Maximum likelihood prediction (MLP) is a core task at the heart of modern large language models. Here, we study a quantum version of this task for a simplified data model consisting of independent and identically distributed samples, as a first step. The quantum maximum likelihood predictor (QMLP) is obtained by embedding of empirical probability distributions into quantum states and performing a minimization of quantum relative entropy over a given class of states. We derive non-asymptotic performance guarantees for QMLP in terms of convergence rates and concentration inequalities, both in trace norm and quantum relative entropy. Our approach provides a unified framework to handle MLP within both classical and quantum LLMs. We also consider the related problem of quantum information projection and generalize the quantum Pythagorean theorem to mixture families specified by possibly non-self-adjoint linear constraints. We further show that the Pythagorean inequality continues to hold in the infinite-dimensional setting whenever the convex information-projection problem attains a finite minimum.
Adapting general-purpose LLMs into domain-specialized dense retrievers typically requires large-scale training on mixed-domain data. We show that merging independently trained domain-specialized experts consistently exceeds this approach across four decoder-only LLM families (0.6B-7B), four merging methods, and twelve medical and general retrieval tasks from MTEB, suggesting that parameter-space composition captures complementary domain strengths that large-scale mixed-domain training averages out. To further maximize expert quality, we introduce Synthesize-Train-Merge (STM), a modular framework that synthesizes hard negatives with a top-tier LLM and fine-tunes domain-specialized experts via LoRA before merging them, without continual pre-training. Synthesized hard negatives yield the largest gains for smaller models, and STM achieves strong performance on biomedical retrieval tasks while maintaining competitive general-domain results across all four backbone families.
Sameh Khattab, Jean-Philippe Corbeil, Osman Alperen \c{C}inar-Kora\c{s} et al.· 0 citations
The Gilbert-Pollak Conjecture \citep{gilbert1968steiner}, also known as the Steiner Ratio Conjecture, states that for any finite point set in the Euclidean plane, the Steiner minimum tree has length at least $\sqrt{3}/2 \approx 0.866$ times that of the Euclidean minimum spanning tree (the Steiner ratio). A sequence of improvements through the 1980s culminated in a lower bound of $0.824$, with no substantial progress reported over the past three decades. Recent advances in LLMs have demonstrated strong performance on contest-level mathematical problems, yet their potential for addressing open, research-level questions remains largely unexplored. In this work, we present a novel AI system for obtaining tighter lower bounds on the Steiner ratio. Rather than directly prompting LLMs to solve the conjecture, we task them with generating rule-constrained geometric lemmas implemented as executable code. These lemmas are then used to construct a collection of specialized functions, which we call verification functions, that yield theoretically certified lower bounds of the Steiner ratio. Through progressive lemma refinement driven by reflection, the system establishes a new certified lower bound of 0.8559 for the Steiner ratio. The entire research effort involves only thousands of LLM calls, demonstrating the strong potential of LLM-based systems for advanced mathematical research.
Yisi Ke, Tianyu Huang, Yankai Shu et al.· 0 citations
Machine Learning (ML) has deeply changed some fields recently, like Language and Vision and we may expect it to be relevant also to the analysis of of complex systems. Here we want to tackle the question of how and to which extent can one regress scale-free processes, i.e. processes displaying power law behavior, like earthquakes or avalanches? We are interested in predicting the large ones, i.e. rare events in the training set which therefore require extrapolation capabilities of the model. For this we consider two paradigmatic problems that are statistically self-similar. The first one is a 2-dimensional fractional Gaussian field obeying linear dynamics, self-similar by construction and amenable to exact analysis. The second one is the Abelian sandpile model, exhibiting self-organized criticality. The emerging paradigm of Geometric Deep Learning shows that including known symmetries into the model's architecture is key to success. Here one may hope to extrapolate only by leveraging scale invariance. This is however a peculiar symmetry, as it involves possibly non-trivial coarse-graining operations and anomalous scaling. We perform experiments on various existing architectures like U-net, Riesz network (scale invariant by construction), or our own proposals: a wavelet-decomposition based Graph Neural Network (with discrete scale symmetry), a Fourier embedding layer and a Fourier-Mellin Neural Operator. Based on these experiments and a complete characterization of the linear case, we identify the main issues relative to spectral biases and coarse-grained representations, and discuss how to alleviate them with the relevant inductive biases.
