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Theory · Everything Else

Zachary Izzo, Iain Melvin

We study the problem of subgroup discovery for survival analysis, where the goal is to find an interpretable subset of the data on which a Cox model is highly accurate. We examine why existing quality functions are insufficient for this problem and introduce two technical innovations: the *expected prediction entropy (EPE)*, a novel metric for evaluating survival models that predict hazard functions, and the *conditional rank statistics (CRS)*, which quantifies individual point deviation from a subgroup's survival time distribution. We study the EPE and CRS theoretically and show they address problems with existing metrics. We then introduce seven algorithms for Cox subgroup discover. Our main algorithm is based on the DDGroup framework of Izzo et al. (2023) and leverages both the EPE and CRS, allowing theoretical correctness guarantees in well-specified settings. Empirical evaluation on synthetic and real data confirms our theory, showing our methods recover ground-truth subgroups in well-specified cases and achieve better model fit than naively fitting the Cox model to the entire dataset. A case study on NASA jet engine simulation data demonstrates that discovered subgroups uncover known nonlinearities in the data and suggest design choices mirrored in practice.

Theory · Learning Theory

Xi Huang, Lixing Zhang, Di Luo

Characterizing the Hamiltonians of continuous-variable (CV) quantum systems remains a fundamental challenge due to the infinite-dimensional Hilbert space and the presence of unbounded operators. Existing learning protocols are often restricted to low-order Hamiltonian structures and can be sensitive to experimental noise, leaving generic multi-mode settings largely unresolved. In this work, we introduce the Displacement-Random Unitary Transformation (D-RUT), an experimentally accessible protocol for learning the coefficients of generic multi-mode bosonic Hamiltonians of arbitrary finite order. We prove that D-RUT achieves Heisenberg-limited scaling while remaining robust to state preparation and measurement (SPAM) errors. To extend the method efficiently to multi-mode systems, we develop a hierarchical coefficient recovery strategy that yields superior statistical efficiency compared to existing simultaneous estimation schemes. Importantly, we further show that our framework applies naturally to Hamiltonian coefficient learning in the first-quantized formulations, substantially broadening its scope beyond prior CV approaches. Numerical experiments validate the predicted Heisenberg scaling our approach in both single- and multi-mode nonlinear systems.

Deep Learning · Graph Neural Networks

Adrien Lagesse, Marc Lelarge

We propose a novel benchmarking methodology for graph neural networks (GNNs) based on the graph alignment problem, a combinatorial optimization task that generalizes graph isomorphism by aligning two unlabeled graphs to maximize overlapping edges. We frame this problem as a self-supervised learning task and present several methods to generate graph alignment datasets using synthetic random graphs and real-world graph datasets from multiple domains. For a given graph dataset, we generate a family of graph alignment datasets with increasing difficulty, allowing us to rank the performance of various architectures. Our experiments prove that there is an optimal task difficulty for having a statistically relevant ranking of different models and that, even on a structure-only task, anisotropic models perform better compared to isotropic ones. To further prove that our synthetic task capture meaningful information, we show its effectiveness for self-supervised GNN pre-training: the learned node embeddings can be leveraged as positional encodings by transformers for graph regression or can be used to reconstruct the full structure of the graph with 98% accuracy. To support reproducibility and further research, we provide an open-source Python package to generate graph alignment datasets and benchmark new GNN architectures.

Social Aspects · Everything Else

Xinlei Wang, Ruibo Ming, Jing Qiu, Junhua Zhao, Jinjin Gu

The scaling-law era has transformed artificial intelligence from research into a global industry, but its rapid growth raises concerns over energy usage, carbon emissions, and environmental sustainability. Unlike traditional sectors, the AI industry still lacks systematic carbon accounting methods that support large-scale estimates without reproducing the original model. This leaves open questions about how large the problem is today and how large it might be in the near future. Given that the Hugging Face (HF) platform well represents the broader open-source community, we treat it as a large-scale, publicly accessible, and audit-ready corpus for carbon accounting. We propose a FLOPs-based framework to estimate aggregate training emissions of HF open-source models. Considering their uneven disclosure quality, we introduce a tiered approach to handle incomplete metadata, supported by empirical regressions that verify the statistical significance. Compute is also converted to AI training carbon intensity (ATCI, emissions per compute), a metric to assess the sustainability efficiency of model training. Our results show that training the most popular models (with over 5,000 downloads) has resulted in approximately 5.8×10^4 tons of carbon emissions. This paper provides a framework for large-scale emission estimations and a practical methodology to guide future standards and sustainability strategies in the AI industry.

