For many real-world applications, understanding feature-outcome relationships is as crucial as achieving high predictive accuracy. While traditional neural networks excel at prediction, their black-box nature obscures underlying functional relationships. Kolmogorov--Arnold Networks (KANs) address this by employing learnable spline-based activation functions on edges, enabling recovery of symbolic representations while maintaining competitive performance. However, KAN's architecture presents unique challenges for network pruning. Conventional magnitude-based methods become unreliable due to sensitivity to input coordinate shifts. We propose \textbf{ShapKAN}, a pruning framework using Shapley value attribution to assess node importance in a shift-invariant manner. Unlike magnitude-based approaches, ShapKAN quantifies each node's actual contribution, ensuring consistent importance rankings regardless of input parameterization. Extensive experiments on synthetic and real-world datasets demonstrate that ShapKAN preserves true node importance while enabling effective network compression. Our approach improves KAN's interpretability advantages, facilitating deployment in resource-constrained environments.

Autoregressive Large Language Models (LLMs) demonstrate exceptional performance in language understanding and generation. However, their application in text embedding tasks has been relatively slow, along with the analysis of their semantic representation in probing tasks, due to the constraints of the unidirectional attention mechanism. This paper aims to explore whether such constraints can be overcome by enabling bidirectional attention in LLMs. We tested different variants of the Llama architecture through additional training steps, progressively enabling bidirectional attention and unsupervised/supervised contrastive learning.

Neural network pruning is a promising technique to mitigate the excessive computational and memory requirements of large language models (LLMs). Despite its promise, however, progress in this area has diminished, as conventional methods are seemingly unable to surpass moderate sparsity levels (50-60%) without severely degrading model accuracy. This work breaks through the current impasse, presenting a principled and effective method called $\texttt{Elsa}$, which achieves extreme sparsity levels of up to 90% while retaining high model fidelity. This is done by identifying several limitations in current practice, all of which can be traced back to their reliance on a surrogate objective formulation. $\texttt{Elsa}$ tackles this issue directly and effectively via standard and well-established constrained optimization techniques based on ADMM. Our extensive experiments across a wide range of models and scales show that $\texttt{Elsa}$ achieves substantial improvements over existing methods; e.g., it achieves 7.8$\times$ less perplexity than the best existing method on LLaMA-2-7B at 90% sparsity. Furthermore, we present $\texttt{Elsa}_{\text{-L}}$, a quantized variant that scales to extremely large models (27B), and establish its theoretical convergence guarantees. These results highlight meaningful progress in advancing the frontier of LLM sparsity, while promising that significant opportunities for further advancement may remain in directions that have so far attracted limited exploration.

The discourse on privacy risks in Large Language Models (LLMs) has disproportionately focused on verbatim memorization of training data, while a constellation of more immediate and scalable privacy threats remain underexplored. This position paper argues that the privacy landscape of LLM systems extends far beyond training data extraction, encompassing risks from data collection practices, inference-time context leakage, autonomous agent capabilities, and the democratization of surveillance through deep inference attacks. We present a comprehensive taxonomy of privacy risks across the LLM lifecycle -- from data collection through deployment -- and demonstrate through case studies how current privacy frameworks fail to address these multifaceted threats. Through a longitudinal analysis of 1,322 AI/ML privacy papers published at leading conferences over the past decade (2016--2025), we reveal that while memorization receives outsized attention in technical research, the most pressing privacy harms lie elsewhere, where current technical approaches offer little traction and viable paths forward remain unclear. We call for a fundamental shift in how the research community approaches LLM privacy, moving beyond the narrow focus of current technical solutions and embracing interdisciplinary approaches that address the sociotechnical nature of these emerging threats.

The quadratic complexity of softmax attention remains a central bottleneck in scaling large language models (LLMs). [Alman and Song, NeurIPS 2023] proposed a sub-quadratic attention approximation algorithm, but it works only under the restrictive bounded-entry assumption. Since this assumption rarely holds in practice, its applicability to modern LLMs is limited. In this paper, we introduce support-basis decomposition, a new framework for efficient attention approximation beyond bounded entries. We empirically demonstrate that the entries of the query and key matrices exhibit sub-Gaussian behavior. Our approach uses this property to split large and small entries, enabling exact computation on sparse components and polynomial approximation on dense components. We establish rigorous theoretical guarantees, proving a sub-quadratic runtime, and extend the method to a multi-threshold setting that eliminates all distributional assumptions. Furthermore, we provide the first theoretical justification for the empirical success of polynomial attention [Kacham, Mirrokni, and Zhong, ICML 2024], showing that softmax attention can be closely approximated by a combination of multiple polynomial attentions with sketching.

We explore the geospatial reasoning capabilities of Large Language Models (LLMs), specifically, whether LLMs can read road network maps and perform navigation. Using road network as context, our prompting framework enables LLMs to generate valid paths without accessing any external navigation tools. Experiments show that LLMs outperform off-the-shelf baselines and specialized trajectory recovery models, with strong zero-shot generalization. Fine-grained analysis shows that LLMs have strong comprehension of the road network and coordinate systems, but also pose systematic biases with respect to regions and transportation modes. Finally, we demonstrate how LLMs can enhance navigation experiences by reasoning over maps in flexible ways to incorporate user preferences. Large Language Models (LLMs) are increasingly recognized as general-purpose systems, showing strong performance across domains ranging from mathematics and coding to vision and robotics. An emerging yet underex-plored question is whether these models possess geospa-tial understanding, the ability to reason about maps, paths, and spatial relationships. Such capabilities are fundamental to many real-world applications, e.g., autonomous vehicle navigation, logistics, and urban planning. While prior work has studied LLMs in contexts such as geographic knowledge retrieval (Manvi et al., 2024a;b) and map-based multiple-choice question answering (Dihan et al., 2025), the ability of LLMs to read road networks and plan paths has not been systematically evaluated. We investigate whether LLMs can perform navigation through the trajectory recovery task: reconstructing masked segments of GPS traces from the road network context, to bypass the restriction of relying on shortest path-type of ground truth which may not reflect human navigation pattern in practice (Golledge, 1995; Duckham & Kulik, 2003). Our dataset is framed in away that is harder than the traditional point-wise trajectory recovery task (Newson & Krumm, 2009; Song et al., 2017; Si et al., 2024), and closer to the higher-level navigation problem.