Anaclara Alvez-Canepa, Cyril Furtlehner, Fran\c{c}ois P. Landes· 0 citations
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We introduce Cost-Aware (CA) Sequential Hypothesis Testing (CASHT), in which an active decision-maker selects sensing actions with differing, random costs to identify the true hypothesis under an average-error constraint $\delta$ while minimizing the expected total cost rather than the number of samples. For fixed costs, we prove that the optimal expected total cost scales as $\Theta(\log(1/\delta))$, and is achievable by Multihypothesis Sequential Probability Ratio Test-based procedures. We show that the CA design principle is to maximize the ratio of expected information gain to expected cost under the policy-induced action distribution. Guided by this principle, we adapt two classic policies to the CA setting and establish their asymptotic optimality. We then treat random costs under two revelation models: ex-post, where costs are disclosed only after a sample is obtained, and the cost-error tradeoff coincides with the fixed-cost case, and ex-ante, where costs accrue before acquisition, and the decision maker may cancel an action mid-operation. For the ex-ante model, we characterize when cancellation lowers the total cost and analyze several cost distributions in detail. Simulations confirm our findings that the CA variants consistently reduce total cost relative to their classical counterparts, and when action cancellation helps or hurts.
George Vershinin, Asaf Cohen, Omer Gurewitz· 0 citations
Immersive formats such as 360{\deg} and 6DoF point cloud videos require high bandwidth and low latency, posing challenges for real-time AR/VR streaming. This work focuses on reducing bandwidth consumption and encryption/decryption delay, two key contributors to overall latency. We design a system that downsamples point cloud content at the origin server and applies partial encryption. At the client, the content is decrypted and upscaled using an ML-based super-resolution model. Our evaluation demonstrates a nearly linear reduction in bandwidth/latency, and encryption/decryption overhead with lower downsampling resolutions, while the super-resolution model effectively reconstructs the original full-resolution point clouds with minimal error and modest inference time.
Mohammad Waquas Usmani, Sankalpa Timilsina, Michael Zink et al.· 0 citations
Traffic safety analysis at signalized intersections is essential for reducing vehicle and pedestrian collisions, yet traditional crash-based studies are limited by data sparsity and reporting latency. This paper presents a multi-camera computer vision framework for real-time safety assessment through Post-Encroachment Time (PET) computation, demonstrated at the intersection of H Street and Broadway in Chula Vista, California. Four synchronized cameras provide continuous visual coverage, with frames processed on NVIDIA Jetson AGX Xavier edge devices using YOLOv11 segmentation for vehicle detection. Detected vehicle polygons are transformed into a unified bird's-eye map via homography, enabling alignment across overlapping camera views. A pixel-level PET algorithm tracks temporal occupancy at each spatial location by measuring the time between successive vehicle passages, enabling fine-grained hazard visualization through dynamic heatmaps with 3.3 sq-cm spatial resolution. Timestamped vehicle trajectories and PET data are stored in an SQL database for longitudinal analysis. Results across multiple time intervals demonstrate the framework's ability to identify high-risk regions with sub-second temporal sensitivity and real-time edge throughput, generating 800 x 800 logarithmic heatmaps at an average of 2.68 FPS. This paper validates decentralized vision-based PET analysis for intelligent transportation systems and presents a scalable methodology for high-resolution, real-time intersection safety evaluation.
Shounak Ray Chaudhuri, Arash Jahangiri, Christopher Paolini· 0 citations
Large Language Model (LLM) routing has demonstrated strong capability in balancing response quality with computational cost. As users exhibit diverse preferences, personalization has attracted increasing attention in LLM routing, since even identical queries may require different models to generate responses tailored to individual needs. However, existing approaches are not fully personalized and often fail to faithfully capture the complex interactions between users and LLMs. Moreover, user preference data is typically scarce and inconsistent in format, which limits the effectiveness of methods that directly leverage user-specific data. To address these challenges, we propose GMTRouter, which represents multi-turn user-LLM interactions as a heterogeneous graph with five node types: user, LLM, query, response and turn, thereby maximally preserving the rich relational structure of the interaction. Through a lightweight inductive graph learning framework combined with a tailored user-conditioned graph sampling mechanism, GMTRouter learns to capture user preferences from few-shot data, enabling effective personalization. Extensive experiments demonstrate that GMTRouter outperforms the strongest baselines, achieving up to a 0.108 absolute improvement in accuracy and a 0.124 improvement in AUC. More importantly, we further demonstrate that GMTRouter can adapt to new users using only few-shot data, without extensive fine-tuning. The code for GMTRouter is publicly available at https://github.com/ulab-uiuc/GMTRouter.
