OpenRaiser/Intern-Atlas huggingface dataset:
Hilbert's Nullstellensatz is in the Counting Hierarchy
Venue: arXiv cs.CC 2026
Year: 2026

We show that Hilbert's Nullstellensatz, the problem of deciding if a system of multivariate polynomial equations has a solution in the algebraic closure of the underlying field, lies in the counting hierarchy. More generally, we show that the number of solutions to a system of equations can be computed in polynomial time with oracle access to the counting hierarchy. Our results hold in particular for polynomials with coefficients in either the rational numbers or a finite field. Previously, the best-known bounds on the complexities of these problems were PSPACE and FPSPACE, respectively. Our main technical contribution is the construction of a uniform family of constant-depth arithmetic circuits that compute the multivariate resultant.
Improving Neural Topic Modeling with Semantically-Grounded Soft Label Distributions
Venue: arXiv cs.CL 2026
Year: 2026

Traditional neural topic models are typically optimized by reconstructing the document's Bag-of-Words (BoW) representations, overlooking contextual information and struggling with data sparsity. In this work, we propose a novel approach to construct semantically-grounded soft label targets using Language Models (LMs) by projecting the next token probabilities, conditioned on a specialized prompt, onto a pre-defined vocabulary to obtain contextually enriched supervision signals. By training the topic models to reconstruct the soft labels using the LM hidden states, our method produces higher-quality topics that are more closely aligned with the underlying thematic structure of the corpus. Experiments on three datasets show that our method achieves substantial improvements in topic coherence, purity over existing baselines. Additionally, we also introduce a retrieval-based metric, which shows that our approach significantly outperforms existing methods in identifying semantically similar documents, highlighting its effectiveness for retrieval-oriented applications.
Latent Diffeomorphic Co-Design of End-Effectors for Deformable and Fragile Object Manipulation
Venue: arXiv cs.RO 2026
Year: 2026

Manipulating deformable and fragile objects remains a fundamental challenge in robotics due to complex contact dynamics and strict requirements on object integrity. Existing approaches typically optimize either end-effector design or control strategies in isolation, limiting achievable performance. In this work, we present the first co-design framework that jointly optimizes end-effector morphology and manipulation control for deformable and fragile object manipulation. We introduce (1) a latent diffeomorphic shape parameterization enabling expressive yet tractable end-effector geometry optimization, (2) a stress-aware bi-level co-design pipeline coupling morphology and control optimization, and (3) a privileged-to-pointcloud policy distillation scheme for zero-shot real-world deployment. We evaluate our approach on challenging food manipulation tasks, including grasping and pushing jelly and scooping fillets. Simulation and real-world experiments demonstrate the effectiveness of the proposed method.
Memory-Based Advantage Shaping for LLM-Guided Reinforcement Learning
Venue: arXiv cs.LG 2026
Year: 2026

In environments with sparse or delayed rewards, reinforcement learning (RL) incurs high sample complexity due to the large number of interactions needed for learning. This limitation has motivated the use of large language models (LLMs) for subgoal discovery and trajectory guidance. While LLMs can support exploration, frequent reliance on LLM calls raises concerns about scalability and reliability. We address these challenges by constructing a memory graph that encodes subgoals and trajectories from both LLM guidance and the agent's own successful rollouts. From this graph, we derive a utility function that evaluates how closely the agent's trajectories align with prior successful strategies. This utility shapes the advantage function, providing the critic with additional guidance without altering the reward. Our method relies primarily on offline input and only occasional online queries, avoiding dependence on continuous LLM supervision. Preliminary experiments in benchmark environments show improved sample efficiency and faster early learning compared to baseline RL methods, with final returns comparable to methods that require frequent LLM interaction.
Analyzing LLM Instruction Optimization for Tabular Fact Verification
Venue: arXiv cs.CL 2026
Year: 2026

