The next time you're scrolling your phone, take a moment to appreciate the feat: The seemingly mundane act is possible thanks to the coordination of 34 muscles, 27 joints, and over 100 tendons and ligaments in your hand. Indeed, our hands are the most nimble parts of our bodies. Mimicking their many nuanced gestures has been a longstanding challenge in robotics and virtual reality. Now, MIT engineers have designed an ultrasound wristband that precisely tracks a wearer's hand movements in real-time. The wristband produces ultrasound images of the wrist's muscles, tendons, and ligaments as the hand moves, and is paired with an artificial intelligence algorithm that continuously translates the images into the corresponding positions of the five fingers and palm.

The latest interview in our series with the AAAI/SIGAI Doctoral Consortium participants features Thi Kieu Khanh Ho who is studying time-series anomaly detection. We found out more about her research, and what inspired her to study AI, and what she plans to work on next. Tell us a bit about your PhD -- where are you studying, and what is the topic of your research? I am doing my PhD at McGill University and Mila - Québec AI Institute, in the Department of Electrical and Computer Engineering, supervised by Professor Narges Armanfard. My research focuses on time-series anomaly detection, the problem of teaching AI systems to recognize when something unusual or abnormal is happening in complex, real-world data streams, without relying on large amounts of labeled examples.

Traditional variational Kalman filtering with unknown noise statistics suffers from inconsistent process covariance estimation and slow convergence speed, limiting its practical utility. To address these issues, we introduce a surrogate variable representing the process-noise-free state, which enables explicit modeling and inference of process noise statistics. In addition, we reformulate the conventional coordinate ascent variation inference (CAVI) as a marginalized maximum a posteriori problem, followed by a single-step hyperparameter fitting. This reformulation obviates the need for multiple inner iterations inherent to CAVI and decouples the design of the covariance tracking filters. Consequently, this architecture permits the deployment of higher-order filters for covariance tracking and enables sliding-window hyperparameter estimation. Notably, when this window encompasses all historical data, the covariance tracking estimator intrinsically operates as a zero-phase filter. Numerical simulations validate the theoretical framework, demonstrating the enhanced convergence speed and superior estimation accuracy compared with existing methods.

Deep neural networks (DNNs) frequently fail to generalize to out-of-distribution (OOD) medical images because of variations in scanners and acquisition protocols. Retraining DNN models to address these distribution shifts is often impractical due to the high cost of acquiring and annotating new medical datasets. To address this, we introduce VarDeepPCA, a novel lightweight variational DNN framework designed to restore/refine degraded segmentation maps by leveraging intrinsic geometric priors. Unlike existing approaches that require target-domain data or extensive pre-training, our VarDeepPCA explicitly learns a distribution of valid anatomical geometries using only small in-distribution (ID) datasets. Theoretically, our novel variational learning framework leverages a reinterpretation of the softmax mapping to implicitly perform exact distribution modeling, thereby enabling computationally efficient, sampling-free learning and inference. This also enables VarDeepPCA to provide uncertainty estimates associated with its restored segmentation maps. We empirically validate our framework across 4 distinct clinical applications, using 14 publicly available datasets, involving segmentation of the myocardium, neuroretinal rim, prostate, and fetal head. Comparisons against 15 existing methods demonstrate that VarDeepPCA consistently restores segmentation maps produced by the existing methods on OOD data to (i) significantly improve anatomical plausibility of geometries and clinical utility of the segmentations, and (ii) significantly reduce errors, without needing any more training data than that used by existing methods.

An essential catalyst for the remarkable breakthroughs in AI that led to the modern large language models (LLMs) such as ChatGPT and Gemini has been the algorithms used to train these models on massive datasets. While the LLM architectures have gotten progressively more complex, the training algorithms have stayed relatively simple, and in fact, they have all been based on the decades-old paradigm of stochastic gradient descent (SGD). The key idea behind SGD is that in order to minimize a certain objective function (such as an LLM's error on the training data), it suffices to access only a noisy estimate of that objective at any given time (e.g., based on a small sample of the data) while making incremental progress towards the solution. This is essential for LLM training, as the datasets have become so massive one could not hope to perform computations on everything all at once. Commonly attributed to a 1951 paper by Robbins and Monro [34], SGD has seen a resurgence of interest over the last 20 years by AI researchers and computer scientists striving to understand its effectiveness, leading to numerous variants and extensions used in modern LLMs [12, 9], most notably the Adam algorithm [25]. As a result, we have gained a robust mathematical understanding of the computational complexity of SGD algorithms in a wide range of settings (e.g., see [11, 15, 5, 17]). Yet, despite this progress there is a surprising gap in the understanding of SGD: The complexity of an algorithm proposed by Stefan Kaczmarz in 1937 [24] for solving a system of linear equations - the oldest published example of an SGD algorithm, which predates Robbins and Monro's paper by over a decade - has not been settled.