Yihang Sun, Encheng Xie, Tao Feng et al.· 0 citations
In many applications, one must propagate parameter uncertainty from an earlier (upstream) analysis, available as samples, to subsequent (downstream) analyses without feedback. This problem is called cutting feedback or cut-Bayes, and the cut-posterior, the optimal posterior preserving information-flow constraints, is well characterized. However, sampling from it (e.g., via nested MCMC) is computationally intensive, while existing variational inference methods for cut-Bayes require access to upstream data and model, often unavailable. We propose a modular and provably accurate cut-Bayes approach requiring no access to upstream data or model. We leverage the characterization of the cut-posterior as the minimizer of the expected downstream conditional Kullback-Leibler divergence over the upstream posterior, replacing the expectation with the sample average over upstream draws. Our method, NeVI-Cut (neural variational inference for cut-Bayes), employs conditional normalizing flows as the variational family for downstream parameters. We provide fixed-data convergence rates of NeVI-Cut in terms of the richness of neural architecture and complexity of the cut-posterior. We establish, to our knowledge, first results on uniform Kullback-Leibler approximation rates of conditional distributions by common flow classes, yielding widely applicable fixed-data error rates for variational flows. A stochastic algorithm implements NeVI-Cut efficiently, and we demonstrate its speed and accuracy on multiple applications.
Quantum error correction (QEC) is essential for scalable quantum computing, yet decoding errors via conventional algorithms result in limited accuracy (i.e., suppression of logical errors) and high overheads, both of which can be alleviated by inference-based decoders. To date, such machine-learning (ML) decoders lack two key properties crucial for practical fault tolerance: reliable uncertainty quantification and robust generalization to previously unseen QEC codes. To address this gap, we propose a Quantum Bayesian graph Attention decoder \textbf{(QuBA)} that enables expressive error-pattern recognition alongside calibrated uncertainty estimates. Building on QuBA, we further develop a multi-phase training framework with enhanced cross-domain robustness enabling decoding beyond the training set called Sequential Aggregate Generalization under Uncertainty \textbf{(SAGU)}. Experiments on bivariate bicycle (BB) codes and their coprime variants demonstrate that (i) both QuBA and SAGU consistently outperform the classical baseline belief propagation (BP), achieving up to a \emph{two orders of magnitude} reduction in logical error rate (LER) under confident-decision bounds on the coprime BB code $[[154,6,16]]$; (ii) SAGU achieves decoding performance comparable to or even outperforming QuBA's domain-specific training approach.
In subjective image and video quality assessment, observers rate or compare selected stimuli. Before calculating mean opinion scores (MOSs), unreliable ratings should be identified and handled as outliers. Several outlier-detection methods are available, including standardized procedures, but their comparative performance is often evaluated using only specific types of synthetic outliers such as random clickers. Such tests do not necessarily reveal the worst-case behavior of these methods. To address this gap, we introduce and demonstrate a general empirical worst-case framework for outlier-detection methods, with proof-of-concept adversarial attack generators for both discrete absolute category and continuous visual analog scale ratings. The attacks use optimization algorithms to identify ratings that maximize the discrepancy between the resulting MOS estimates and the ground truth. We apply the proposed framework to several hard and soft outlier-detection methods and demonstrate substantial differences in their worst-case reconstruction performance under adversarial stress. We also propose several low-complexity outlier-detection methods that achieve excellent empirical worst-case performance.
Swarm-based optimization algorithms have demonstrated remarkable success in solving complex problems, yet their widespread adoption remains limited due to poor transparency in how algorithmic components influence performance. This work presents a multi-faceted explainability framework for Particle Swarm Optimization (PSO) through two complementary perspectives: landscape-based and algorithmic explainability. From the landscape-based perspective, we develop a comprehensive characterization framework using Exploratory Landscape Analysis (ELA) to quantify problem difficulty, multimodality, and ruggedness, extracting ELA meta-features, dispersion measures, and information content statistics, while a machine learning approach employing Decision Tree and Random Forest classifiers enables prediction of optimal topology-specific hyperparameter configurations for unseen problems. From the algorithmic explainability perspective, we integrate IOHxplainer for temporal convergence profiling and Search Trajectory Networks (STN) for spatial navigation mapping, proposing three novel STN metrics-Connectivity Density, Fragmentation Score, and Search Efficiency-that enhance visual explainability by quantifying topology-specific search organization and transition effectiveness. Through systematic experimentation across 24 benchmark functions in multiple dimensions with Star, Ring, and Von Neumann topologies, we establish practical guidelines for topology selection and parameter configuration. Our findings uncover the black-box nature of PSO, providing greater transparency and interpretability to swarm intelligence systems. The source code is available at https://github.com/GitNitin02/ioh_pso.
A new machine-learning framework aims to improve the success rate of computational protein design while moving away from results that reproduce sequences found in nature.
MIT News · Artificial Intelligence· news.mit.eduAug 24, 2026
A new method for surgically removing training examples from a model reveals that as datasets grow, the link between what a model learns and what it produces dissolves.
