We study kernel ridge regression under anisotropic Gaussian data, where the input covariance decays as a power law with exponent $\alpha\geq 0$ for polynomial inner-product kernels. We derive asymptotically sharp expressions for the kernel spectrum and the generalization error in the polynomial high-dimensional regime $n=\Theta(d^\kappa)$, revealing how anisotropy reshapes the learning curves. For weak anisotropy ($0<\alpha<1$), the problem remains effectively high-dimensional and retains some features of the isotropic case, while departing from it in others: the variance still peaks at integer sample complexities $\kappa\in\mathbb{N}$, but these peaks are progressively damped as $\alpha$ grows; meanwhile, for targets strongly aligned with the data's principal directions, the bias drops at fractional sample complexities, decoupling the bias transitions from the interpolation peaks. For strong anisotropy ($\alpha > 1$), the effective dimension of the problem is constant, and the variance stops depending on sample size altogether, plateauing under ridgeless interpolation or vanishing at an explicit rate under fixed ridge penalty. The bias undergoes a sharp transition governed by the target's decay rate: below a threshold, learning is abrupt rather than gradual; above it, the bias decays as a power law that recovers the classical source and capacity rates. We finally specialize these results to single-index targets, showing how the alignment of the index with the data's principal directions determines the effect of anisotropy on learning. Together, our results clarify how the input geometry shapes the kernel features and fundamentally impacts its generalization properties.
Lorenzo Rizzi, Arie Wortsman Zurich, Bruno Loureiro· 0 citations
Interactive dialogue games test a capability that static benchmarks largely leave implicit: a model must carry state across turns, interpret feedback, and choose valid actions under changing constraints. We study this setting in the LM Playschool Challenge with a 2B open-weight model, and find that many failures are not only broad knowledge failures but also local decision failures: repeated guesses, malformed actions, and violations of feedback that the model has just seen. These diagnostics motivate a training recipe organized around three steps: acquire broad game participation through supervised fine-tuning, repair mechanically verifiable failures within one targeted dialogue-game family using turn-local preference pairs, and preserve general capabilities beyond these dialogue games. In the official final evaluation, our submission improves public clemscore from 10.67 to 38.92 and closed in-domain score from 13.41 to 41.17, while approximately preserving aggregate static performance (44.14 vs. 44.24 for the baseline). Out-of-domain clemscore remains low at 7.88, with the largest gains concentrated in unseen variants of the targeted family. Our results suggest that broad SFT brings most of the model's capability improvement; turn-local supervision can be effective when failure detection is precise, with observed transfer concentrated primarily within-family.
For finite-dimensional linear inverse problems where the variables are Gaussian, it is well-known that the minimum-mean-square error estimator takes the form of a regularized least-squares data fit. In this chapter, we show that this equivalence extends to a much broader infinite-dimensional setting where generalized splines take the role of linear regressors and generalized Gaussian processes on a nuclear space $S$ are the counterpart of Gaussian random vectors. The scope of this extension is of the same nature as the switch from the classic notion of function to that of a distribution, also known as a "generalized function." Our formalism involves a whitening/regularization operator $L: S\to S'$ whose continuous extension induces a native Hilbert space $H\subset S'$ that plays a central role in our characterization. The presentation is self-contained for the most part and remarkably general and powerful. It allows for the recovery of all known instances of such equivalences; in particular, the methods involving innovations and reproducing-kernel Hilbert spaces developed by Kailath and his students, and the mathematical correspondence between fractional splines and Mandelbrot's fractional Brownian motion (fractals), with the former being the optimal estimators of the latter. It also covers general Bayesian methods for the resolution of infinite-dimensional inverse problems.
Due to the nature of quadratic attention, Large Language Models (LLMs) consume a lot of memory and energy. Every new token costs more than the previous one. For each additional token, the keys and values must be stored in memory indefinitely, which is unsustainable.
Several alternatives have been proposed to fix the quadratic scaling problem, one of which is retrofitting LLMs to use Linear Attention. This idea has attracted a lot of attention, given its promise to solve the quadratic scaling problem with state-of-the-art performance at low cost. However, this line of research has not been properly compared to simpler baselines.
In this work, we show that Sliding Window Attention (SWA) with sinks performs as well or better than post-trained Linear Attention models. We observe this across multiple LLMs on various downstream tasks. For long-context reasoning tasks (Needle-in-a-Haystack and BABILong), SWA achieves massively higher performance (2 to 10 times higher than linear attention). SWA requires no post-training, is extremely fast, and requires low memory; therefore, making it an extremely cheap and reliable solution.
To reduce inference memory cost, we strongly recommend switching to SWA instead of post-training linear models. Linear attention models may have shown some promise, but they likely require to be trained from scratch or extensive post-training in order to even match SWA.