Instruction optimization provides a lightweight, model-agnostic approach to enhancing the reasoning performance of large language models (LLMs). This paper presents the first systematic comparison of instruction optimization, based on the DSPy optimization framework, for tabular fact verification. We evaluate four out-of-the-box prompting techniques that cover both text-only prompting and code use: direct prediction, Chain-of-Thought (CoT), ReAct with SQL tools, and CodeAct with Python execution. We study three optimizers from the DSPy framework -- COPRO, MiPROv2, and SIMBA -- across four benchmarks and three model families. We find that instruction optimization consistently improves verification accuracy, with MiPROv2 yielding the most stable gains for CoT, and SIMBA providing the largest benefits for ReAct agents, particularly at larger model scales. Behavioral analyses reveal that SIMBA encourages more direct reasoning paths by applying heuristics, thereby improving numerical comparison abilities in CoT reasoning and helping avoid unnecessary tool calls in ReAct agents. Across different prompting techniques, CoT remains effective for tabular fact checking, especially with smaller models. Although ReAct agents built with larger models can achieve competitive performance, they require careful instruction optimization.
Tighter Regret Lower Bound for Gaussian Process Bandits with Squared Exponential Kernel in Hypersphere
Venue: arXiv cs.LG 2026
Year: 2026

We study an algorithm-independent, worst-case lower bound for the Gaussian process (GP) bandit problem in the frequentist setting, where the reward function is fixed and has a bounded norm in the known reproducing kernel Hilbert space (RKHS). Specifically, we focus on the squared exponential (SE) kernel, one of the most widely used kernel functions in GP bandits. One of the remaining open questions for this problem is the gap in the \emph{dimension-dependent} logarithmic factors between upper and lower bounds. This paper partially resolves this open question under a hyperspherical input domain. We show that any algorithm suffers $Ω(\sqrt{T (\ln T)^{d} (\ln \ln T)^{-d}})$ cumulative regret, where $T$ and $d$ represent the total number of steps and the dimension of the hyperspherical domain, respectively. Regarding the simple regret, we show that any algorithm requires $Ω(ε^{-2}(\ln \frac{1}ε)^d (\ln \ln \frac{1}ε)^{-d})$ time steps to find an $ε$-optimal point. We also provide the improved $O((\ln T)^{d+1}(\ln \ln T)^{-d})$ upper bound on the maximum information gain for the SE kernel. Our results guarantee the optimality of the existing best algorithm up to \emph{dimension-independent} logarithmic factors under a hyperspherical input domain.
ROCKET: Residual-Oriented Multi-Layer Alignment for Spatially-Aware Vision-Language-Action Models
Venue: arXiv cs.CV 2026
Year: 2026

Vision-Language-Action (VLA) models enable instruction-following robotic manipulation, but they are typically pretrained on 2D data and lack 3D spatial understanding. An effective approach is representation alignment, where a strong vision foundation model is used to guide a 2D VLA model. However, existing methods usually apply supervision at only a single layer, failing to fully exploit the rich information distributed across depth; meanwhile, naïve multi-layer alignment can cause gradient interference. We introduce ROCKET, a residual-oriented multi-layer representation alignment framework that formulates multi-layer alignment as aligning one residual stream to another. Concretely, ROCKET employs a shared projector to align multiple layers of the VLA backbone with multiple layers of a powerful 3D vision foundation model via a layer-invariant mapping, which reduces gradient conflicts. We provide both theoretical justification and empirical analyses showing that a shared projector is sufficient and outperforms prior designs, and further propose a Matryoshka-style sparse activation scheme for the shared projector to balance multiple alignment losses. Our experiments show that, combined with a training-free layer selection strategy, ROCKET requires only about 4% of the compute budget while achieving 98.5% state-of-the-art success rate on LIBERO. We further demonstrate the superior performance of ROCKET across LIBERO-Plus and RoboTwin, as well as multiple VLA models. The code and model weights can be found at https://github.com/CASE-Lab-UMD/ROCKET-VLA.
Graph-Neural Multi-Agent Coordination for Distributed Access-Point Selection in Cell-Free Massive MIMO
Venue: arXiv cs.NI 2026
Year: 2026