Applications · Time Series

Jiegang Xu, Fuyuan CAO, Jiye Liang

Federated causal discovery for time series is becoming increasingly important in many application domains. In practice, intervention policies on each client often change over time, causing the local underlying causal mechanisms to drift rather than remain fixed. Moreover, different sampling frequencies across clients yield incompatible time scales in the observed data, making the resulting local causal graphs naturally heterogeneous and difficult to aggregate consistently. Accordingly, we propose Fed-CAW, a Credibility-Aware Weighting Federated causal discovery framework for time series. Specifically, we define edge-level credibility scores that quantify per-edge reliability by summarizing (i) within-client temporal stability across windows and (ii) cross-client temporal consistency after mapping heterogeneous sampling frequencies onto a unified time scale. We then aggregate privatized edge statistics under differential privacy, treating credibility scores as weights to recover a global causal graph while preserving personalized local structures without sharing raw data. Theoretically, we demonstrate the rationale for the unified time scale mapping and establish rigorous differential privacy guarantees. Experimental results on synthetic and real-world datasets demonstrate the effectiveness of our proposed method.

General Machine Learning · Transfer, Multitask and Meta-learning

Shaoran Lv, Xinyao Li, Jingjing Li

Test-time adaptation (TTA) adapts pretrained models to test data on-the-fly. Current TTA methods have focused on what to adapt: lightweight domain-aware components (prompts, normalization statistics) updated with consistency-aware self-supervised losses. This work investigates the more fundamental yet underexplored optimization process, providing insights and guidelines on how to appropriately update models for TTA. By analyzing the optimization error during TTA, we identify a pivotal stability-plasticity trade-off: the model should adapt to novel distributions while retaining learned knowledge, which motivates our design of a CONfidence-and-Gradient-Aware scheduler (CONGA) to constrain model learning rate (LR) within an adaptive exploration interval. For each iteration, the lower bound encourages model exploration on informative confident samples, while the upper bound prevents aggressive overfitting to noisy optimization gradients. Based on our theoretical findings, an adaptation-progress-conditioned cosine decay function decides the specific LR within the interval. As an LR scheduler, CONGA is naturally applicable on existing TTA methods as a plug-in module, introducing little computation overheads. Extensive experiments and analysis demonstrate the superiority and validness of CONGA.

Probabilistic Methods · Monte Carlo and Sampling Methods

Xiaoning Wang, Huo Yuyang, Liuhua Peng, Changliang Zou

$U$-statistics play a central role in statistical inference. In many modern applications, however, acquiring the labels required for $U$-statistics is costly. Motivated by recent advances in active inference, we develop an active inference framework for $U$-statistics that selectively queries informative labels to improve estimation efficiency under a fixed labeling budget, while preserving valid statistical inference. Our approach is built on the augmented inverse probability weighting $U$-statistic, which is proposed to incorporate the sampling rule and machine learning predictions. We characterize the optimal sampling rule that minimizes its variance and design practical sampling strategies. We further extend the framework to $U$-statistic-based empirical risk minimization. Experiments on real datasets demonstrate substantial gains in estimation efficiency over baseline methods, while maintaining target coverage.

Deep Learning · Foundation Models

Jungin Park, Jiyoung Lee, Kwanghoon Sohn

This study introduces an intriguing phenomenon in Video LLMs: rather than merely translating frames into textual embeddings, Video LLMs establish a continuous manifold, token interface, allowing visual tokens to operate as standalone entities within the architecture. Exploiting this discovery, we propose LynX, a scalable framework that integrates novel modalities by repurposing the internalized interface. Departing from conventional paradigms that necessitate heavy modality-specific encoders or paired supervision, LynX employs a lightweight auxiliary pathway in parallel with the frozen vision encoder. By aligning both the attention responses and the statistical distributions using unimodal data alone, our method synchronizes new sensory inputs with intrinsic video priors. Crucially, our distributional alignment ensures manifold compatibility while preserving the integrity of the Video LLMs. Extensive benchmarks demonstrate that LynX achieves state-of-the-art performance and efficiency across audio-visual QA, 3D reasoning, high-frame-rate, and multi-view video understanding. The code is available at https://anonymous.4open.science/r/lynx-DDC8/.