Human mistakes are inevitable when following instructions, yet they can lead to severe consequences. As such, there has been an increased interest in developing methods for detecting mistakes in videos, with current methods mostly focusing on closed-set protocols. While successful in controlled settings, the closed-set assumption limits their wider applicability, as any changes to the task require collecting new data and re-training models. Instead, we argue that mistake detection methods should learn the general concept of a mistake, rather than overfitting to step-specific details. To reflect this, we introduce the Mistake Detection Video Question Answering (MD-VQA) protocol and accompanying benchmark. MD-VQA tests whether methods can discern if a step was executed correctly with respect to its description, for both seen and unseen actions. To address this important challenge, we propose the first video-language-model post-training technique for mistake detection. Our method uses a tailored reward function to encourage the model to identify discrepancies between an instruction and the corresponding video. Extensive evaluations demonstrate that this approach outperforms zero-shot, supervised fine-tuning, and post-training baselines. Notably, our method generalizes especially well to unseen procedures, for instance, with an improvement of up to 11.6% over the best-performing baseline on EP-VQA, paving the way toward general mistake detection. We release our code and benchmark at https://github.com/FedeSpu/mstk.
Federico Spurio, Olga Zatsarynna, Lars Doorenbos et al.· 0 citations
Quantum federated learning enables collaborative model training across quantum devices without sharing raw data, and it faces the data and hardware heterogeneity inherent to noisy quantum devices. Utilizing the quantum geometric tensor is a natural remedy, yet pure-state approaches and diagonal approximations discard the correlations that encode parameter incompatibility. To address this, we extend the parameter-space geometry to the mixed states that noisy clients actually prepare. The real part of the resulting mixed-state geometric tensor is the Bures metric, which measures how fast the physical state changes under parameter variation, and the imaginary part is the mean Uhlmann curvature, which quantifies the incompatibility of estimating multiple parameters simultaneously. Accordingly, we employ the Bures metric as a local preconditioner and use the mean Uhlmann curvature to develop an achievable-precision aggregation rule that dynamically down-weights unreliable clients. Furthermore, we establish theoretical guarantees by proving a convergence theorem and a variance-dominance proposition. Empirical evaluations on a trapped-ion quantum emulator demonstrate that the proposed method maintains high accuracy across diverse device-heterogeneity conditions and outperforms standard federated averaging, whose accuracy degrades under strong noise.
Global goodness-of-fit and discrepancy statistics can establish that a sample departs from a reference distribution without identifying which observations drive the departure. We develop a framework for this localization problem by assigning to each observation its conditional or marginal contribution across random statistical contexts. This connects resampling diagnostics and data valuation to projection theory and event-level anomaly detection. For symmetric statistics, fixed-size replacement is exactly equivalent to centered conditional localization. For U-statistics, the addition score equals the first Hoeffding/H\'ajek contribution; for smooth distributional functionals it is related at leading order to the influence function; and for unbiased known-background MMD it reduces exactly to the MMD witness.
This viewpoint also yields more efficient estimators. Matched-context subtraction removes fluctuations unrelated to the observation, while for pairwise MMD the event-containing terms give a simple localizer. On the LHC Olympics anomaly-detection benchmark, the pair estimator converges to the direct empirical MMD witness with the predicted 1/(Rm^2) scaling, where m is batch size and R the number of batches. At m=1000 and R=5x106 it reaches correlation 0.9993 with essentially identical AUC.
We also ask when context contains information beyond an event's own features. In a shared-latent toy model, the full single-event signal and background distributions are identical by construction, forcing isolated-event AUC=0.5. Discriminating information survives only in cross-event dependence induced by the shared latent parameter; the ensemble recovers this information, whereas an independent-latent control does not. This separates two roles of context: efficient localization of a global discrepancy and genuinely additional class information when the alternative contains shared structure.
State estimation in magnetohydrodynamic flows is critical for real-time monitoring of liquid metal blankets in tokamak fusion reactors. Due to the multiphysics nature of these phenomena, high-fidelity simulations are computationally prohibitive for real-time applications. This work investigates a data- driven Reduced Order Model framework: the Shallow Recurrent Decoder (SHRED) coupled with Principal Component Analysis, to map sparse temperature measurements to the full thermo-hydraulic system's state. The major contribution of this work lies in the two-parameter analysis of a fully three-dimensional domain representative of the DEMO breeding blanket configuration. Here, the flow is subjected to an external magnetic field varying in direction and intensity and is hindered by two cylinders acting as a water-cooling system, which impose a temperature boundary condition on their surfaces. This double-parametric magnetic variation induces nonlinear transitions in the flow dynamics, ranging from chaotic behavior at low magnetic field intensities to laminarized regimes at high intensities, characterized by the formation of asymmetric side layers at an inclination angle of 30 degrees. SHRED reconstruction maintains a mean relative error of approximately 5% for the temperature, pressure, and velocity fields. This accuracy is maintained across both weak and strong magnetic fields, ranging from 0.075 T to 0.300 T, and for inclination angles from 5 to 30 degrees, reflecting its dominant toroidal component. These errors are only slightly larger than the lower error bound dictated by low-rank truncation. The results establish SHRED as a reliable state estimator for complex and realistic engineering applications involving completely unseen parametric scenarios and validate it as an accurate real-time state estimation technique suitable for online monitoring and control of real facilities.
