In this work we consider generic Gaussian Multi-index models, in which the labels only depend on the (Gaussian) $d$-dimensional inputs through their projection onto a low-dimensional $r = O_d(1)$ subspace, and we study efficient agnostic estimation procedures for this hidden subspace. We introduce the \emph{generative leap} exponent $k^\star$, a natural extension of the generative exponent from [Damian et al.'24] to the multi-index setting. We first show that a sample complexity of $n=Θ(d^{1 \vee \k/2})$ is necessary in the class of algorithms captured by the Low-Degree-Polynomial framework. We then establish that this sample complexity is also sufficient, by giving an agnostic sequential estimation procedure (that is, requiring no prior knowledge of the multi-index model) based on a spectral U-statistic over appropriate Hermite tensors. We further compute the generative leap exponent for several examples including piecewise linear functions (deep ReLU networks with bias), and general deep neural networks (with $r$-dimensional first hidden layer).

Depression is one of the most prevalent mental health disorders worldwide, with estimates indicating that around 5% of the worlds' adult population [1, 2] suffers from this condition. The primary methods for screening and monitoring depression rely on self-reported questionnaires, such as the Patient Health Questionnaire (PHQ-9) [3], Beck's Depression Inventory (BDI) [4] and Hamilton Depression Ratings Scale (HDRS) [5]. While these questionnaires are effective to varying degrees at screening patients for depression, they provide only limited information about the affected underlying neuro-cognitive processes in individuals, limiting the ability to personalize treatments. Given the heterogeneity of depressive symptomatology across patient populations [6, 7], it is crucial to elucidate the underlying neurophysiological mechanisms to support the development of more effective and individualized procedures for screening, monitoring, and treatment. Prior functional imaging studies have identified increased activity in anterior cin-gulate cortex (especially the subgenual anterior cingulate) during presentation of emotional stimuli, altered connectivity in prefrontal cortical areas, and default mode network as potential differentiating markers in depressed participants [8-13].

We propose $\textbf{MGCL}$, a model-driven graph contrastive learning (GCL) framework that leverages graphons (probabilistic generative models for graphs) to guide contrastive learning by accounting for the data's underlying generative process. GCL has emerged as a powerful self-supervised framework for learning expressive node or graph representations without relying on annotated labels, which are often scarce in real-world data. By contrasting augmented views of graph data, GCL has demonstrated strong performance across various downstream tasks, such as node and graph classification. However, existing methods typically rely on manually designed or heuristic augmentation strategies that are not tailored to the underlying data distribution and operate at the individual graph level, ignoring similarities among graphs generated from the same model. Conversely, in our proposed approach, MGCL first estimates the graphon associated with the observed data and then defines a graphon-informed augmentation process, enabling data-adaptive and principled augmentations. Additionally, for graph-level tasks, MGCL clusters the dataset and estimates a graphon per group, enabling contrastive pairs to reflect shared semantics and structure. Extensive experiments on benchmark datasets demonstrate that MGCL achieves state-of-the-art performance, highlighting the advantages of incorporating generative models into GCL.

This report documents the development and evaluation of domain-specific language models for neurology. Initially focused on building a bespoke model, the project adapted to rapid advances in open-source and commercial medical LLMs, shifting toward leveraging retrieval-augmented generation (RAG) and representational models for secure, local deployment. Key contributions include the creation of neurology-specific datasets (case reports, QA sets, textbook-derived data), tools for multi-word expression extraction, and graph-based analyses of medical terminology. The project also produced scripts and Docker containers for local hosting. Performance metrics and graph community results are reported, with future possible work open for multimodal models using open-source architectures like phi-4.

Patient stratification--identifying clinically meaningful subgroups--is essential for advancing personalized medicine through improved diagnostics and treatment strategies. Electronic health records (EHRs), particularly those from intensive care units (ICUs), contain rich temporal clinical data that can be leveraged for this purpose. In this work, we introduce ICU-TSB (Temporal Stratification Benchmark), the first comprehensive benchmark for evaluating patient stratification based on temporal patient representation learning using three publicly available ICU EHR datasets. A key contribution of our benchmark is a novel hierarchical evaluation framework utilizing disease taxonomies to measure the alignment of discovered clusters with clinically validated disease groupings. In our experiments with ICU-TSB, we compared statistical methods and several recurrent neural networks, including LSTM and GRU, for their ability to generate effective patient representations for subsequent clustering of patient trajectories. Our results demonstrate that temporal representation learning can rediscover clinically meaningful patient cohorts; nevertheless, it remains a challenging task, with v-measuring varying from up to 0.46 at the top level of the taxonomy to up to 0.40 at the lowest level. To further enhance the practical utility of our findings, we also evaluate multiple strategies for assigning interpretable labels to the identified clusters.

