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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., Comment: 30 pages, 1 figure

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 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.

Mental health concerns are prevalent among college students, highlighting the need for effective interventions that promote self-awareness and holistic well-being. MindScape pioneers a novel approach to AI-powered journaling by integrating passively collected behavioral patterns such as conversational engagement, sleep, and location with Large Language Models (LLMs). This integration creates a highly personalized and context-aware journaling experience, enhancing self-awareness and well-being by embedding behavioral intelligence into AI. We present an 8-week exploratory study with 20 college students, demonstrating the MindScape app's efficacy in enhancing positive affect (7%), reducing negative affect (11%), loneliness (6%), and anxiety and depression, with a significant week-over-week decrease in PHQ-4 scores (-0.25 coefficient), alongside improvements in mindfulness (7%) and self-reflection (6%). The study highlights the advantages of contextual AI journaling, with participants particularly appreciating the tailored prompts and insights provided by the MindScape app. Our analysis also includes a comparison of responses to AI-driven contextual versus generic prompts, participant feedback insights, and proposed strategies for leveraging contextual AI journaling to improve well-being on college campuses. By showcasing the potential of contextual AI journaling to support mental health, we provide a foundation for further investigation into the effects of contextual AI journaling on mental health and well-being., Comment: arXiv admin note: text overlap with arXiv:2404.00487

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., Comment: A gap in the proof of Eq. (3.15) is fixed in the new pages 44-47

MindScape aims to study the benefits of integrating time series behavioral patterns (e.g., conversational engagement, sleep, location) with Large Language Models (LLMs) to create a new form of contextual AI journaling, promoting self-reflection and well-being. We argue that integrating behavioral sensing in LLMs will likely lead to a new frontier in AI. In this Late-Breaking Work paper, we discuss the MindScape contextual journal App design that uses LLMs and behavioral sensing to generate contextual and personalized journaling prompts crafted to encourage self-reflection and emotional development. We also discuss the MindScape study of college students based on a preliminary user study and our upcoming study to assess the effectiveness of contextual AI journaling in promoting better well-being on college campuses. MindScape represents a new application class that embeds behavioral intelligence in AI.

MoodCapture presents a novel approach that assesses depression based on images automatically captured from the front-facing camera of smartphones as people go about their daily lives. We collect over 125,000 photos in the wild from N=177 participants diagnosed with major depressive disorder for 90 days. Images are captured naturalistically while participants respond to the PHQ-8 depression survey question: \textit{``I have felt down, depressed, or hopeless''}. Our analysis explores important image attributes, such as angle, dominant colors, location, objects, and lighting. We show that a random forest trained with face landmarks can classify samples as depressed or non-depressed and predict raw PHQ-8 scores effectively. Our post-hoc analysis provides several insights through an ablation study, feature importance analysis, and bias assessment. Importantly, we evaluate user concerns about using MoodCapture to detect depression based on sharing photos, providing critical insights into privacy concerns that inform the future design of in-the-wild image-based mental health assessment tools.

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., Comment: 60 pages, 11 figures, 6 tables; ICML 2024

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, Comment: Preprint. Code: https://github.com/ microsoft/frame-flow

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., Comment: 20 pages, 14 figures Accepted for presentation at SciTech 2024 in Orlando, Florida, USA

Social isolation is a common problem faced by individuals with serious mental illness (SMI), and current intervention approaches have limited effectiveness. This paper presents a blended intervention approach, called mobile Social Interaction Therapy by Exposure (mSITE), to address social isolation in individuals with serious mental illness. The approach combines brief in-person cognitive-behavioral therapy (CBT) with context-triggered mobile CBT interventions that are personalized using mobile sensing data. Our approach targets social behavior and is the first context-aware intervention for improving social outcomes in serious mental illness.

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.

We present FrameFlow, a method for fast protein backbone generation using SE(3) flow matching. Specifically, we adapt FrameDiff, a state-of-the-art diffusion model, to the flow-matching generative modeling paradigm. We show how flow matching can be applied on SE(3) and propose modifications during training to effectively learn the vector field. Compared to FrameDiff, FrameFlow requires five times fewer sampling timesteps while achieving two fold better designability. The ability to generate high quality protein samples at a fraction of the cost of previous methods paves the way towards more efficient generative models in de novo protein design., Comment: Preprint

This paper presents a data processing pipeline designed to extract information from the hyperspectral signature of unknown space objects. The methodology proposed in this paper determines the material composition of space objects from single pixel images. Two techniques are used for material identification and classification: one based on machine learning and the other based on a least square match with a library of known spectra. From this information, a supervised machine learning algorithm is used to classify the object into one of several categories based on the detection of materials on the object. The behaviour of the material classification methods is investigated under non-ideal circumstances, to determine the effect of weathered materials, and the behaviour when the training library is missing a material that is present in the object being observed. Finally the paper will present some preliminary results on the identification and classification of space objects., Comment: 30 pages, 24 figures