Cell-free massive MIMO (CFmMIMO) systems require scalable and reliable distributed coordination mechanisms to operate under stringent communication and latency constraints. A central challenge is the Access Point Selection (APS) problem, which seeks to determine the subset of serving Access Points (APs) for each User Equipment (UE) that can satisfy UEs' Spectral Efficiency (SE) requirements while minimizing network power consumption. We introduce APS-GNN, a scalable distributed multi-agent learning framework that decomposes APS into agents operating at the granularity of individual AP-UE connections. Agents coordinate via local observation exchange over a novel Graph Neural Network (GNN) architecture and share parameters to reuse their knowledge and experience. APS-GNN adopts a constrained reinforcement learning approach to provide agents with explicit observability of APS' conflicting objectives, treating SE satisfaction as a cost and power reduction as a reward. Both signals are defined locally, facilitating effective credit assignment and scalable coordination in large networks. To further improve training stability and exploration efficiency, the policy is initialized via supervised imitation learning from a heuristic APS baseline. We develop a realistic CFmMIMO simulator and demonstrate that APS-GNN delivers the target SE while activating 50-70% fewer APs than heuristic and centralized Multi-agent Reinforcement Learning (MARL) baselines in different evaluation scenarios. Moreover, APS-GNN achieves one to two orders of magnitude lower inference latency than centralized MARL approaches due to its fully parallel and distributed execution. These results establish APS-GNN as a practical and scalable solution for APS in large-scale CFmMIMO networks.
Mining Type Constructs Using Patterns in AI-Generated Code
Venue: arXiv cs.SE 2026
Year: 2026

Artificial Intelligence (AI) increasingly automates various parts of the software development tasks. Although AI has enhanced the productivity of development tasks, it remains unstudied whether AI essentially outperforms humans in type-related programming tasks, such as employing type constructs properly for type safety, during its tasks. Moreover, there is no systematic study that evaluates whether AI agents overuse or misuse the type constructs under the complicated type systems to the same extent as humans. In this study, we present the first empirical analysis to answer these questions in the domain of TypeScript projects. Our findings show that, in contrast to humans, AI agents are 9x more prone to use the 'any' keyword. In addition, we observed that AI agents use advanced type constructs, including those that ignore type checks, more often compared to humans. Surprisingly, even with all these issues, Agentic pull requests (PRs) have 1.8x higher acceptance rates compared to humans for TypeScript. We encourage software developers to carefully confirm the type safety of their codebases whenever they coordinate with AI agents in the development process.
DuoTouch: Passive Two-Footprint Attachments Using Binary Sequences to Extend Touch Interaction
Venue: arXiv cs.HC 2026
Year: 2026

DuoTouch is a passive attachment for capacitive touch panels that adds tangible input while minimizing content occlusion and loss of input area. It uses two contact footprints and two traces to encode motion as binary sequences and runs on unmodified devices through standard touch APIs. We present two configurations with paired decoders: an aligned configuration that maps fixed-length codes to discrete commands and a phase-shifted configuration that estimates direction and distance from relative timing. To characterize the system's reliability, we derive a sampling-limited bound that links actuation speed, internal trace width, and device touch sampling rate. Through technical evaluations on a smartphone and a touchpad, we report performance metrics that describe the relationship between these parameters and decoding accuracy. Finally, we demonstrate the versatility of DuoTouch by embedding the mechanism into various form factors, including a hand strap, a phone ring holder, and touchpad add-ons.
Student Flow Modeling for School Decongestion via Stochastic Gravity Estimation and Constrained Spatial Allocation
Venue: arXiv cs.LG 2026
Year: 2026

