While Large language models (LLMs) are driving the rapid advancement of artificial intelligence, effectively and reliably training these large models remains one of the field's most significant challenges. To address this challenge, we propose POET, a novel reParameterized training algorithm that uses Orthogonal Equivalence Transformation to optimize neurons. Specifically, POET reparameterizes each neuron with two learnable orthogonal matrices and a fixed random weight matrix. Because of its provable preservation of spectral properties of weight matrices, POET can stably optimize the objective function with improved generalization. We further develop efficient approximations that make POET flexible and scalable for training large-scale neural networks.

Inspired by the workings of biological brains, humans have designed artificial neural networks (ANNs), sparking profound advancements across various fields. However, the biological brain possesses high plasticity, enabling it to develop simple, efficient, and powerful structures to cope with complex external environments. In contrast, the superior performance of ANNs often relies on meticulously crafted architectures, which can make them vulnerable when handling complex inputs. Moreover, overparameterization often characterizes the most advanced ANNs. This paper explores the path toward building streamlined and plastic ANNs.

We introduce Time-Conditioned Contraction Matching (TCCM), a novel method for semi-supervised anomaly detection in tabular data. TCCM is inspired by flow matching, a recent generative modeling framework that learns velocity fields between probability distributions and has shown strong performance compared to diffusion models and generative adversarial networks. Instead of directly applying flow matching as originally formulated, TCCM builds on its core idea--learning velocity fields between distributions--but simplifies the framework by predicting a time-conditioned contraction vector toward a fixed target (the origin) at each sampled time step. This design offers three key advantages: (1) a lightweight and scalable training objective that removes the need for solving ordinary differential equations during training and inference; (2) an efficient scoring strategy called one time-step deviation, which quantifies deviation from expected contraction behavior in a single forward pass, addressing the inference bottleneck of existing continuous-time models such as DTE (a diffusion-based model with leading anomaly detection accuracy but heavy inference cost); and (3) explainability and provable robustness, as the learned velocity field operates directly in input space, making the anomaly score inherently feature-wise attributable; moreover, the score function is Lipschitz-continuous with respect to the input, providing theoretical guarantees under small perturbations. Extensive experiments on the ADBench benchmark show that TCCM strikes a favorable balance between detection accuracy and inference cost, outperforming state-of-the-art methods--especially on high-dimensional and large-scale datasets.

Many Deep Reinforcement Learning (DRL) algorithms are sensitive to time discretization, which reduces their performance in real-world scenarios. We propose Continuous Soft Actor-Critic, an off-policy actor-critic DRL algorithm in continuous time and space. It is robust to environment time discretization. We also extend the framework to multi-agent scenarios. This Multi-Agent Reinforcement Learning (MARL) algorithm is suitable for both competitive and cooperative settings.

In-context learning (ICL) is a hallmark capability of transformers, through which trained models learn to adapt to new tasks by leveraging information from the input context. Prior work has shown that ICL emerges in transformers due to the presence of special circuits called induction heads. Given the equivalence between induction heads and conditional k-grams, a recent line of work modeling sequential inputs as Markov processes has revealed the fundamental impact of model depth on its ICL capabilities: while a two-layer transformer can efficiently represent a conditional 1-gram model, its single-layer counterpart cannot solve the task unless it is exponentially large. However, for higher order Markov sources, the best known constructions require at least three layers (each with a single attention head) -- leaving open the question: can a two-layer single-head transformer represent any kth-order Markov process? In this paper, we precisely address this and theoretically show that a two-layer transformer with one head per layer can indeed represent any conditional k-gram. Thus, our result provides the tightest known characterization of the interplay between transformer depth and Markov order for ICL. Building on this, we further analyze the learning dynamics of our two-layer construction, focusing on a simplified variant for first-order Markov chains, illustrating how effective in-context representations emerge during training. Together, these results deepen our current understanding of transformer-based ICL and illustrate how even shallow architectures can surprisingly exhibit strong ICL capabilities on structured sequence modeling tasks. Code is available at thelink.

Designing model architectures requires decisions such as selecting operators (e.g., attention, convolution) and configurations (e.g., depth, width). However, evaluating the impact of these decisions on model quality requires costly pretraining, limiting architectural investigation. Inspired by how new software is built on existing code, we ask: can new architecture designs be studied using pretrained models? To this end, we present grafting, a simple approach for editing pretrained diffusion transformers (DiTs) to materialize new architectures under small compute budgets. Informed by our analysis of activation behavior and attention locality, we construct a testbed based on the DiT-XL/2 design to study the impact of grafting on model quality. Using this testbed, we develop a family of hybrid designs via grafting: replacing softmax attention with gated convolution, local attention, and linear attention, and replacing MLPs with variable expansion ratio and convolutional variants. Notably, many hybrid designs achieve good quality (FID: 2.38-2.64 vs. 2.27 for DiT-XL/2) using < 2% pretraining compute.