Policy gradient (PG) methods are a class of effective reinforcement learning algorithms, particularly when dealing with continuous control problems. These methods learn the parameters of parametric policies via stochastic gradient ascent, typically using on-policy trajectory data to estimate the policy gradient. However, such reliance on fresh data makes them sample-inefficient. Indeed, vanilla PG methods require $O(ε^{-2})$ trajectories to reach an $ε$-approximate stationary point. A common strategy to improve efficiency is to reuse off-policy information from past iterations, such as previous gradients or trajectories. While gradient reuse has received substantial theoretical attention, leading to improved rates of $O(ε^{-3/2})$, the reuse of past trajectories remains largely unexplored from a theoretical perspective. In this work, we provide the first rigorous theoretical evidence that extensive reuse of past off-policy trajectories can significantly accelerate convergence in PG methods. We introduce a power mean correction to the multiple importance weighting estimator and propose RPG (Retrospective Policy Gradient), a PG algorithm that combines old and new trajectories for policy updates. Through a novel analysis, we show that, under established assumptions, RPG achieves a sample complexity of $\widetilde{O}(ε^{-1})$, the best known rate in the literature. We further validate empirically our approach against PG methods with state-of-the-art rates.

The multi-task learning ($MTL$) paradigm aims to simultaneously learn multiple tasks within a single model capturing higher-level, more general hidden patterns that are shared by the tasks. In deep learning, a significant challenge in the backpropagation training process is the design of advanced optimisers to improve the convergence speed and stability of the gradient descent learning rule. In particular, in multi-task deep learning ($MTDL$) the multitude of tasks may generate potentially conflicting gradients that would hinder the concurrent convergence of the diverse loss functions. This challenge arises when the gradients of the task objectives have either different magnitudes or opposite directions, causing one or a few to dominate or to interfere with each other, thus degrading the training process. Gradient surgery methods address the problem explicitly dealing with conflicting gradients by adjusting the overall gradient trajectory. This work introduces a novel gradient surgery method, the Similarity-Aware Momentum Gradient Surgery (SAM-GS), which provides an effective and scalable approach based on a gradient magnitude similarity measure to guide the optimisation process. The SAM-GS surgery adopts gradient equalisation and modulation of the first-order momentum. A series of experimental tests have shown the effectiveness of SAM-GS on synthetic problems and $MTL$ benchmarks. Gradient magnitude similarity plays a crucial role in regularising gradient aggregation in $MTDL$ for the optimisation of the learning process.

Growing concerns over data privacy and security highlight the importance of machine unlearning--removing specific data influences from trained models without full retraining. Techniques like Membership Inference Attacks (MIAs) are widely used to externally assess successful unlearning. However, existing methods face two key limitations: (1) maximizing MIA effectiveness (e.g., via online attacks) requires prohibitive computational resources, often exceeding retraining costs; (2) MIAs, designed for binary inclusion tests, struggle to capture granular changes in approximate unlearning. To address these challenges, we propose the Interpolated Approximate Measurement (IAM), a framework natively designed for unlearning inference. IAM quantifies sample-level unlearning completeness by interpolating the model's generalization-fitting behavior gap on queried samples. IAM achieves strong performance in binary inclusion tests for exact unlearning and high correlation for approximate unlearning--scalable to LLMs using just one pre-trained shadow model. We theoretically analyze how IAM's scoring mechanism maintains performance efficiently. We then apply IAM to recent approximate unlearning algorithms, revealing general risks of both over-unlearning and under-unlearning, underscoring the need for stronger safeguards in approximate unlearning systems. The code is available at https://github.com/Happy2Git/Unlearning_Inference_IAM.

Machine unlearning addresses the problem of updating a machine learning model/system trained on a dataset $S$ so that the influence of a set of deletion requests $U \subseteq S$ on the unlearned model is minimized. The gold standard definition of unlearning demands that the updated model, after deletion, be nearly identical to the model obtained by retraining. This definition is designed for a worst-case attacker (one who can recover not only the unlearned model but also the remaining data samples, i.e., $S \setminus U$). Such a stringent definition has made developing efficient unlearning algorithms challenging. However, such strong attackers are also unrealistic. In this work, we propose a new definition, system-aware unlearning, which aims to provide unlearning guarantees against an attacker that can at best only gain access to the data stored in the system for learning/unlearning requests and not all of $S\setminus U$. With this new definition, we use the simple intuition that if a system can store less to make its learning/unlearning updates, it can be more secure and update more efficiently against a system-aware attacker. Towards that end, we present an exact system-aware unlearning algorithm for linear classification using a selective sampling-based approach, and we generalize the method for classification with general function classes. We theoretically analyze the tradeoffs between deletion capacity, accuracy, memory, and computation time.

Efficient Coverage Path Planning (CPP) is necessary for autonomous robotic lawnmowers to effectively navigate and maintain lawns with diverse and irregular shapes. This paper introduces a comprehensive end-to-end pipeline for CPP, designed to convert user-defined boundaries on an aerial map into optimized coverage paths seamlessly. The pipeline includes user input extraction, coordinate transformation, area decomposition and path generation using our novel AdaptiveDecompositionCPP algorithm, preview and customization through an interactive coverage path visualizer, and conversion to actionable GPS waypoints. The AdaptiveDecompositionCPP algorithm combines cellular decomposition with an adaptive merging strategy to reduce non-mowing travel thereby enhancing operational efficiency. Experimental evaluations, encompassing both simulations and real-world lawnmower tests, demonstrate the effectiveness of the framework in coverage completeness and mowing efficiency.