Watermarking has become a key technique for proprietary language models, enabling the distinction between AI-generated and human-written text. However, in many real-world scenarios, LLM-generated content may undergo post-generation edits, such as human revisions or even spoofing attacks, making it critical to detect and localize such modifications. In this work, we introduce a new task: detecting post-generation edits locally made to watermarked LLM outputs. To this end, we propose a combinatorial pattern-based watermarking framework, which partitions the vocabulary into disjoint subsets and embeds the watermark by enforcing a deterministic combinatorial pattern over these subsets during generation. We accompany the combinatorial watermark with a global statistic that can be used to detect the watermark. Furthermore, we design lightweight local statistics to flag and localize potential edits. We introduce two task-specific evaluation metrics, Type-I error rate and detection accuracy, and evaluate our method on open-source LLMs across a variety of editing scenarios, demonstrating strong empirical performance in edit localization.

Transformers achieve strong performance across diverse domains but implicitly assume Euclidean geometry in their attention mechanisms, limiting their effectiveness on data with non-Euclidean structure. While recent extensions to hyperbolic and spherical spaces show promise for hierarchical and cyclical patterns, respectively, they require committing to a single geometry a priori, reducing flexibility when data exhibits mixed geometric properties. We introduce the Curvature-Adaptive Transformer (CAT), a novel architecture that dynamically learns per-token routing across three geometric attention branches through a lightweight, differentiable gating mechanism. Unlike fixed-geometry approaches, CAT enables adaptive geometric specialization, routing tokens to the appropriate curvature based on their local relational structure. The routing network provides interpretable curvature preferences while each branch employs geometry-specific operations optimized for its respective manifold. On knowledge graph completion benchmarks (FB15k-237, WN18RR), CAT achieves approximately 10% improvements in MRR and Hits@10 over fixed-geometry baselines with minimal overhead (5% parameter increase, comparable inference time). These results demonstrate that learned geometric adaptation outperforms any single fixed geometry for complex relational reasoning, establishing CAT as a scalable and interpretable foundation for mixture-of-geometry architectures across language, vision, and multimodal domains.

Training data plays a crucial role in Large Language Models (LLM) scaling, yet high quality data is of limited supply. Synthetic data techniques offer a potential path toward sidestepping these limitations. We conduct a large-scale empirical investigation (>1000 LLMs with >100k GPU hours) using a unified protocol and scaling laws, comparing natural web data, diverse synthetic types (rephrased text, generated textbooks), and mixtures of natural and synthetic data. Specifically, we found pre-training on rephrased synthetic data \textit{alone} is not faster than pre-training on natural web texts; while pre-training on 1/3 rephrased synthetic data mixed with 2/3 natural web texts can speed up 5-10x (to reach the same validation loss) at larger data budgets. Pre-training on textbook-style synthetic data \textit{alone} results in notably higher loss on many downstream domains especially at small data budgets. "Good" ratios of synthetic data in training data mixtures depend on the model size and data budget, empirically converging to ~30% for rephrased synthetic data. Larger generator models do not necessarily yield better pre-training data than ~8B-param models. These results contribute mixed evidence on "model collapse" during large-scale single-round (n=1) model training on synthetic data--training on rephrased synthetic data shows no degradation in performance in foreseeable scales whereas training on mixtures of textbook-style pure-generated synthetic data shows patterns predicted by "model collapse". Our work demystifies synthetic data in pre-training, validates its conditional benefits, and offers practical guidance.

In post-training for reasoning Large Language Models (LLMs), the current state of practice trains LLMs in two independent stages: Supervised Fine-Tuning (SFT) and Reinforcement Learning with Verifiable Rewards (RLVR, shortened as ``RL'' below). In this work, we challenge whether high SFT scores translate to improved performance after RL. We provide extensive counter-examples where this is not true. We find high SFT scores can be biased toward simpler or more homogeneous data and are not reliably predictive of subsequent RL gains or scaled-up post-training effectiveness. In some cases, RL training on models with improved SFT performance could lead to substantially worse outcome compared to RL on the base model without SFT. We study alternative metrics and identify generalization loss on held-out reasoning examples and Pass@large k performance to provide strong proxies for the RL outcome. We trained hundreds of models up to 12B-parameter with SFT and RLVR via GRPO and ran extensive evaluations on 7 math benchmarks with up to 256 repetitions, spending $>$1M GPU hours. Experiments include models from Llama3, Mistral-Nemo, Qwen3 and multiple state-of-the-art SFT/RL datasets. Compared to directly predicting from pre-RL performance, prediction based on generalization loss and Pass@large k achieves substantial higher precision, improving $R^2$ coefficient and Spearman's rank correlation coefficient by up to 0.5 (2x). This provides strong utility for broad use cases. For example, in most experiments, we find SFT training on unique examples for a one epoch underperforms training on half examples for two epochs, either after SFT or SFT-then-RL; With the same SFT budget, training only on short examples may lead to better SFT performance, though, it often leads to worse outcome after RL compared to training on examples with varying lengths. Evaluation tool will be open-sourced.