In sequence modeling, the parametric memory of atomic facts has been predominantly abstracted as a brute-force lookup of co-occurrences between entities. We contrast this associative view against a geometric view of how memory is stored. We begin by isolating a clean and analyzable instance of Transformer reasoning that is incompatible with memory as strictly a storage of the local co-occurrences specified during training. Instead, the model must have somehow synthesized its own geometry of atomic facts, encoding global relationships between all entities, including non-co-occurring ones. This in turn has simplified a hard reasoning task involving an $\ell$-fold composition into an easy-to-learn 1-step geometric task. From this phenomenon, we extract fundamental aspects of neural embedding geometries that are hard to explain. We argue that the rise of such a geometry, despite optimizing over mere local associations, cannot be straightforwardly attributed to typical architectural or optimizational pressures. Counterintuitively, an elegant geometry is learned even when it is not more succinct than a brute-force lookup of associations. Then, by analyzing a connection to Node2Vec, we demonstrate how the geometry stems from a spectral bias that -- in contrast to prevailing theories -- indeed arises naturally despite the lack of various pressures. This analysis also points to practitioners a visible headroom to make Transformer memory more strongly geometric. We hope the geometric view of parametric memory encourages revisiting the default intuitions that guide researchers in areas like knowledge acquisition, capacity, discovery and unlearning.

The technique of data augmentation (DA) is often used in machine learning for regularization purposes to better generalize under i.i.d. settings. In this work, we present a unifying framework with topics in causal inference to make a case for the use of DA beyond just the i.i.d. setting, but for generalization across interventions as well. Specifically, we argue that when the outcome generating mechanism is invariant to our choice of DA, then such augmentations can effectively be thought of as interventions on the treatment generating mechanism itself. This can potentially help to reduce bias in causal effect estimation arising from hidden confounders. In the presence of such unobserved confounding we typically make use of instrumental variables (IVs) -- sources of treatment randomization that are conditionally independent of the outcome. However, IVs may not be as readily available as DA for many applications, which is the main motivation behind this work. By appropriately regularizing IV based estimators, we introduce the concept of IV-like (IVL) regression for mitigating confounding bias and improving predictive performance across interventions even when certain IV properties are relaxed. Finally, we cast parameterized DA as an IVL regression problem and show that when used in composition can simulate a worst-case application of such DA, further improving performance on causal estimation and generalization tasks beyond what simple DA may offer. This is shown both theoretically for the population case and via simulation experiments for the finite sample case using a simple linear example. We also present real data experiments to support our case.

Pretrained Transformers demonstrate remarkable in-context learning (ICL) capabilities, enabling them to adapt to new tasks from demonstrations without parameter updates. However, theoretical studies often rely on simplified architectures (e.g., omitting MLPs), data models (e.g., linear regression with isotropic inputs), and single-source training, limiting their relevance to realistic settings. In this work, we study ICL in pretrained Transformers with nonlinear MLP heads on nonlinear tasks drawn from multiple data sources with heterogeneous input, task, and noise distributions. We analyze a model where the MLP comprises two layers, with the first layer trained via a single gradient step and the second layer fully optimized. Under high-dimensional asymptotics, we prove that such models are equivalent in ICL error to structured polynomial predictors, leveraging results from the theory of Gaussian universality and orthogonal polynomials. This equivalence reveals that nonlinear MLPs meaningfully enhance ICL performance, particularly on nonlinear tasks, compared to linear baselines. It also enables a precise analysis of data mixing effects: we identify key properties of high-quality data sources (low noise, structured covariances) and show that feature learning emerges only when the task covariance exhibits sufficient structure. These results are validated empirically across various activation functions, model sizes, and data distributions. Finally, we experiment with a real-world scenario involving multilingual sentiment analysis where each language is treated as a different source. Our experimental results for this case exemplify how our findings extend to real-world cases. Overall, our work advances the theoretical foundations of ICL in Transformers and provides actionable insight into the role of architecture and data in ICL.

