Several recently introduced deep learning optimizers utilizing matrix-level preconditioning have shown promising speedups relative to the current dominant optimizer AdamW, particularly in relatively small-scale experiments. However, efforts to validate and replicate their successes have reported mixed results. To better understand the effectiveness of these optimizers at scale, in this work we investigate how to scale preconditioned optimizers via hyperparameter transfer, building on prior works such as µP. We study how the optimal learning rate and weight decay should scale with model width and depth for a wide range of optimizers, including Shampoo, SOAP, and Muon, accounting for the impact of commonly used techniques such as blocking and grafting. We find that scaling the learning rate according to µP improves transfer, but can still suffer from significant finite-width deviations that cause drifting optimal learning rates, which we show can be mitigated by blocking and explicit spectral normalization. For compute-optimal scaling, we find scaling independent weight decay as 1/width is nearly optimal across optimizers. Applying these scaling rules, we show Muon, SOAP and Shampoo consistently achieve near 1.4 speedup over AdamW for training Llama-architecture language models of sizes ranging from 190M to 1.4B, whereas the speedup vanishes rapidly with scale under incorrect scaling. Based on these results and further ablations, we argue that studying optimal hyperparameter transfer is essential for reliably comparing optimizers at scale given a realistic tuning budget.

Prompt tuning has emerged as a powerful parameter-efficient fine-tuning technique, allowing large pretrained Transformers to adapt to downstream tasks by optimizing a small set of prompt embeddings. Despite its empirical success, the extent to which prompt tuning can memorize data remains poorly understood. In this paper, we provide both theoretical and empirical analyses of data memorization ability of prompt-tuned Transformers. Building on recent theoretical frameworks, we derive an upper bound on the required prompt length for exact memorization of finite datasets and establish a trade-off between prompt length and the number of autoregressive generation steps. Specifically, we show that a constant-size Transformer can memorize ninput-output pairs with prompts of length O( nN), where N denotes the sequence length. Empirical results further demonstrate that prompt-tuned, randomly initialized Transformers are able to effectively memorize finite datasets. These models also capture the intrinsic low-rank structure of the data, leading to a reduction in the required prompt length. Finally, we analyze how the initialization of the Transformer backbone affects the performance of prompt tuning. Our findings provide new insights into the expressivity, efficiency, and underlying mechanisms of prompt tuning, bridging theoretical memorization limits with observed empirical behaviors.

The success of Graph Neural Networks (GNNs) leverages the homophily principle, where connected nodes share similar features and labels. However, this assumption breaks down in heterophilic graphs, where same-class nodes are often distributed across distant neighborhoods rather than immediate connections. Recent attempts expand the receptive field through multi-hop aggregation schemes that explicitly preserve intermediate representations from each hop distance. While effective at capturing heterophilic patterns, these methods require separate weight matrices per hop and feature concatenation, causing parameters to scale linearly with hop count. This leads to high computational complexity and GPU memory consumption. We propose Gated Multi-hop Message Passing (GAMMA), where nodes assess how relevant the aggregated information is from their k-hop neighbors. This assessment occurs through multiple refinement steps where the node compares each hop's embedding with its current representation, allowing it to focus on the most informative hops. During the forward pass, GAMMA finds the optimal mix of multi-hop information local to each node using a single feature vector without needing separate representations for each hop, thereby maintaining dimensionality comparable to single hop GNNs. In addition, we propose a weight sharing scheme that leverages a unified transformation for aggregated features from multiple hops so the global heterophilic patterns specific to each hop are learned during training.

The proliferation of large-scale and structurally complex data has spurred the integration of machine learning methods into statistical modeling. Recurrent neural networks (RNNs), a foundational class of models for time-dependent data, can be viewed as nonlinear extensions of classical autoregressive moving average models. Despite their flexibility and empirical success in machine learning, RNNs often suffer from limited interpretability and slow training, which hinders their use in statistics. This paper proposes the Parallelized RNN (ParaRNN), a novel model composed of multiple small recurrent units. ParaRNN admits an additive representation that decouples recurrent dynamics into interpretable components, whose behavior can be characterized through recurrence features. This interpretability enables its applications in nonparametric regression for time-dependent data, while the design also allows efficient parallelization. The approximation capacity and non-asymptotic prediction error bounds in a nonparametric regression setting are established for ParaRNN. Empirical results on three sequential modeling tasks further demonstrate that ParaRNN achieves performance comparable to vanilla RNNs while offering improved interpretability and efficiency.

A machine learning model is traditionally considered robust if its prediction remains (almost) constant under input perturbations with small norm. However, real-world tasks like molecular property prediction or point cloud segmentation have inherent equivariances, such as rotation or permutation equivariance. In such tasks, even perturbations with large norm do not necessarily change an input's semantic content. Furthermore, there are perturbations for which a model's prediction explicitly needs to change. For the first time, we propose a sound notion of adversarial robustness that accounts for task equivariance.