School congestion, where student enrollment exceeds school capacity, is a major challenge in low- and middle-income countries. It highly impacts learning outcomes and deepens inequities in education. While subsidy programs that transfer students from public to private schools offer a mechanism to alleviate congestion without capital-intensive construction, they often underperform due to fragmented data systems that hinder effective implementation. The Philippine Educational Service Contracting program, one of the world's largest educational subsidy programs, exemplifies these challenges, falling short of its goal to decongest public schools. This prevents the science-based and data-driven analyses needed to understand what shapes student enrollment flows, particularly how families respond to economic incentives and spatial constraints. We introduce a computational framework for modeling student flow patterns and simulating policy scenarios. By synthesizing heterogeneous government data across nearly 3,000 institutions, we employ a stochastic gravity model estimated via negative binomial regression to derive behavioral elasticities for distance, net tuition cost, and socioeconomic determinants. These elasticities inform a doubly constrained spatial allocation mechanism that simulates student redistribution under varying subsidy amounts while respecting both origin candidate pools and destination slot capacities. We find that geographic proximity constrains school choice four times more strongly than tuition cost and that slot capacity, not subsidy amounts, is the binding constraint. Our work demonstrates that subsidy programs alone cannot resolve systemic overcrowding, and computational modeling can empower education policymakers to make equitable, data-driven decisions by revealing the structural constraints that shape effective resource allocation, even when resources are limited.
Decomposing Retrieval Failures in RAG for Long-Document Financial Question Answering
Venue: arXiv cs.CL 2026
Year: 2026

Retrieval-augmented generation is increasingly used for financial question answering over long regulatory filings, yet reliability depends on retrieving the exact context needed to justify answers in high stakes settings. We study a frequent failure mode in which the correct document is retrieved but the page or chunk that contains the answer is missed, leading the generator to extrapolate from incomplete context. Despite its practical significance, this within-document retrieval failure mode has received limited systematic attention in the Financial Question Answering (QA) literature. We evaluate retrieval at multiple levels of granularity, document, page, and chunk level, and introduce an oracle based analysis to provide empirical upper bounds on retrieval and generative performance. On a 150 question subset of FinanceBench, we reproduce and compare diverse retrieval strategies including dense, sparse, hybrid, and hierarchical methods with reranking and query reformulation. Across methods, gains in document discovery tend to translate into stronger page recall, yet oracle performance still suggests headroom for page and chunk level retrieval. To target this gap, we introduce a domain fine-tuned page scorer that treats pages as an intermediate retrieval unit between documents and chunks. Unlike prior passage-based hierarchical retrieval, we fine-tune a bi-encoder specifically for page-level relevance on financial filings, exploiting the semantic coherence of pages. Overall, our results demonstrate a significant improvement in page recall and chunk retrieval.
Image Quality Assessment: Exploring Quality Awareness via Memory-driven Distortion Patterns Matching
Venue: arXiv cs.CV 2026
Year: 2026

Existing full-reference image quality assessment (FR-IQA) methods achieve high-precision evaluation by analysing feature differences between reference and distorted images. However, their performance is constrained by the quality of the reference image, which limits real-world applications where ideal reference sources are unavailable. Notably, the human visual system has the ability to accumulate visual memory, allowing image quality assessment on the basis of long-term memory storage. Inspired by this biological memory mechanism, we propose a memory-driven quality-aware framework (MQAF), which establishes a memory bank for storing distortion patterns and dynamically switches between dual-mode quality assessment strategies to reduce reliance on high-quality reference images. When reference images are available, MQAF obtains reference-guided quality scores by adaptively weighting reference information and comparing the distorted image with stored distortion patterns in the memory bank. When the reference image is absent, the framework relies on distortion patterns in the memory bank to infer image quality, enabling no-reference quality assessment (NR-IQA). The experimental results show that our method outperforms state-of-the-art approaches across multiple datasets while adapting to both no-reference and full-reference tasks.
MUOT_3M: A 3 Million Frame Multimodal Underwater Benchmark and the MUTrack Tracking Method
Venue: arXiv cs.CV 2026
Year: 2026