Polynomial chaos expansions (PCE) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully Bayesian formulations remain rare--especially with implementations in R. Motivated by the success of adaptive Bayesian machine learning models such as BART, BASS, and BPPR, we develop a new fully Bayesian adaptive PCE method with an efficient and accessible R implementation: khaos. Our approach includes a novel proposal distribution that enables data-driven interaction selection, and supports a modified g-prior tailored to PCE structure. Through simulation studies and real-world UQ applications, we demonstrate that Bayesian adaptive PCE provides competitive performance for surrogate modeling, global sensitivity analysis, and ordinal regression tasks.

This paper proposes Stochastic Geographic Gradient Fusion (SGFusion), a novel training algorithm to leverage the geographic information of mobile users in Federated Learning (FL). SGFusion maps the data collected by mobile devices onto geographical zones and trains one FL model per zone, which adapts well to the data and behaviors of users in that zone. SGFusion models the local data-based correlation among geographical zones as a hierarchical random graph (HRG) optimized by Markov Chain Monte Carlo sampling. At each training step, every zone fuses its local gradient with gradients derived from a small set of other zones sampled from the HRG. This approach enables knowledge fusion and sharing among geographical zones in a probabilistic and stochastic gradient fusion process with self-attention weights, such that "more similar" zones have "higher probabilities" of sharing gradients with "larger attention weights." SGFusion remarkably improves model utility without introducing undue computational cost. Extensive theoretical and empirical results using a heart-rate prediction dataset collected across 6 countries show that models trained with SGFusion converge with upper-bounded expected errors and significantly improve utility in all countries compared to existing approaches without notable cost in system scalability.

Information cascade popularity prediction is a key problem in analyzing content diffusion in social networks. However, current related works suffer from three critical limitations: (1) temporal leakage in current evaluation--random cascade-based splits allow models to access future information, yielding unrealistic results; (2) feature-poor datasets that lack downstream conversion signals (e.g., likes, comments, or purchases), which limits more practical applications; (3) computational inefficiency of complex graph-based methods that require days of training for marginal gains. We systematically address these challenges from three perspectives: task setup, dataset construction, and model design. First, we propose a time-ordered splitting strategy that chronologically partitions data into consecutive windows, ensuring models are evaluated on genuine forecasting tasks without future information leakage. Second, we introduce Taoke, a large-scale e-commerce cascade dataset featuring rich promoter/product attributes and ground-truth purchase conversions--capturing the complete diffusion lifecycle from promotion to monetization. Third, we develop CasTemp, a lightweight framework that efficiently models cascade dynamics through temporal walks, Jaccard-based neighbor selection for inter-cascade dependencies, and GRU-based encoding with time-aware attention. Under leak-free evaluation, CasTemp achieves state-of-the-art performance across four datasets with orders-of-magnitude speedup. Notably, it excels at predicting second-stage popularity conversions--a practical task critical for real-world applications.

Recent advancements in language models (LMs) have marked a shift toward the growing importance of post-training. Yet, post-training approaches such as supervised fine-tuning (SFT) do not guarantee the effective use of knowledge acquired during pretraining. We therefore introduce InfoSteer, a lightweight method that encourages parametric information utilization in LMs during post-training. Specifically, InfoSteer treats the feed-forward network (FFN) layer as associate key-value memory and promotes the use of stored memory vectors via forward-pass interventions or regularization during backpropagation. This simple guidance during post-training phase yields consistent performance improvements across diverse model families -- including Qwen, Gemma and Llama -- spanning 15 downstream tasks in both in-distribution (ID) and out-of-distribution (OOD) evaluations. Beyond performance gains, we also find that steered LMs can adaptively allocate information by placing more emphasis on generating semantically meaningful tokens, while using fewer resources on simple transition ones (e.g., `\texttt{,}' or `\texttt{and}'). Our work underscores that vanilla post-training does not fully exploit the potential gained during pre-training, and that steering LMs in latent representation space offers a promising approach to enhance both performance and interpretability. The code is available at: https://github.com/chili-lab/InfoSteer.