Weight-Decomposed Low-Rank Adaptation (DoRA) extends LoRA by decoupling weight magnitude from direction, but its forward pass requires the row-wise norm of W + sBA, a computation that every major framework we surveyed implements by materializing the dense [d_out, d_in] product BA. At d_in = 8192 and rank r = 384, a single module's norm requires about 512 MB of transient working memory in bf16, making high-rank DoRA costly and often infeasible on common single-GPU setups once hundreds of adapted modules and checkpointing are involved. We present two systems contributions. A factored norm decomposes the squared norm into base, cross, and Gram terms computable through O(d_out r + r^2) intermediates, eliminating the dense product. Fused Triton kernels collapse the four-kernel DoRA composition into a single pass, reducing memory traffic by about 4x and using a numerically stable form that avoids catastrophic cancellation in the near-unity rescaling regime where magnitude scales concentrate in practice. Across six 8-32B vision-language models (VLMs) on three NVIDIA GPUs (RTX 6000 PRO, H200, B200) at r = 384 in bf16, the fused implementation is 1.5-2.0x faster than Hugging Face PEFT's DoRA implementation for inference and 1.5-1.9x faster for gradient computation (optimizer step excluded), with up to 7 GB lower peak VRAM. Microbenchmarks on six GPUs spanning four architecture generations (L40S, A100, RTX 6000 PRO, H200, B200, B300) confirm 1.5-2.7x compose-kernel speedup. Final-logit cosine similarity exceeds 0.9999 across all model/GPU pairs, and multi-seed training curves match within 7.1 x 10^-4 mean per-step loss delta over 2000 steps.

A deterministic path uses a self-attention and cross-attention to summarize contexts. B.1 1DRegression Architectures For models without attention (CNP, NP, BNP), we set`pre = 4,`post = 2,`dec = 3,dh = 128. For NP we set dz = 128. For Student-t noise, we addedε γ T(2.1) to the curves generated from GP with RBF kernel, whereT(2.1) is a Student'st distribution with degree of freedom2.1 and γ Unif(0,0.15). After realizing them, the prior functions are used to optimize via Bayesian optimization.

Object search in large-scale, unstructured environments remains a fundamental challenge in robotics, particularly in dynamic or expansive settings such as outdoor autonomous exploration. This task requires robust spatial reasoning and the ability to leverage prior experiences. While Large Language Models (LLMs) offer strong semantic capabilities, their application in embodied contexts is limited by a grounding gap in spatial reasoning and insufficient mechanisms for memory integration and decision consistency.To address these challenges, we propose GET (Goal-directed Exploration and Targeting), a framework that enhances object search by combining LLM-based reasoning with experience-guided exploration. At its core is DoUT (Diagram of Unified Thought), a reasoning module that facilitates real-time decision-making through a role-based feedback loop, integrating task-specific criteria and external memory. For repeated tasks, GET maintains a probabilistic task map based on a Gaussian Mixture Model, allowing for continual updates to object-location priors as environments evolve.Experiments conducted in real-world, large-scale environments demonstrate that GET improves search efficiency and robustness across multiple LLMs and task settings, significantly outperforming heuristic and LLM-only baselines. These results suggest that structured LLM integration provides a scalable and generalizable approach to embodied decision-making in complex environments.

Prescriptive process monitoring methods seek to improve the performance of a process by selectively triggering interventions at runtime (e.g., offering a discount to a customer) to increase the probability of a desired case outcome (e.g., a customer making a purchase). The backbone of a prescriptive process monitoring method is an intervention policy, which determines for which cases and when an intervention should be executed. Existing methods in this field rely on predictive models to define intervention policies; specifically, they consider policies that trigger an intervention when the estimated probability of a negative outcome exceeds a threshold. However, the probabilities computed by a predictive model may come with a high level of uncertainty (low confidence), leading to unnecessary interventions and, thus, wasted effort. This waste is particularly problematic when the resources available to execute interventions are limited. To tackle this shortcoming, this paper proposes an approach to extend existing prescriptive process monitoring methods with so-called conformal predictions, i.e., predictions with confidence guarantees. An empirical evaluation using real-life public datasets shows that conformal predictions enhance the net gain of prescriptive process monitoring methods under limited resources.

The paper tackles four basic questions associated with human brain as a learning system. How can the brain learn to (1) mentally simulate different external memory aids, (2) perform, in principle, any mental computations using imaginary memory aids, (3) recall the real sensory and motor events and synthesize a combinatorial number of imaginary events, (4) dynamically change its mental set to match a combinatorial number of contexts? We propose a uniform answer to (1)-(4) based on the general postulate that the human neocortex processes symbolic information in a "nonclassical" way. Instead of manipulating symbols in a read/write memory, as the classical symbolic systems do, it manipulates the states of dynamical memory representing different temporary attributes of immovable symbolic structures stored in a long-term memory. The approach is formalized as the concept of E-machine. Intuitively, an E-machine is a system that deals mainly with characteristic functions representing subsets of memory pointers rather than the pointers themselves. This nonclassical symbolic paradigm is Turing universal, and, unlike the classical one, is efficiently implementable in homogeneous neural networks with temporal modulation topologically resembling that of the neocortex.