We extend the free convolution of Brown measures of $R$-diagonal elements introduced by K\"{o}sters 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., Comment: 35 pages, 2 figures. Corrections and reorganized presentation. Final version

Rare life events significantly impact mental health, and their detection in behavioral studies is a crucial step towards health-based interventions. We envision that mobile sensing data can be used to detect these anomalies. However, the human-centered nature of the problem, combined with the infrequency and uniqueness of these events makes it challenging for unsupervised machine learning methods. In this paper, we first investigate granger-causality between life events and human behavior using sensing data. Next, we propose a multi-task framework with an unsupervised autoencoder to capture irregular behavior, and an auxiliary sequence predictor that identifies transitions in workplace performance to contextualize events. We perform experiments using data from a mobile sensing study comprising N=126 information workers from multiple industries, spanning 10106 days with 198 rare events (<2%). Through personalized inference, we detect the exact day of a rare event with an F1 of 0.34, demonstrating that our method outperforms several baselines. Finally, we discuss the implications of our work from the context of real-world deployment., Comment: 15 pages, 4 figures, CHIL 2023 (Accepted)

We propose a new class of generative models that naturally handle data of varying dimensionality by jointly modeling the state and dimension of each datapoint. The generative process is formulated as a jump diffusion process that makes jumps between different dimensional spaces. We first define a dimension destroying forward noising process, before deriving the dimension creating time-reversed generative process along with a novel evidence lower bound training objective for learning to approximate it. Simulating our learned approximation to the time-reversed generative process then provides an effective way of sampling data of varying dimensionality by jointly generating state values and dimensions. We demonstrate our approach on molecular and video datasets of varying dimensionality, reporting better compatibility with test-time diffusion guidance imputation tasks and improved interpolation capabilities versus fixed dimensional models that generate state values and dimensions separately., Comment: 41 pages, 11 figures, 8 tables; NeurIPS 2023

Flare frequency distributions represent a key approach to addressing one of the largest problems in solar and stellar physics: determining the mechanism that counter-intuitively heats coronae to temperatures that are orders of magnitude hotter than the corresponding photospheres. It is widely accepted that the magnetic field is responsible for the heating, but there are two competing mechanisms that could explain it: nanoflares or Alfv\'en waves. To date, neither can be directly observed. Nanoflares are, by definition, extremely small, but their aggregate energy release could represent a substantial heating mechanism, presuming they are sufficiently abundant. One way to test this presumption is via the flare frequency distribution, which describes how often flares of various energies occur. If the slope of the power law fitting the flare frequency distribution is above a critical threshold, $\alpha=2$ as established in prior literature, then there should be a sufficient abundance of nanoflares to explain coronal heating. We performed $>$600 case studies of solar flares, made possible by an unprecedented number of data analysts via three semesters of an undergraduate physics laboratory course. This allowed us to include two crucial, but nontrivial, analysis methods: pre-flare baseline subtraction and computation of the flare energy, which requires determining flare start and stop times. We aggregated the results of these analyses into a statistical study to determine that $\alpha = 1.63 \pm 0.03$. This is below the critical threshold, suggesting that Alfv\'en waves are an important driver of coronal heating., Comment: 1,002 authors, 14 pages, 4 figures, 3 tables, published by The Astrophysical Journal on 2023-05-09, volume 948, page 71

Hallucination is an apparent perception in the absence of real external sensory stimuli. An auditory hallucination is a perception of hearing sounds that are not real. A common form of auditory hallucination is hearing voices in the absence of any speakers which is known as Auditory Verbal Hallucination (AVH). AVH is fragments of the mind's creation that mostly occur in people diagnosed with mental illnesses such as bipolar disorder and schizophrenia. Assessing the valence of hallucinated voices (i.e., how negative or positive voices are) can help measure the severity of a mental illness. We study N=435 individuals, who experience hearing voices, to assess auditory verbal hallucination. Participants report the valence of voices they hear four times a day for a month through ecological momentary assessments with questions that have four answering scales from ``not at all'' to ``extremely''. We collect these self-reports as the valence supervision of AVH events via a mobile application. Using the application, participants also record audio diaries to describe the content of hallucinated voices verbally. In addition, we passively collect mobile sensing data as contextual signals. We then experiment with how predictive these linguistic and contextual cues from the audio diary and mobile sensing data are of an auditory verbal hallucination event. Finally, using transfer learning and data fusion techniques, we train a neural net model that predicts the valance of AVH with a performance of 54\% top-1 and 72\% top-2 F1 score.