Deep Learning · Sequential Models, Time series

Michael Menezes, Anastasios Kyrillidis

While Mamba2's expanded state dimension enhances temporal modeling, it incurs substantial inference overhead that saturates bandwidth during autoregressive generation. Standard pruning methods fail to address this bottleneck: unstructured sparsity leaves activations dense, magnitude-based selection ignores runtime dynamics, and gradient-based methods impose prohibitive costs. We introduce GHOST (Grouped Hidden-state Output-aware Selection and Truncation), a structured pruning framework that approximates control-theoretic balanced truncation using only forward-pass statistics. By jointly measuring controllability and observability, GHOST rivals the fidelity of gradient-based methods without requiring backpropagation. As a highlight, on models ranging from 130M to 2.7B parameters, our approach achieves a 50% state-dimension reduction with approximately 1 perplexity point increase on WikiText-2. Code is available at https://anonymous.4open.science/r/mamba2_ghost-7BCB/.

Social Aspects · Privacy

Yuzheng Hu, Ryan McKenna, Da Yu, Shanshan Wu, Han Zhao, Zheng Xu, Peter Kairouz

Generating high-quality synthetic text under differential privacy (DP) is critical for training and evaluating language models without compromising user privacy. Prior work on synthesizing DP *datasets* often fail to preserve key statistical attributes, suffer utility loss from the noise required by DP, and lack fine-grained control over generation. To address these challenges, we make two contributions. First, we introduce a hierarchical framework that decomposes DP synthetic text generation into two subtasks: *feature learning* and *conditional text generation*. This design explicitly incorporates learned features into the generation process and simplifies the end-to-end synthesis task. Through systematic ablations, we identify the most effective configuration: a rich tabular schema as feature, a DP tabular synthesizer, and a DP fine-tuned conditional generator, which we term ACTG (**A**ttribute-**C**onditioned **T**ext **G**eneration). Second, we propose Anchored RL (ARL), a post-training method that improves the instruction-following ability of ACTG for conditional generation. ARL combines RL to boost control with an SFT anchor on best-of-$N$ data to prevent reward hacking. Together, these components form our end-to-end algorithm **ACTG-ARL**, which advances both the quality of DP synthetic text (+20% MAUVE over prior work) and the control of the conditional generator under strong privacy guarantees. Our code is at https://github.com/actg-arl/ACTG-ARL.

Applications · Health / Medicine

ZONGHENG GUO, Tao Chen, Yang Jiao, Yi Pan, Xiao Hu, Manuela Ferrario

Current foundation model for photoplethysmography (PPG) signals is challenged by the intrinsic redundancy and noise of the signal. Standard masked modeling often yields trivial solutions while contrastive methods lack morphological precision. To address these limitations, we propose a Statistical-prior Informed Generative Masking Architecture (SIGMA-PPG), a generative foundation model featuring a prior-guided adversarial masking mechanism, where a reinforcement learning-driven teacher leverages statistical priors to create challenging learning paths that prevent overfitting to noise. We also incorporate a semantic consistency constraint via vector quantization to ensure that physiologically identical waveforms—even those altered by recording artifacts or minor perturbations—map to shared indices. This enhances codebook semantic density and eliminates redundant feature structures. Pre-trained on over 120,000 hours of data, SIGMA-PPG achieves superior average performance compared to five state-of-the-art baselines across 12 diverse downstream tasks.

Social Aspects · Security

Jane Downer, Yingdan Shi, Ziyan Liu, Ren Wang, Binghui Wang

Graph Neural Networks (GNNs) are widely deployed in industry, making their intellectual property valuable. However, protecting GNNs from unauthorized use remains a challenge. Watermarking offers a solution by embedding ownership information into models. Existing watermarking methods have two limitations: First, they rarely focus on graph data or GNNs. Second, the \emph{de facto} backdoor-based method relies on manipulating training data, which can introduce ownership ambiguity through misclassification and vulnerability to data poisoning attacks that can interrupt the backdoor mechanism. Our explanation-based watermarking inherits the strengths of backdoor-based methods (e.g., black-box verification) without data manipulation, eliminating ownership ambiguity and data dependencies. In particular, we watermark GNN explanations such that these explanations are statistically distinct from others, so ownership claims must be verified through statistical significance. We theoretically prove that, even with full knowledge of our method, locating the watermark is NP-hard. Empirically, our method demonstrates robustness to fine-tuning and pruning attacks. By addressing these challenges, our approach significantly advances GNN intellectual property protection.

