Set Transformer

Recovering divergence-free velocity fields from sparse and corrupted observations requires reconciling physical consistency, expressive representations, and robustness to missing data. We introduce DFK-Former, a set-to-field transformer that reconstructs divergence-free velocity fields from sparse, noisy, and irregularly sampled 3D observations. The model is inherently invariant to the number and ordering of input samples and predicts the parameters of a divergence-free kernel representation, producing continuous, mesh-free velocity fields that satisfy incompressibility exactly by construction rather than approximately through soft constraints or projection operators. Unlike existing divergence-free kernel approaches, which estimate kernel coefficients via a separate optimization for each field, DFK-Former predicts these coefficients directly in a single forward pass. This eliminates costly iterative fitting while providing a learned prior that enables accurate reconstruction even when observations are insufficient to uniquely determine the field. To enhance representational power, we introduce adaptive and anisotropic divergence-free kernels that preserve exact incompressibility guarantees while capturing more complex flow structures. Extensive experiments across varying levels of sparsity, noise, and occlusion, including transfer to real Direct Numerical Simulation (DNS) turbulence data, demonstrate substantial gains in both accuracy and efficiency. DFK-Former reduces endpoint error by up to 4.6x compared to per-field divergence-free-kernel optimization, while reconstructing each field in 7.5 ms instead of 9.8 s, yielding a speedup of more than three orders of magnitude. These results establish direct, feed-forward prediction of divergence-free kernel parameters as a practical and effective paradigm for physically consistent velocity-field reconstruction from sparse observations.

Intracortical motor decoders degrade across sessions because the set of recorded units changes and persisting units can alter how their firing relates to behavior. Most existing methods update network weights on each new session or rely on unlabeled activity, which does not directly reveal such changes. We present APST, an Association Profile-conditioned Set-Temporal transformer that adapts to new sessions with all network weights frozen. From a few labeled calibration trials, APST summarizes how each unit's firing relates to behavior in a four-dimensional association profile computed in closed form. The profiles condition a set-attention encoder that accepts any number and order of units, followed by a causal transformer for streaming decoding. On held-out DANDI688 sessions from two monkeys, APST reaches velocity $R^2$ of $0.78$ and $0.81$, versus $0.40$ and $0.58$ for a variant that uses neural activity alone, and matches or exceeds an RNN fine-tuned on the same trials. On FALCON private held-out evaluation, it attains $R^2$ of $0.65$, $0.42$, and $0.44$ on M1, M2, and H1.

Automated acne severity grading requires both whole-face context and fine-grained lesion evidence. We propose LENS-GRF (Lesion Evidence Network with Set-Transformer and Gated Residual Fusion), an interpretable multi-stage framework for four-class acne severity grading. The method combines Adaptive Facial Skin Segmentation and a global Vision Transformer prior with a permutation-invariant Lesion Set Transformer that encodes localized lesion patches and spatial geometry. Gated Residual Fusion adaptively controls the local residual contribution and reduces to the global prediction when the gate is zero. On ACNE04, fully automated LENS-GRF with YOLOv11s achieved 80.82% accuracy; with ground-truth lesion annotations, it achieved 95.89% +/- 0.59% accuracy and a Quadratic Weighted Kappa of 0.9753. A data-integrity audit identified 15 cross-split duplicate image pairs, including five with conflicting severity labels. In locked zero-shot evaluation on the full PLSBRACNE01 cohort (200 subjects, 600 views), automated LENS-GRF achieved 35.00% accuracy versus 42.50% for the global baseline. On the 148-subject common cohort used for three-dermatologist oracle analysis, ground-truth lesion inputs increased the best oracle accuracy to 47.97%, while the highest oracle QWK was 0.5799. Pairwise oracle agreement ranged from 49.32% to 66.22%, highlighting detector domain shift, annotation variability, and cross-criterion mismatch.