Underwater Object Tracking (UOT) is crucial for efficient marine robotics, large scale ecological monitoring, and ocean exploration; however, progress has been hindered by the scarcity of large, multimodal, and diverse datasets. Existing benchmarks remain small and RGB only, limiting robustness under severe color distortion, turbidity, and low visibility conditions. We introduce MUOT_3M, the first pseudo multimodal UOT benchmark comprising 3 million frames from 3,030 videos (27.8h) annotated with 32 tracking attributes, 677 fine grained classes, and synchronized RGB, estimated enhanced RGB, estimated depth, and language modalities validated by a marine biologist. Building upon MUOT_3M, we propose MUTrack, a SAM-based multimodal to unimodal tracker featuring visual geometric alignment, vision language fusion, and four level knowledge distillation that transfers multimodal knowledge into a unimodal student model. Extensive evaluations across five UOT benchmarks demonstrate that MUTrack achieves up to 8.40% higher AUC and 7.80% higher precision than the strongest SOTA baselines while running at 24 FPS. MUOT_3M and MUTrack establish a new foundation for scalable, multimodally trained yet practically deployable underwater tracking.
Cross-Embodiment Offline Reinforcement Learning for Heterogeneous Robot Datasets
Venue: arXiv cs.AI 2026
Year: 2026

Scalable robot policy pre-training has been hindered by the high cost of collecting high-quality demonstrations for each platform. In this study, we address this issue by uniting offline reinforcement learning (offline RL) with cross-embodiment learning. Offline RL leverages both expert and abundant suboptimal data, and cross-embodiment learning aggregates heterogeneous robot trajectories across diverse morphologies to acquire universal control priors. We perform a systematic analysis of this offline RL and cross-embodiment paradigm, providing a principled understanding of its strengths and limitations. To evaluate this offline RL and cross-embodiment paradigm, we construct a suite of locomotion datasets spanning 16 distinct robot platforms. Our experiments confirm that this combined approach excels at pre-training with datasets rich in suboptimal trajectories, outperforming pure behavior cloning. However, as the proportion of suboptimal data and the number of robot types increase, we observe that conflicting gradients across morphologies begin to impede learning. To mitigate this, we introduce an embodiment-based grouping strategy in which robots are clustered by morphological similarity and the model is updated with a group gradient. This simple, static grouping substantially reduces inter-robot conflicts and outperforms existing conflict-resolution methods.
Mean-Field Reinforcement Learning without Synchrony
Venue: arXiv cs.MA 2026
Year: 2026

Mean-field reinforcement learning (MF-RL) scales multi-agent RL to large populations by reducing each agent's dependence on others to a single summary statistic -- the mean action. However, this reduction requires every agent to act at every time step; when some agents are idle, the mean action is simply undefined. Addressing asynchrony therefore requires a different summary statistic -- one that remains defined regardless of which agents act. The population distribution $μ\in Δ(\mathcal{O})$ -- the fraction of agents at each observation -- satisfies this requirement: its dimension is independent of $N$, and under exchangeability it fully determines each agent's reward and transition. Existing MF-RL theory, however, is built on the mean action and does not extend to $μ$. We therefore construct the Temporal Mean Field (TMF) framework around the population distribution $μ$ from scratch, covering the full spectrum from fully synchronous to purely sequential decision-making within a single theory. We prove existence and uniqueness of TMF equilibria, establish an $O(1/\sqrt{N})$ finite-population approximation bound that holds regardless of how many agents act per step, and prove convergence of a policy gradient algorithm (TMF-PG) to the unique equilibrium. Experiments on a resource selection game and a dynamic queueing game confirm that TMF-PG achieves near-identical performance whether one agent or all $N$ act per step, with approximation error decaying at the predicted $O(1/\sqrt{N})$ rate.
Methods for Pitch Analysis in Contemporary Popular Music: Multiphonic Tones Across Genres
Venue: arXiv cs.SD 2026
Year: 2026

This study argues that electronic tones routinely used in contemporary popular music - including 808-style bass and power chords - are structurally and perceptually equivalent to multiphonics in contemporary classical music. Using listening tests (n=10) and signal analysis, we show that both types of tones elicit multiple, listener-dependent pitch percepts arising from similar spectral and temporal features. These findings suggest that pitch ambiguity is not confined to experimental classical contexts but is also a feature of mainstream music production.