ECA-BLS: An Efficient Complex-Augmented Broad Learning System

Broad Learning System (BLS) is an efficient alternative to deep architectures due to its fast training, analytical learning, and strong generalization under limited data. However, existing BLS variants are confined to real-valued representations, restricting their ability to capture nonlinear interactions and second-order statistical dependencies inherent in real-world data. Notably, no prior BLS model fully exploits the complete second-order statistics that naturally emerge when data are embedded in the complex domain. To address this limitation, this paper introduces the first complex augmented Broad Learning System (CA-BLS), which transforms real-valued inputs into phase-encoded complex representations and adopts widely linear modeling to jointly leverage covariance and pseudo-covariance information via complex conjugate augmentation. This enables effective modeling of latent nonlinearities, coherence structures, and second-order dependencies inaccessible to conventional BLS formulations. To mitigate the additional computational cost of complex augmentation, an Efficient Complex Augmented BLS (ECA-BLS) is further developed, reformulating CA-BLS entirely in the real domain while preserving its exact decision function, achieving up to 75\% fewer multiplications and over 60\% fewer additions. A rigorous theoretical analysis proves the mathematical equivalence between CA-BLS and ECA-BLS, ensuring zero theoretical loss. Extensive experiments on 26 benchmark datasets from the UCI and KEEL repositories demonstrate that ECA-BLS consistently outperforms classical BLS and recent state-of-the-art randomized neural networks in accuracy, average rank, and statistical significance, establishing augmented second-order modeling as a critical and previously missing dimension of BLS research.

GEAR: Generative Expansion and Real Anchoring for Two-Stage Distillation of Tabular Foundation Models

Tabular foundation models (TFMs) achieve strong performance through in-context learning, but context-dependent inference imposes substantial latency and memory costs, hindering large-scale deployment. We propose GEAR (\emph{Generative Expansion and Real Anchoring}), a modular two-stage framework that distills TFMs into lightweight MLP or tree-based predictors that can be deployed on commodity CPUs. Stage 1 uses synthetic covariates solely as teacher-query locations and trains the student on soft TFM targets, expanding coverage beyond observed rows. Stage 2 re-anchors the student to the target distribution using real labels and out-of-fold teacher predictions, whitch avoids self-labeling leakage. We further derive a risk certificate characterizing the trade-off between generated-query volume and generator fidelity. Experiments on TALENT and TabArena demonstrate the broad applicability of GEAR. Two-stage MLPs outperform supervised MLPs by 1.81--2.00 AUC points on binary tasks and 1.19--1.35 points on multiclass tasks, with additional gains over real-data-only distillation of 1.76--2.19 and 2.09--2.40 points, respectively. On binary tasks, the gains also transfer to LightGBM and XGBoost, and all three student families outperform CatBoost, the strongest non-TFM baseline, in mean AUC. Ablations show gains beyond longer training or alternative warm starts, greater stability from staged than mixed optimization, and generator-dependent diminishing returns as query volume increases. Finally, GEAR reduces median inference time by 57--2866 times and peak prediction memory by 1.9--3.3 times, while retaining higher AUC than matched supervised baselines.

TinyCast: Probabilistic Zero-Shot Forecasting with Computed Periodicity

We introduce TinyCast, an attention-free zero-shot forecaster that emits a predictive distribution from 146,505 parameters, on the premise that at this size the periodic structure of a context is worth computing rather than learning. A zero-parameter spectral detector supplies the dominant periods, the context is folded on their phase, and a dilated convolutional encoder and a block-autoregressive quantile decoder model the rest. It is smaller than every zero-shot entry on the GIFT-Eval board whose parameter count can be established. On probabilistic accuracy it defines the size-accuracy frontier. Among zero-shot entries declaring no test-data leakage it is the only one below 1.4M parameters that emits a predictive distribution, and every entry scoring better carries at least that budget. On Chronos-ZS and fev-bench every neural model ahead of it carries at least 28 times its parameters. Because the mixing path is convolutions and matrix multiplications only, it exports to static INT8 and forecasts end to end on an embedded device without per-signal fitting.

FirstDiff: One-Step Diffusion-Based Anomaly Detection for Multivariate Time Series via Initial Noise Prediction

Diffusion models have recently shown strong potential for multivariate time-series anomaly detection by learning the distribution of normal data through iterative denoising. Existing diffusion-based approaches, however, typically perform anomaly detection after completing the reverse diffusion process, relying primarily on the final reconstructed signal and overlooking informative representations produced during denoising. This design incurs substantial computational cost and limits the use of intermediate diffusion information for anomaly detection. In this paper, we propose FirstDiff, a diffusion-based anomaly detection framework based on the observation that the predicted diffusion noise at the initial reverse-diffusion evaluation already contains sufficient information for accurate anomaly detection. FirstDiff models the statistical distribution of predicted diffusion noise under normal behavior using validation data, enabling anomaly inference from a single denoising-network evaluation rather than completing the reverse diffusion trajectory. To model complex temporal and inter-sensor dependencies, FirstDiff employs a Diffusion Transformer as the denoising backbone. Extensive experiments on five public benchmark datasets demonstrate that FirstDiff achieves state-of-the-art performance while reducing diffusion inference from the full reverse trajectory to a single denoising-network evaluation.

TabSwift: An Efficient Tabular Foundation Model with Row-Wise Attention

Tabular foundation models, exemplified by TabPFN, perform prediction via in-context learning, inferring test labels directly from labeled training examples. They have demonstrated competitive performance, particularly on small-to-medium datasets. However, recent tabular foundation models often improve accuracy with increasingly complex architectures, incurring higher inference cost and limiting practical deployment. In this work, we revisit the original TabPFN design and show that a lightweight row-wise attention-only backbone can remain highly competitive with two simple enhancements: a gated attention stabilization mechanism and a small set of learnable register tokens that provide global context and improve pretraining quality. The resulting model, TabSwift, supports both classification and regression, and is competitive with stronger tabular foundation models (e.g., TabPFN v2 and TabICL) while being more efficient at inference. For latency-sensitive serving, we further introduce an adaptive layer-wise early-exit mechanism that dynamically adjusts inference depth per sample. Overall, TabSwift enables efficient and anytime tabular in-context learning for practical deployments.