Optimization · Convex

Nicholas Di, Eric Chi, Samy Wu Fung

Operator splitting algorithms are a cornerstone of modern first-order optimization, decomposing complex problems into simpler subproblems solved via proximal operators. However, most functions lack closed-form proximal operators, which has long restricted these methods to a narrow set of problems. Hamilton-Jacobi-based proximal operator (HJ-Prox) is a recent derivative-free Monte Carlo technique based on Hamilton-Jacobi PDE theory, that approximates proximal operators numerically. In this work, we introduce a unified framework for operator splitting via HJ-Prox, which allows for deployment of operator splitting even when functions are not proximable. We prove that replacing exact proximal steps with HJ-Prox in algorithms such as proximal point, proximal gradient descent, Douglas–Rachford splitting, Davis–Yin splitting, and primal–dual hybrid gradient preserves convergence guarantees under mild assumptions. Numerical experiments demonstrate HJ-Prox is competitive and effective on a wide variety of statistical learning tasks.

General Machine Learning · Sequential, Network, and Time Series Modeling

Dong Huang, Chenyang Tian, Pengkun Yang

This paper studies the problem of recovering a hidden vertex correspondence between two correlated graphs when both edge weights and node features are observed. While most existing work on graph alignment relies primarily on edge information, many real-world applications provide informative node features in addition to graph topology. To capture this setting, we introduce the featured correlated Gaussian Wigner model, where two graphs are coupled through an unknown vertex permutation, and the node features are correlated under the same permutation. We characterize the optimal information-theoretic thresholds for exact recovery and partial recovery of the latent mapping. On the algorithmic side, we propose QPAlign, an efficient method based on a quadratic programming relaxation, and demonstrate its strong empirical performance on both synthetic and real datasets. Moreover, we also derive theoretical guarantees for the proposed procedure, supporting its reliability and providing convergence guarantees.

Theory · Optimization

Zusen Xu, Jia-Jie Zhu

We propose a mathematically principled PDE gradient flow framework for distributionally robust optimization (DRO). Exploiting the recent advances in the intersection of Monte Carlo sampling and statistical optimal transport, we show that our theoretical framework can be implemented as practical algorithms for sampling from worst-case distributions and, consequently, DRO. While numerous previous works have relied on dual reformulation techniques, we contribute a sound and complete gradient flow view based on SDEs or PDEs that can be used to construct new algorithms for general, potentially non-convex, losses. Without loss of generality, we solve a class of Wasserstein and entropy-regularized DRO problems using the recently-discovered Wasserstein Fisher-Rao and Stein variational gradient flows. Notably, we also show some simple reductions of our framework recover exactly previously proposed popular DRO methods, and provide new insights into their theoretical limits and optimization dynamics of DRO. Numerical studies based on stochastic gradient descent on machine learning tasks provide empirical backing for our theoretical findings.

General Machine Learning · Kernel methods

Alejandro de la Concha Duarte, Nicolas Vayatis, Argyris Kalogeratos

This paper introduces the Collaborative Likelihood-ratio Estimation problem, which is relevant for applications involving multiple statistical estimation tasks that can be mapped to the nodes of a fixed graph expressing pairwise task similarity. Each graph node $v$ observes i.i.d data from two unknown node-specific pdfs, $p_{v}$ and $q_{v}$, and the goal is to estimate the likelihood-ratios (or density-ratios), $r_{v}(x)=\frac{q_{v}(x)}{p_{v}(x)}$, for all $v$. Our contribution is multifold: we present a non-parametric collaborative framework that leverages the graph structure of the problem to solve the tasks more efficiently; we present a concrete method that we call Graph-based Relative Unconstrained Least-Squares Importance Fitting (GRULSIF) along with an efficient implementation; we derive convergence rates that highlight the role of the main variables of the problem. Our theoretical results explicit the conditions under which the collaborative estimation leads to performance gains compared to solving each estimation task independently. Finally, in a series of experiments, we demonstrate that the joint likelihood-ratio estimation of GRULSIF at all graph nodes is more accurate compared to state-of-the-art methods that operate independently at each node, and we verify that the behavior of GRULSIF is in agreement with our theoretical analysis.