Claudio Scardino, Stefano Riva, Carolina Introini et al.· 0 citations
We extend the FLOP (fast learning of order and parents) algorithm recently proposed by Wien\"obst et al. (2026) from observational to interventional data. In particular, we use the interventional BIC score of Hauser and B\"uhlmann (2012), adapting it to be used with the iterative Cholesky-based score updates that are partly responsible for FLOP's speed. We show that, in the sample limit, I-FLOP recovers a DAG in the same interventional Markov equivalence class as the data-generating DAG. We compare I-FLOP to existing causal structure learning algorithms on real and simulated interventional data, where it performs favorably in terms of both performance and run time.
Diabetic retinopathy (DR) is a major cause of preventable blindness, creating a need for accurate and trustworthy automated screening. This study investigates an explainable DR classification framework using vision foundation models and multiple transfer learning strategies. Three backbones, DINOv2, CLIP, and Vision Transformer (ViT), were evaluated using full fine-tuning, linear probing, and Low-Rank Adaptation (LoRA). Models were trained and internally evaluated on the ODIR dataset and externally evaluated on APTOS to assess generalization. DINOv2-LoRA achieved the highest internal AUROC of 0.758, while DINOv2 full fine-tuning and ViT full fine-tuning achieved the highest external AUROC of 0.920. Calibration was further assessed using reliability analysis after isotonic regression. For explainability, Grad-CAM and HiResCAM were evaluated against expert-annotated lesion masks from the IDRiD dataset using Dice, Intersection over Union (IoU), and Pointing Game metrics. The results demonstrate that foundation models, particularly DINOv2, can provide strong predictive performance, while LoRA offers a parameter-efficient alternative to full fine-tuning. Quantitative evaluation of explanation maps further supports the assessment of whether model attention corresponds to clinically relevant retinal lesions.
Vision Foundation Models (VFMs) are widely used in computational pathology but remain sensitive to domain shifts arising from variations in staining, tissue preparation, and scanner hardware. A key limitation is that VFM embeddings entangle biological with domain-specific information, hindering cross-domain generalization. We propose Explainable Probing of Cross-Domain Sparse Embeddings (EXPOSE), a framework that uses Sparse Autoencoders (SAEs) as an explainable bottleneck to identify and suppress domain-specific components in VFM embeddings. We train a sparse representation of VFM features, use a linear classifier to identify domain-specific latent dimensions, and mask these features prior to downstream relapse prediction without retraining the backbone model. Experiments on a large prostate cancer dataset with multiple acquisition domains show that SAE features capture both domain- and task-specific information, which are partially disentangled in the latent space. Removing domain-specific features improves cross-domain performance and increases embedding robustness as measured by the Domain Robustness Index (DoRI). Code is available at https://github.com/imsb-uke/expose .
Anja Witte, Maximilian Lennartz, Jan Baumbach et al.· 0 citations
Mango variety identification in Bangladesh is challenging because closely related cultivars can have similar visual characteristics and images are often captured under varying real-world conditions. This work presents a deep learning-based web system for automatic identification of Bangladeshi mango varieties. We collected 2,013 high-quality mango images (3024x4032 pixels) from local markets and farms and organized them into nine classes, combining Bari-4 and Bari-7 as a single Bari class. The dataset was divided into training (70%), validation (15%), and test (15%) sets, with image augmentation applied to improve model generalization. Three pretrained CNN architectures, ResNet18, ResNet50, and EfficientNetB0, were fine-tuned under consistent training settings. EfficientNetB0 achieved the best performance, obtaining 98.01% validation accuracy and 97.36% test accuracy, compared with 86.47% and 78.55% test accuracy for ResNet18 and ResNet50, respectively. Class-wise F1-scores for EfficientNetB0 ranged from 0.93 to 0.99, while the Bari class achieved an F1-score of 0.97. The selected EfficientNetB0 model has approximately 4 million parameters, making it suitable for lightweight deployment. We integrated the model into a Streamlit web application that enables users to upload a mango image and receive a predicted variety with class probabilities. The system provides an accessible, practical tool for mango identification and demonstrates the potential of deep learning for supporting agricultural applications in Bangladesh.
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.