Classical hypothesis testing frameworks break down in contemporary settings in which null hypotheses are increasingly abstract, the same data are used to both generate and test hypotheses, and minimal assumptions about the underlying data are made. In this work, we propose a new framework for conducting valid hypothesis tests in broad contexts. We propose to add and subtract external noise generated from a symmetric shift-family to our data, $X$, to partition it into two pieces, $X^{(1)}$ and $X^{(2)}$. We provide a generic strategy for orthogonalizing $X^{(2)}$ against $X^{(1)}$ under the null hypothesis $H_0$, then show that testing whether the orthogonalization was successful provides a valid test of $H_0$ under mild assumptions. Remarkably, this framework extends naturally to the post-selection inference setting: we simply select a hypothesis on $X^{(1)}$, then perform orthogonalization under the selected null. As our approach neither requires pre-specification of the selection mechanism, nor is restricted to a small class of data-generating distributions, it dramatically expands the settings for which valid post-selection inference can be conducted. We showcase the flexibility of our proposal in several case studies involving challenging pre-specified null hypotheses and post-selection inference scenarios.

The Fisher Information Matrix (FIM) is the canonical local measure of the curvature of a statistical model's log-likelihood surface, and its dominant eigenvalue λmax quantifies the worst-case sensitivity of the model's output distribution to infinitesimal parameter perturbation [1, 2]. The spectral properties of the FIM of neural networks have been studied directly in the random matrix theory literature. Pennington and Worah [4] derive the limiting spectral density of the FIM of a single-hidden-layer network in the high-dimensional asymptotic regime, building on the broader programme of analysing neural network Hessian and kernel spectra via random matrix methods [5, 6], with subsequent work extending these techniques to deeper architectures and non-asymptotic regimes [7, 8]. These results characterize the typical (bulk and edge) spectral behaviour of the FIM for a fixed network and a random or structured input ensemble. This paper studies a complementary question, posed as a perturbation problem rather than an asymptotic-spectrum problem: how does the dominant eigenvalue of a fixed, evaluated empirical FIM change under two specific structured perturbations of the underlying distribution? The first perturbation is a change in the conditioning input away from a reference (in-distribution) ensemble. The second is a structured additive perturbation of the model's own parameters by finite-precision quantization noise -- a perturbation of independent mathematical interest, since it falls outside the i.i.d.-input asymptotic regime treated in the random matrix literature cited above, and instead concerns a fixed network whose parameters, not its input distribution, are perturbed by a noise process with a specific, analytically tractable structure (Definition 4.1). To our knowledge, this parameterperturbation question for the FIM's dominant eigenvalue, under either source of departure, has not been previously formalized.

In recent years, models based on the Transformer architecture have seen widespread applications and have become one of the core tools in the field of deep learning. Numerous successful techniques, such as parameter-efficient fine-tuning and efficient scaling, have been proposed surrounding their applications to further enhance performance. However, the success of these strategies has always lacked the support of rigorous mathematical theory. To study the underlying mechanisms behind Transformers and related techniques, we first propose a Transformer learning framework motivated by distribution regression, with distributions being inputs, connect a two-stage sampling process with natural language processing, and present a mathematical formulation of the attention mechanism called attention operator. We demonstrate that by the attention operator, Transformers can compress distributions into function representations without loss of information. Moreover, with the advantages of our novel attention operator, Transformers exhibit a stronger capability to learn functionals with more complex structures than convolutional neural networks and fully connected networks. Finally, we obtain a generalization bound within the distribution regression framework. Through the aforementioned theoretical results, we further discuss some successful techniques emerging with large language models (LLMs), such as prompt tuning, parameter-efficient fine-tuning, and efficient scaling. We also provide theoretical insights behind these techniques within our novel analysis framework.

Rapid prototyping of algorithms is a critical step in modern machine learning. Most algorithms exploit linear algebra, creating a need for lightweight numerical routines which -- while potentially sub-optimal for the task at hand -- can be rapidly implemented. For the numerical solution of ill-conditioned linear systems of equations, the standard solution for prototyping is Tikhonov-regularised inversion using a nugget. However, selection of the size of nugget is often difficult, and the use of data-adaptive procedures precludes automatic differentiation, introducing instabilities into end-to-end training. Further, while data-adaptive procedures perform multiple linear solves to select the size of nugget, only the result of one such solve is returned, which we argue is wasteful. This paper aims to circumvent the above difficulties, presenting autonugget; a Python package for automatic and stable numerical solution of linear systems suitable for rapid prototyping, and fully compatible with automatic differentiation using JAX. autonugget combines multiple linear solves using Richardson extrapolation to determine the solution of the ill-conditioned system, improving in accuracy over approximations based on a single nugget.

This paper examines how metric adjustments to Multidimensional Scaling (MDS) can enhance its effectiveness as a visual tool for pattern recognition. The distance under consideration, referred to as Max-D-SW, is an adjustment of the Max-Sliced Wasserstein distance. In contrast to the original formulation, which optimizes over single unit directions, Max-D-SW aggregates contributions over orthonormal bases. This modification provides a clear numerical advantage in MDS outcomes, particularly when applied to heavy-tailed distributions. We also establish sample-complexity bounds showing that Max-D-SW remains statistically tractable, with rates comparable to those of its max-sliced counterpart. Moreover, we show that a better sample complexity for a metric does not necessarily translate into better performance when the metric is used as an input for MDS.