, 359--384] to fractional powers. We then show how this fractional free convolution arises naturally when studying the roots of random polynomials with independent coefficients under repeated differentiation. When the proportion of derivatives to the degree approaches one, we establish central limit theorem-type behavior and discuss stable distributions.

math.PR↗

arXiv2023

Hyperspectral Lightcurve Inversion for Attitude Determination

Spectral lightcurves consisting of time series single-pixel spectral measurements of spacecraft are used to infer the spacecraft's attitude and rotation. Two methods are used. One based on numerical optimisation of a regularised least squares cost function, and another based on machine learning with a neural network model. The aim is to work with minimal information, thus no prior is available on the attitude nor on the inertia tensor. The theoretical and practical aspects of this task are investigated, and the methodology is tested on synthetic data. Results are shown based on synthetic data.

eess.SP↗