Dynamic 4DGaussian Splatting (4DGS) effectively extends the high-speed rendering capabilities of 3DGaussian Splatting (3DGS) to represent volumetric videos.

An established measure of the expressive power of a given ReLU neural network is the number of linear regions into which it partitions the input space. There exist many different, non-equivalent definitions of what a linear region actually is. We systematically assess which papers use which definitions and discuss how they relate to each other. We then analyze the computational complexity of counting the number of such regions for the various definitions. Generally, this turns out to be an intractable problem. We prove NPand #P-hardness results already for networks with one hidden layer and strong hardness of approximation results for two or more hidden layers. Finally, on the algorithmic side, we demonstrate that counting linear regions can at least be achieved in polynomial space for some common definitions.

We consider the following question: given a submodular/supermodular set function f: 2V R, how should one minimize/maximize its average value f(S)/|S| over non-empty subsets S V? This problem generalizes several well-known objectives, including Densest Subgraph (DSG), Densest Supermodular Set (DSS), and Submodular Function Minimization (SFM). Motivated by recent applications [42, 34], we formalize two new broad problems: the Unrestricted Sparsest Submodular Set (USSS) and Unrestricted Densest Supermodular Set (UDSS), both of which allow negative and non-monotone functions. Using classical results, we show that DSS, SFM, USSS, UDSS, and Minimum Norm Point (MNP) are all equivalent under strongly polynomial-time reductions. This equivalence enables algorithmic cross-over: methods designed for one problem can be repurposed to solve others efficiently. In particular, we use the perspective of the minimum norm point in the base polyhedron of a sub/supermodular function, which, via Fujishige's results, yields the dense decomposition as a byproduct.

Attention sink (AS) is a consistent pattern in transformer attention maps where certain tokens (often special tokens or positional anchors) disproportionately attract attention from other tokens. We show that in transformers, AS is not an architectural artifact, but it is the manifestation of a fundamental geometric principle: the establishment of reference frames that anchor representational spaces. We analyze several architectures and identify three distinct reference frame types, centralized, distributed, and bidirectional, that correlate with the attention sink phenomenon. We show that they emerge during the earliest stages of training as optimal solutions to the problem of establishing stable coordinate systems in high-dimensional spaces. We show the influence of architecture components, particularly position encoding implementations, on the specific type of reference frame. This perspective transforms our understanding of transformer attention mechanisms and provides insights for both architecture design and the relationship with AS.

This paper investigates the computational complexity of reinforcement learning within a novel linear function approximation regime, termed partial qπ-realizability. In this framework, the objective is to learn an ϵ-optimal policy with respect to a predefined policy set Π, under the assumption that all value functions corresponding to policies in Π are linearly realizable. This framework adopts assumptions that are weaker than those in the qπ-realizability setting yet stronger than those in the q -realizability setup. As a result, it provides a more practical model for reinforcement learning scenarios where function approximation naturally arise. We prove that learning an ϵ-optimal policy in this newly defined setting is computationally hard. More specifically, we establish NP-hardness under a parameterized greedy policy set (i.e., argmax) and, further, show that--unless NP = RP--an exponential lower bound (exponential in feature vector dimension) holds when the policy set contains softmax policies, under the Randomized Exponential Time Hypothesis. Our hardness results mirror those obtained in the q -realizability settings, and suggest that computational difficulty persists even when the policy class Πis expanded beyond the optimal policy, reinforcing the unbreakable nature of the computational hardness result regarding partial qπ-realizability under two important policy sets. To establish our negative result, our primary technical contribution is a reduction from two complexity problems, δ-MAX-3SAT and δ-MAX-3SAT(b), to instances of our problem settings: GLINEAR-κ-RL (under the greedy policy set) and SLINEAR-κ-RL (under the softmax policy set), respectively. Our findings indicate that positive computational results are generally unattainable in the context of partial qπ-realizability, in sharp contrast to the qπ-realizability setting under a generative access model.

Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by performing a fixed number of a single type of these operations. Although we discover that the corresponding problems are NP-complete in general, we provide a comprehensive parameterized-complexity analysis with the aim of determining those properties of the problems that explain the hardness and those that make the problems tractable. For instance, we show that the problems remain hard for a small number d of features or small domain size D but the combination of both yields fixed-parameter tractability. That is, the problems are solvable in (D+1)2d |I|O(1) time, where |I|is the size of the input. We also provide a proof-of-concept implementation of this algorithm and report on empirical results.

AI-powered attacks on Learning with Errors (LWE)--an important hard math problem in post-quantum cryptography--rival or outperform "classical" attacks on LWE under certain parameter settings. Despite the promise of this approach, a dearth of accessible data limits AI practitioners' ability to study and improve these attacks. Creating LWE data for AI model training is time-and compute-intensive and requires significant domain expertise. To fill this gap and accelerate AI research on LWE attacks, we propose the TAPAS datasets, a toolkit for analysis of postquantum cryptography using AI systems. These datasets cover several LWE settings and can be used off-the-shelf by AI practitioners to prototype new approaches to cracking LWE. This work documents TAPAS dataset creation, establishes attack performance baselines, and lays out directions for future work.

We study how training data contributes to the emergence of toxic behaviors in large language models. Most prior work on reducing model toxicity adopts reactive approaches, such as fine-tuning pre-trained (and potentially toxic) models to align them with human values. In contrast, we propose a proactive approach-- IF-GUIDE--that leverages influence functions to identify and suppress harmful tokens in the training data. To this end, we first show that standard influence functions are ineffective at discovering harmful training records. We then present a novel adaptation that measures token-level attributions from training data to model toxicity, along with techniques for selecting toxic training documents and a learning objective that can be integrated into both pre-training and fine-tuning. Moreover, IF-GUIDE does not rely on human-preference data, which is typically required by existing alignment methods. In our evaluation, we demonstrate that IF-GUIDE substantially reduces both explicit and implicit toxicity--by up to 10 compared to uncensored models, and up to 3 compared to baseline alignment methods such as DPO and RAD--across both pre-training and fine-tuning scenarios. IF-GUIDE is computationally efficient: a billion-parameter model is not necessary for computing influence scores; a million-parameter model--with 7.5 fewer parameters--can effectively serve as a proxy for identifying harmful data.

Mobile agents rely on Large Language Models (LLMs) to plan and execute tasks on smartphone user interfaces (UIs). While cloud-based LLMs achieve high task accuracy, they require uploading the full UI state at every step, exposing unnecessary and often irrelevant information. In contrast, local LLMs avoid UI uploads but suffer from limited capacity, resulting in lower task success rates. We propose CORE, a COllaborative framework that combines the strengths of cloud and local LLMs to Reduce UIExposure, while maintaining task accuracy for mobile agents. CORE comprises three key components: (1) Layout-aware block partitioning, which groups semantically related UI elements based on the XML screen hierarchy; (2) Co-planning, where local and cloud LLMs collaboratively identify the current sub-task; and (3) Co-decision-making, where the local LLM ranks relevant UI blocks, and the cloud LLM selects specific UI elements within the top-ranked block. CORE further introduces a multi-round accumulation mechanism to mitigate local misjudgment or limited context. Experiments across diverse mobile apps and tasks show that CORE reduces UI exposure by up to 55.6% while maintaining task success rates slightly below cloud-only agents, effectively mitigating unnecessary privacy exposure to the cloud.2

Correlated equilibria--and their generalizations known as Φ-equilibria--are a fundamental object of study in game theory, offering a more tractable alternative to Nash equilibria in multi-player settings. While computational aspects of equilibrium computation are well-understood in some settings, fundamental questions are still open in generalized games, that is, games in which the set of strategies allowed to each player depends on the other players' strategies. These classes of games model fundamental settings in economics, and have been a cornerstone of economics research since the seminal paper of Arrow and Debreu [1954]. Recently, there has been growing interest, both in economics and in computer science, in studying correlated equilibria in generalized games. It is known that finding a social welfare maximizing correlated equilibrium in generalized games is NP-hard. However, the existence of efficient algorithms to find any equilibrium remains an important open question.