Theory · Learning Theory

QUOC TUNG LE, Anh Nguyen, Viet Anh Nguyen

Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures like Vehicle Routing or Unit Commitment. By relaxing coupling constraints, LR enables parallel solving of subproblems and frequently yields tighter dual bounds than standard linear programming relaxations, which is crucial for efficient branch-and-bound pruning. While recent empirical works showed promising results using machine learning to predict these multipliers, a theoretical understanding of such methods remains an open question. In this work, we bridge this gap by analyzing the problem of learning LR through the lens of Data-driven Algorithm Design, i.e., a statistical learning problem over a distribution of problem instances. Our contributions are as follows: first, we derive a generalization bound of $\cO(s^{1.5}/\sqrt{N})$ for the learned multipliers, where $s$ is the number of coupled constraints and $N$ is the sample size. Second, we provide a minimax lower-bound of $\Omega(s/\sqrt{N})$, proving that a linear dependency is unavoidable. Finally, we extend our framework to the problem of learning to warm-start sub-gradient ascent.

Applications · Time Series

Vincent Zheng, Étienne Marcotte, Arjun Ashok, Andrew Williams, Lijun Sun, Alexandre Drouin, Valentina Zantedeschi

Context-aided forecasting (CAF) holds promise for integrating domain knowledge and forward-looking information, enabling AI systems to surpass traditional statistical methods. However, recent empirical studies reveal a puzzling gap: multimodal models often fail to outperform their unimodal counterparts. We hypothesize that this underperformance stems from poor context quality in existing datasets, as verification is challenging. To address these limitations, we introduce a semi-synthetic data augmentation method that generates contexts both descriptive of temporal dynamics and verifiably complementary to numerical histories. This approach enables massive-scale dataset creation, resulting in CAF-7M, a corpus of 7 million context-augmented time series windows, including a rigorously verified test set. We demonstrate that semi-synthetic pre-training transfers effectively to real-world evaluation, and show clear evidence of context utilization. Our results suggest that dataset quality, rather than architectural limitations, has been the primary bottleneck in context-aided forecasting.

Applications · Time Series

Huayu Li, ZhengXiao He, Xiwen Chen, Jingjing Wang, Siyuan Tian, Jinghao Wen, Ao Li

Learning meaningful representations from medical time series (MedTS), such as ECG or EEG signals, is a critical challenge. These signals are often high-dimensional, variable-length, and rife with noise. Existing self-supervised approaches, such as Masked Autoencoders (MAEs), are highly effective for pre-training general-purpose encoders. However, they do not explicitly learn compact, fixed-size, or semantically interpretable latent representations, typically relying on heuristic aggregation strategies such as global average pooling or a designated [CLS] token. We propose a novel framework that compresses a variable-length MedTS into a fixed-size set of $k$ latent Fingerprint Tokens. Our architecture employs a cross-attention bottleneck to generate these tokens and is trained with a dual-objective function. The first objective is a reconstruction loss, which ensures the tokens are \textit{sufficient statistics} for the original data. The second, a diversity penalty based on the Total Coding Rate (TCR), explicitly minimizes the redundancy between tokens, encouraging them to become statistically \textit{disentangled} representations. We present the theoretical justification for our method, framing it as a novel \textbf{Disentangled Rate-Distortion} problem. This approach produces a low-dimensional, interpretable, and sample-efficient representation, where each token is encouraged to capture an independent factor of variation, paving the way for more robust digital biomarkers.

Applications · Everything Else

Andrea Rubbi, Arpit Merchant, Samuel Ogden, Amir Akbarnejad, Pietro Lió, Sattar Vakili, Mohammad Lotfollahi

High-throughput gene perturbation experiments can test several genetic interventions in parallel, yet experimental budgets remain limited. A central goal is hit discovery: identifying as many perturbations as possible whose phenotypic effect exceeds a predefined threshold. Pure exploration strategies are statistically inefficient, wasting budget on low-value regions. Bayesian optimization methods offer a principled alternative but target a single global optimum, over-exploiting dominant modes while neglecting other high-value regions. We formalize hit discovery as a sequential experimental design problem and propose Probability-of-Hit, an acquisition function that directly targets threshold exceedance by ranking candidates according to their posterior probability of being a hit. We prove asymptotic optimality of this approach and demonstrate strong empirical performance on both synthetic benchmarks and real biological immunology datasets, including upto 6.4\% improvement over baselines on the Schmidt IL-2 dataset.