Solving transport problems, i.e. finding a map transporting one given distribution to another, has numerous applications in machine learning. Novel mass transport methods motivated by generative modeling have recently been proposed, e.g. Denoising Diffusion Models (DDMs) and Flow Matching Models (FMMs) implement such a transport through a Stochastic Differential Equation (SDE) or an Ordinary Differential Equation (ODE). However, while it is desirable in many applications to approximate the deterministic dynamic Optimal Transport (OT) map which admits attractive properties, DDMs and FMMs are not guaranteed to provide transports close to the OT map. In contrast, Schr\"odinger bridges (SBs) compute stochastic dynamic mappings which recover entropy-regularized versions of OT. Unfortunately, existing numerical methods approximating SBs either scale poorly with dimension or accumulate errors across iterations. In this work, we introduce Iterative Markovian Fitting (IMF), a new methodology for solving SB problems, and Diffusion Schr\"odinger Bridge Matching (DSBM), a novel numerical algorithm for computing IMF iterates. DSBM significantly improves over previous SB numerics and recovers as special/limiting cases various recent transport methods. We demonstrate the performance of DSBM on a variety of problems.

Normalizing flows model probability distributions through an expressive tractable density. They transform a simple base distribution, such as a Gaussian, through a sequence of invertible functions, which are referred to as layers. These layers typically use neural networks to become very expressive. Flows are ubiquitous in machine learning and have been applied to image generation, text modeling, variational inference, approximating Boltzmann distributions, and many other problems. Here, we present normflows, a Python package for normalizing flows. It allows to build normalizing flow models from a suite of base distributions, flow layers, and neural networks. The package is implemented in the popular deep learning framework PyTorch, which simplifies the integration of flows in larger machine learning models or pipelines. It supports most of the common normalizing flow architectures, such as Real NVP, Glow, Masked Autoregressive Flows, Neural Spline Flows, Residual Flows, and many more. The package can be easily installed via pip and the code is publicly available on GitHub.

We provide an order of convergence for a version of the Carath\'eodory convergence for the multiple SLE model with a Dyson Brownian motion driver towards its hydrodynamic limit, for $\beta=1$ and $\beta=2$. The result is obtained by combining techniques from the field of Schramm-Loewner Evolutions with modern techniques from random matrices. Our approach shows how one can apply modern tools used in the proof of universality in random matrix theory, in the field of Schramm-Loewner Evolutions., Comment: 19 pages, no figures

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., Comment: 53 pages. Appendix by Santiago Arenas-Velilla and Victor P\'{e}rez-Abreu. Added results concerning the k largest eigenvalues as well as additional references

We consider the spectrum of random Laplacian matrices of the form $L_n=A_n-D_n$ where $A_n$ is a real symmetric random matrix and $D_n$ is a diagonal matrix whose entries are equal to the corresponding row sums of $A_n$. If $A_n$ is a Wigner matrix with entries in the domain of attraction of a Gaussian distribution the empirical spectral measure of $L_n$ is known to converge to the free convolution of a semicircle distribution and a standard real Gaussian distribution. We consider real symmetric random matrices $A_n$ with independent entries (up to symmetry) whose row sums converge to a purely non-Gaussian infinitely divisible distribution, which fall into the class of L\'evy-Khintchine random matrices first introduced by Jung [Trans Am Math Soc, \textbf{370}, (2018)]. Our main result shows that the empirical spectral measure of $L_n$ converges almost surely to a deterministic limit. A key step in the proof is to use the purely non-Gaussian nature of the row sums to build a random operator to which $L_n$ converges in an appropriate sense. This operator leads to a recursive distributional equation uniquely describing the Stieltjes transform of the limiting empirical spectral measure., Comment: 32 pages, no figures. Minor corrections and updates

We provide the first complete continuous time framework for denoising diffusion models of discrete data. This is achieved by formulating the forward noising process and corresponding reverse time generative process as Continuous Time Markov Chains (CTMCs). The model can be efficiently trained using a continuous time version of the ELBO. We simulate the high dimensional CTMC using techniques developed in chemical physics and exploit our continuous time framework to derive high performance samplers that we show can outperform discrete time methods for discrete data. The continuous time treatment also enables us to derive a novel theoretical result bounding the error between the generated sample distribution and the true data distribution., Comment: 44 pages, 15 figures; NeurIPS 2022

As emerging technologies increasingly integrate into all facets of our lives, the workplace stands at the forefront of potential transformative changes. A notable development in this realm is the advent of passive sensing technology, designed to enhance both cognitive and physical capabilities by monitoring human behavior. This paper reviews current research on the application of passive sensing technology in the workplace, focusing on its impact on employee wellbeing and productivity. Additionally, we explore unresolved issues and outline prospective pathways for the incorporation of passive sensing in future workplaces., Comment: Added references and other minor revisions. Also udated to include relevant works published after 2022