In the era of large-scale training, model merging has evolved into a tool for creating multitasking models efficiently. It enables the knowledge of models to be fused, without the need for heavy computation as required in traditional multitask learning. Existing merging methods often assume that entries at identical positions in weight matrices serve the same function, enabling straightforward entry-wise comparison and merging. However, this assumption overlooks the complexity of finetuned neural networks, where neurons may develop distinct feature compositions, making direct entry-wise merging problematic. We present Decom-Renorm-Merge (DRM), a simple yet effective approach that leverages Singular Value Decomposition to decompose and coordinate weight matrices into an aligned joint space, where entry-wise merging becomes possible. We showcase the effectiveness of DRM across various settings ranging from smaller encoder-based such as ViT and DeBERTa, encoder-decoder-based such as T5, and larger decoder-based such as Llama3.1-8B. Our experimental results show that DRM outperforms several state-of-the-art merging techniques across full finetuning and low-rank adaptation settings. Moreover, our analysis reveals renormalization as the crucial component for creating a robust and even joint space for merging, significantly contributing to the method's performance.

We study a sequential decision-making problem on a $n$-node graph $\mathcal{G}$ where each node has an unknown label from a finite set $\mathbfΩ$, drawn from a joint distribution $\mathcal{P}$ that is Markov with respect to $\mathcal{G}$. At each step, selecting a node reveals its label and yields a label-dependent reward. The goal is to adaptively choose nodes to maximize expected accumulated discounted rewards. We impose a frontier exploration constraint, where actions are limited to neighbors of previously selected nodes, reflecting practical constraints in settings such as contact tracing and robotic exploration. We design a Gittins index-based policy that applies to general graphs and is provably optimal when $\mathcal{G}$ is a forest. Our implementation runs in $\mathcal{O}(n^2 \cdot |\mathbfΩ|^2)$ time while using $\mathcal{O}(n \cdot |\mathbfΩ|^2)$ oracle calls to $\mathcal{P}$ and $\mathcal{O}(n^2 \cdot |\mathbfΩ|)$ space. Experiments on synthetic and real-world graphs show that our method consistently outperforms natural baselines, including in non-tree, budget-limited, and undiscounted settings. For example, in HIV testing simulations on real-world sexual interaction networks, our policy detects nearly all positive cases with only half the population tested, substantially outperforming other baselines.

Graph neural networks have become the de facto model for learning from structured data. However, the decision-making process of GNNs remains opaque to the end user, which undermines their use in safety-critical applications. Several explainable AI techniques for graphs have been developed to address this major issue. Focusing on graph classification, these explainers identify subgraph motifs that explain predictions. Therefore, a robust benchmarking of graph explainers is required to ensure that the produced explanations are of high quality, i.e., aligned with the GNN's decision process. However, current graph-XAI benchmarks are limited to simplistic synthetic datasets or a few real-world tasks curated by domain experts, hindering rigorous and reproducible evaluation, and consequently stalling progress in the field. To overcome these limitations, we propose a method to automate the construction of graph XAI benchmarks from generic graph classification datasets. Our approach leverages the Weisfeiler-Leman color refinement algorithm to efficiently perform approximate subgraph matching and mine class-discriminating motifs, which serve as proxy ground-truth class explanations. At the same time, we ensure that these motifs can be learned by GNNs because their discriminating power aligns with WL expressiveness. This work also introduces the OpenGraphXAI benchmark suite, which consists of 15 ready-made graph-XAI datasets derived by applying our method to real-world molecular classification datasets. The suite is available to the public along with a codebase to generate over 2,000 additional graph-XAI benchmarks. Finally, we present a use case that illustrates how the suite can be used to assess the effectiveness of a selection of popular graph explainers, demonstrating the critical role of a sufficiently large benchmark collection for improving the significance of experimental results.