Chess engines have evolved from search-based systems optimized solely for strength to neural policies capable of modeling human decisions across much of the rating spectrum. Maia-3, the strongest human-like move policy for chess, models the typical moves of a given rating but does not model high Elo strength well (2500+ Lichess Elo) nor has an extensible architecture for modeling individual play style. On the other hand, search-based engines like Stockfish are far stronger than any known human but struggle to model human-like play. To solve these problems, we present Matilda, a permutation-invariant set transformer that re-ranks the full legal-move distribution produced by a frozen Maia-3 and improves it along both dimensions with one 1.7M-parameter model. Matilda uses Maia-3 to provide both global context and search candidates. Context is encoded from Maia-3's hidden representation, time control, and an optional 32-dimensional player-style vector, while the top-16 candidate moves are optionally rescored by Stockfish. A zero-initialized head scatters per-candidate adjustments back into the policy logits, so the untrained model is exactly Maia-3 and every gain is value-added under full-vocabulary NLL. On a 2500+ Elo benchmark from Lichess, Matilda improves on Maia-3 by +0.5-0.6% below 2800 but +4.3%, +11.9%, and +21.9% at 2800-2900, 2900-3000, and 3000+, respectively, and an additional +0.41% overall from player-style embeddings. Ablations show that the improvements are primarily driven by the engine-derived features, the mechanism is not engine-specific, and the gains survive memorization, sibling, and account audits while preserving Maia-3 at 1000-2500 Elo. Because search supervision is modular, Matilda naturally supports interchangeable search engines, demonstrated by replacing Stockfish with an AlphaZero-family engine.

Passive long-wave infrared (LWIR) hyperspectral imaging under a standoff geometry depends on atmospheric absorption and emission, as well as reflected radiance, thus making atmospheric compensation essential to get knowledge of a target of interest. Despite its importance, this compensation has been largely overlooked due to its practical and modeling difficulty. In this paper, we present a lightweight set-based deep learning framework that takes multiple radiance measurements, collected at different standoff ranges, as input and jointly estimates transmittance, atmospheric path radiance, and a shared downwelling spectrum. We analyze the learned representation with a sparse autoencoder and observe that several latent features do activate on geographically coherent subsets of the test data despite the absence of location supervision. Experiments on a MODTRAN generated standoff LWIR dataset demonstrate low spectral distortion across all estimated products. The dataset and code is publicly available at: https://factral.co/SAE-LWIR/

Finding symmetries is crucial for understanding physical models. In this work, we present an optimization framework that searches Pauli symmetries of Hamiltonians, merging the fields of machine learning with automated symmetry finding. Built on a Set-Transformer architecture, our framework uses self-attention to encode the pairwise and higher-order correlations among the Pauli-Strings. The relations are then decoded as a candidate, which is further optimized with a custom commutation-based objective, and mapped to a symmetry of the input Hamiltonian. We apply our method to random Pauli Hamiltonians, periodic one and two dimensional transverse-field Ising model and the Toric code. We show that for physical Hamiltonians (Ising and Toric), our framework succeeds with near-deterministic probability while providing substantial advantage compared to state-of-the-art strategies. For random Pauli Hamiltonians, we estimate the required computational resources, specifically the number of parallel starts and the number of GPUs, to find a symmetry with high success probability under fixed design specifications.

Dynamic feature selection (DFS) is a machine learning framework in which features are acquired sequentially for individual samples under budget constraints. The exponential growth in the number of possible feature acquisition paths forces a DFS model to balance fitting specific scenarios against maintaining general performance, even when the feature space is moderate in size. In this paper, we study the structural limitations of existing DFS approaches to achieve an optimal solution. Then, we propose Hyper-DFS, a hypernetwork-based DFS approach that generates feature subset-specific classifier parameters on demand. We show that the use of hypernetworks compared to mask-embedding methods results in a smaller structural complexity bound. We also use a Set Transformer encoding to create a smooth conditioning space for the hypernetwork, so that functionally similar tasks are also geometrically close. In our benchmarks, Hyper-DFS performed best or second best compared to all state-of-the-art approaches on synthetic and real-life tabular data. It is also best or second best across all image datasets tested, and shows stronger zero-shot generalisation to feature subsets never seen during training than existing DFS approaches. Code available in: https://github.com/Fuminides/hyper_DFS

Electronic health records (EHR) are irregular, asynchronous multivariate time series. As time-series foundation models increasingly tokenize events rather than discretizing time, the input layout becomes a key design choice. Grids expose time$\times$variable structure but require imputation or missingness masks, risking error or sampling-policy shortcuts. Point-set tokenization avoids discretization but loses within-variable trajectories and time-local cross-variable context (Fig.1). We restore these priors in STructure-AwaRe (STAR) Set Transformer by adding parameter-efficient soft attention biases: a temporal locality penalty $-|Δt|/τ$ with learnable timescales and a variable-type affinity $B_{s_i,s_j}$ from a learned feature-compatibility matrix. We benchmark 10 depth-wise fusion schedules (Fig.2). On three ICU prediction tasks, STAR-Set achieves AUC/APR of 0.7158/0.0026 (CPR), 0.9164/0.2033 (mortality), and 0.8373/0.1258 (vasopressor use), outperforming regular-grid, event-time grid, and prior set baselines. Learned $τ$ and $B$ provide interpretable summaries of temporal context and variable interactions, offering a practical plug-in for context-informed time-series models.