Kolmogorov-Arnold Networks (KANs) approximate multivariate functions using learnable univariate edge functions, typically parameterized by B-spline bases. Although effective, spline-based implementations can be computationally expensive. A modified version of KANs, called FastKAN, improves efficiency by replacing splines with Gaussian radial basis functions (RBFs), but it relies on a fixed kernel and shape parameter. In this work, we extend the RBF-based KAN framework by introducing a broader family of radial basis kernels and by initializing the kernel shape parameter using leave-one-out cross-validation (LOOCV). To the best of our knowledge, this is the first study that integrates LOOCV-based kernel scale estimation with deep KAN training. We also introduce Matérn and Wendland kernels into the KAN framework for the first time, enabling more flexible basis representations beyond the Gaussian kernel used in FastKAN. The LOOCV estimate provides a data-driven initialization of the kernel scale, which is subsequently refined during network training. The proposed adaptive RBF-KAN is evaluated on several two-dimensional benchmark functions. The results highlight the importance of kernel selection and adaptive shape parameters, with different kernels showing advantages for smooth functions, discontinuities, and oscillatory patterns. Overall, combining LOOCV-based initialization with adaptive kernel learning provides a practical strategy for improving RBF-based KAN models.

In modern deep learning, weight decay is often credited with "stabilizing" training dynamics, diverging from its classical role as a static regularization penalty. We investigate a fundamental question: *does weight decay stabilize training dynamics, and if so, through which mechanism?* Indeed, training stability is understood through different but related notions in the literature. We consider how weight decay affects the parameter-space dynamics and loss sharpness by analyzing its effects at the \emph{Edge of Stability} (EoS). We show that weight decay robustly slows *progressive sharpening}. Furthermore, we uncover a striking architecture-dependent phase transition. In CNNs, weight decay dampens the oscillations at the EoS, while in MLPs, increasing weight decay causes a phase transition in which the sharpness stabilizes at a threshold significantly below the theoretical $\frac{2}η$ boundary. We develop a mathematical framework that accurately models these phenomena and identify the global alignment of the parameter vector and the sharpness gradient as the mechanistic driver of the phase transition. Importantly, we show that these phenomena translate into stability in terms of search in function-space (NTK). Last, this shows that curvature thresholds obtained from convex/quadratic heuristics may not be reliable stability diagnostics under regularization.

Transformer blocks typically combine multi-head attention (MHA) for token mixing with gated MLPs for token-wise feature transformation, yet many choices in their parameterization remain largely empirical. We introduce Causal Energy Minimization (CEM), a framework that recasts Transformer layers as optimization steps on conditional energy functions while explicitly accounting for layer parameterization. Extending prior energy-based interpretations of attention, CEM shows that weight-tied MHA can be derived as a gradient update on an interaction energy, and that a gated MLP with shared up/down projections can be viewed through an element-wise energy. This perspective identifies a design space for Transformer layers that includes within-layer weight sharing, diagonal-plus-low-rank interactions, lightweight preconditioners, and recursive updates. We evaluate CEM-derived layers in language-modeling experiments at the moderate hundred-million-parameter scale. Despite their constrained parameterizations, these layers train stably and can match corresponding Transformer baselines. Overall, our results suggest that CEM provides a useful lens for understanding Transformer layer parameterization, connecting Transformer architectures to energy-based models and motivating further exploration of energy-guided layer designs.

Survival analysis on tabular data is a well-studied problem. However, existing deep learning methods are often highly task-specific, which can limit the transfer of new approaches from other domains and introduce constraints that may affect performance. We propose TabSurv, an approach that adapts modern tabular architectures to survival analysis using either the Weibull distribution or non-parametric survival prediction. TabSurv optimizes SurvHL, a novel histogram loss function supporting censored data. In addition to a baseline feed-forward network, we implement deep ensembles of MLPs for survival analysis within TabSurv. In contrast to prior work, the ensemble components are trained in parallel, optimizing survival distribution parameters before averaging, which promotes diversity across ensemble component predictions. We perform a comprehensive empirical evaluation of different proposed architectures on 10 diverse real-world survival datasets. Our results show that TabSurv consistently outperforms on average established classical and deep learning baselines, such as RSF, DeepSurv, DeepHit, SurvTRACE. Notably, deep ensembles with Weibull parametrization instead of non-parametric models achieve the highest average rank by C-index. Overall, our study clarifies how modern tabular neural networks can be adapted and trained to tackle survival analysis problems, offering a strong and reliable approach. The TabSurv implementation is publicly available.