Figure 1: Fourteen queries used in the experiments. They do not contain personally identifiable information or offensive content. All the models are implemented in Pytorch [5] and based on the official implementation of BETAE [6]2 for a fair comparison. Forall the modules using multi-layer perceptron (MLP), we use a three-layer MLP with 1600 hidden neurons and ReLU activation. We apply dropout to the min function inCardMin and search the dropout rate in{0.05,0.10,0.15,0.20}.

Normative modeling estimates reference distributions of biological measures conditional on covariates, enabling centiles and clinically interpretable deviation scores to be derived. Most neuroimaging pipelines fit one model per imaging-derived phenotype (IDP), which scales well but discards multivariate dependence that may encode coordinated patterns. We propose denoising diffusion probabilistic models (DDPMs) as a unified conditional density estimator for tabular IDPs, from which univariate centiles and deviation scores are derived by sampling. We utilise two denoiser backbones: (i) a feature-wise linear modulation (FiLM) conditioned multilayer perceptron (MLP) and (ii) a tabular transformer with feature self-attention and intersample attention (SAINT), conditioning covariates through learned embeddings. We evaluate on a synthetic benchmark with heteroscedastic and multimodal age effects and on UK Biobank FreeSurfer phenotypes, scaling from dimension of 2 to 200. Our evaluation suite includes centile calibration (absolute centile error, empirical coverage, and the probability integral transform), distributional fidelity (Kolmogorov-Smirnov tests), multivariate dependence diagnostics, and nearest-neighbour memorisation analysis. For low dimensions, diffusion models deliver well-calibrated per-IDP outputs comparable to traditional baselines while jointly modeling realistic dependence structure. At higher dimensions, the transformer backbone remains substantially better calibrated than the MLP and better preserves higher-order dependence, enabling scalable joint normative models that remain compatible with standard per-IDP pipelines. These results support diffusion-based normative modeling as a practical route to calibrated multivariate deviation profiles in neuroimaging.

Ultrafast online learning is essential for high-frequency systems, such as controls for quantum computing and nuclear fusion, where adaptation must occur on sub-microsecond timescales. Meeting these requirements demands low-latency, fixed-precision computation under strict memory constraints, a regime in which conventional Multi-Layer Perceptrons (MLPs) are both inefficient and numerically unstable. We identify key properties of Kolmogorov-Arnold Networks (KANs) that align with these constraints. Specifically, we show that: (i) KAN updates exploiting B-spline locality are sparse, enabling superior on-chip resource scaling, and (ii) KANs are inherently robust to fixed-point quantization. By implementing fixed-point online training on Field-Programmable Gate Arrays (FPGAs), a representative platform for on-chip computation, we demonstrate that KAN-based online learners are significantly more efficient and expressive than MLPs across a range of low-latency and resource-constrained tasks. To our knowledge, this work is the first to demonstrate model-free online learning at sub-microsecond latencies.

We study potential presence of statistical-computational gaps (SCG) in symmetric binary perceptrons (SBP) via a parametric utilization of \emph{fully lifted random duality theory} (fl-RDT) [96]. A structural change from decreasingly to arbitrarily ordered $c$-sequence (a key fl-RDT parametric component) is observed on the second lifting level and associated with \emph{satisfiability} ($α_c$) -- \emph{algorithmic} ($α_a$) constraints density threshold change thereby suggesting a potential existence of a nonzero computational gap $SCG=α_c-α_a$. The second level estimate is shown to match the theoretical $α_c$ whereas the $r\rightarrow \infty$ level one is proposed to correspond to $α_a$. For example, for the canonical SBP ($κ=1$ margin) we obtain $α_c\approx 1.8159$ on the second and $α_a\approx 1.6021$ (with converging tendency towards $\sim 1.59$ range) on the seventh level. Our propositions remarkably well concur with recent literature: (i) in [20] local entropy replica approach predicts $α_{LE}\approx 1.58$ as the onset of clustering defragmentation (presumed driving force behind locally improving algorithms failures); (ii) in $α\rightarrow 0$ regime we obtain on the third lifting level $κ\approx 1.2385\sqrt{\frac{α_a}{-\log\left ( α_a \right ) }}$ which qualitatively matches overlap gap property (OGP) based predictions of [43] and identically matches local entropy based predictions of [24]; (iii) $c$-sequence ordering change phenomenology mirrors the one observed in asymmetric binary perceptron (ABP) in [98] and the negative Hopfield model in [100]; and (iv) as in [98,100], we here design a CLuP based algorithm whose practical performance closely matches proposed theoretical predictions.

Graph Neural Networks (GNNs) have shown superior performance in node classification. However, GNNs perform poorly in the Few-Shot Node Classification (FSNC) task that requires robust generalization to make accurate predictions for unseen classes with limited labels. To tackle the challenge, we propose the integration of Sharpness-Aware Minimization (SAM)--a technique designed to enhance model generalization by finding a flat minimum of the loss landscape--into GNN training. The standard SAM approach, however, consists of two forward-backward steps in each training iteration, doubling the computational cost compared to the base optimizer (e.g., Adam). To mitigate this drawback, we introduce a novel algorithm, Fast Graph Sharpness-Aware Minimization (FGSAM), that integrates the rapid training of Multi-Layer Perceptrons (MLPs) with the superior performance of GNNs. Specifically, we utilize GNNs for parameter perturbation while employing MLPs to minimize the perturbed loss so that we can find a flat minimum with good generalization more efficiently.

The remarkable capabilities of modern large language models are rooted in their vast repositories of knowledge encoded within their parameters, enabling them to perceive the world and engage in reasoning. The inner workings of how these models store knowledge have long been a subject of intense interest and investigation among researchers. To date, most studies have concentrated on isolated components within these models, such as the Multilayer Perceptrons and attention head. In this paper, we delve into the computation graph of the language model to uncover the knowledge circuits that are instrumental in articulating specific knowledge. The experiments, conducted with GPT2 and TinyLLAMA, has allowed us to observe how certain information heads, relation heads, and Multilayer Perceptrons collaboratively encode knowledge within the model. Moreover, we evaluate the impact of current knowledge editing techniques on these knowledge circuits, providing deeper insights into the functioning and constraints of these editing methodologies. Finally, we utilize knowledge circuits to analyze and interpret language model behaviors such as hallucinations and in-context learning. We believe the knowledge circuit holds potential for advancing our understanding of Transformers and guiding the improved design of knowledge editing.