In this paper, we construct a class of stochastic interpolation neural network operators (SINNOs) with random coefficients activated by sigmoidal functions. We establish their boundedness, interpolation accuracy, and approximation capabilities in the mean square sense, in probability, as well as path-wise within the space of second-order stochastic (random) processes \( L^2(Ω, \mathcal{F},\mathbb{P}) \). Additionally, we provide quantitative error estimates using the modulus of continuity of the processes. These results highlight the effectiveness of SINNOs for approximating stochastic processes with potential applications in COVID-19 case prediction.

Large Language Model (LLM) agents have demonstrated impressive capabilities for social interaction and are increasingly being deployed in situations where they might engage with both human and artificial agents. These interactions represent a critical frontier for LLM-based agents, yet existing evaluation methods fail to measure how well these capabilities generalize to novel social situations. In this paper, we introduce a method for evaluating the ability of LLM-based agents to cooperate in zero-shot, mixed-motive environments using Concordia, a natural language multi-agent simulation environment. Our method measures general cooperative intelligence by testing an agent's ability to identify and exploit opportunities for mutual gain across diverse partners and contexts. We present empirical results from the NeurIPS 2024 Concordia Contest, where agents were evaluated on their ability to achieve mutual gains across a suite of diverse scenarios ranging from negotiation to collective action problems. Our findings reveal significant gaps between current agent capabilities and the robust generalization required for reliable cooperation, particularly in scenarios demanding persuasion and norm enforcement.

Prior-data fitted networks (PFNs) are a promising alternative to time-consuming Gaussian process (GP) inference for creating fast surrogates of physical systems. PFN reduces the computational burden of GP-training by replacing Bayesian inference in GP with a single forward pass of a learned prediction model. We introduce Decoupled-V alue Attention (DV A)- motivated by the GP property that the function space is fully characterized by the kernel over inputs and the predictive mean is a weighted sum of training targets. DV A computes similarities from inputs only and propagates labels solely through values. Thus, the proposed DV A mirrors the GP update while remaining kernel-free. We demonstrate that PFNs are backbone architecture invariant and the crucial factor for scaling PFNs is the attention rule rather than the architecture itself. Specifically, our results demonstrate that (a) localized attention consistently reduces out-of-sample validation loss in PFNs across different dimensional settings, with validation loss reduced by more than 50% in five-and ten-dimensional cases, and (b) the role of attention is more decisive than the choice of backbone architecture, showing that CNN, RNN and LSTM-based PFNs can perform at par with their Transformer-based counterparts. Bayesian inference provides a powerful framework for reasoning under uncertainty, with methods like Gaussian processes (GPs) offering well-calibrated predictions and principled uncertainty estimates (Williams & Rasmussen, 2006). However, the practical application of these methods is often hindered by the heavy computational burden of learning kernel hyperparameters. For example, exact GP inference scales cubically with the number of data points, making its deployment infeasible for large datasets or problems requiring repeated training. Consider a physical system where a surrogate GP is chosen due to its uncertainty estimates and differentiable closed-form expressions. However, the underlying input dataset and configuration changes frequently, and the surrogate is supposed to work for these new, previously unseen variations. In such conditions, GP needs to be trained repeatedly, incurring significant computing cost, each time the dataset changes.

Attention is the brain's ability to selectively focus on a few specific aspects while ignoring irrelevant ones. This biological principle inspired the attention mechanism in modern Transformers. Transformers now underpin large language models (LLMs) such as GPT, but at the cost of massive training and inference energy, leading to a large carbon footprint. While brain attention emerges from neural circuits, Transformer attention relies on dot-product similarity to weight elements in the input sequence. Neuromorphic computing, especially spiking neural networks (SNNs), offers a brain-inspired path to energy-efficient intelligence. Despite recent work on attention-based spiking Transformers, the core attention layer remains non-neuromorphic. Current spiking attention (i) relies on dot-product or element-wise similarity suited to floating-point operations, not event-driven spikes; (ii) keeps attention matrices that suffer from the von Neumann bottleneck, limiting in-memory computing; and (iii) still diverges from brain-like computation. To address these issues, we propose the Spiking STDP Transformer (S$^{2}$TDPT), a neuromorphic Transformer that implements self-attention through spike-timing-dependent plasticity (STDP), embedding query--key correlations in synaptic weights. STDP, a core mechanism of memory and learning in the brain and widely studied in neuromorphic devices, naturally enables in-memory computing and supports non-von Neumann hardware. On CIFAR-10 and CIFAR-100, our model achieves 94.35\% and 78.08\% accuracy with only four timesteps and 0.49 mJ on CIFAR-100, an 88.47\% energy reduction compared to a standard ANN Transformer. Grad-CAM shows that the model attends to semantically relevant regions, enhancing interpretability. Overall, S$^{2}$TDPT illustrates how biologically inspired attention can yield energy-efficient, hardware-friendly, and explainable neuromorphic models.

In this work, Yoshikawa's manipulability index is used to investigate reinforcement learning (RL) as a framework for morphology optimization in planar robotic manipulators. A 2R manipulator tracking a circular end-effector path is first examined because this case has a known analytical optimum: equal link lengths and the second joint orthogonal to the first. This serves as a validation step to test whether RL can rediscover the optimum using reward feedback alone, without access to the manipulability expression or the Jacobian. Three RL algorithms (SAC, DDPG, and PPO) are compared with grid search and black-box optimizers, with morphology represented by a single action parameter phi that maps to the link lengths. All methods converge to the analytical solution, showing that numerical recovery of the optimum is possible without supplying analytical structure. Most morphology design tasks have no closed-form solutions, and grid or heuristic search becomes expensive as dimensionality increases. RL is therefore explored as a scalable alternative. The formulation used for the circular path is extended to elliptical and rectangular paths by expanding the action space to the full morphology vector (L1, L2, theta2). In these non-analytical settings, RL continues to converge reliably, whereas grid and black-box methods require far larger evaluation budgets. These results indicate that RL is effective for both recovering known optima and solving morphology optimization problems without analytical solutions.

Diffusion models, though successful, are known to suffer from hallucinations that create incoherent or unrealistic samples. Recent works have attributed this to the phenomenon of mode interpolation and score smoothening, but they lack a method to prevent their generation during sampling. In this paper, we propose a post-hoc adjustment to the score function during inference that leverages the Laplacian (or sharpness) of the score to reduce mode interpolation hallucination in unconditional diffusion models across 1D, 2D, and high-dimensional image data. We derive an efficient Laplacian approximation for higher dimensions using a finite-difference variant of the Hutchinson trace estimator. We show that this correction significantly reduces the rate of hallucinated samples across toy 1D/2D distributions and a high-dimensional image dataset. Furthermore, our analysis explores the relationship between the Laplacian and uncertainty in the score.

To date, there exist almost no culturally-specific evaluation benchmarks for large language models (LLMs) that cover a large number of languages and cultures. In this paper, we present Global PIQA, a participatory commonsense reasoning benchmark for over 100 languages, constructed by hand by 335 researchers from 65 countries around the world. The 116 language varieties in Global PIQA cover five continents, 14 language families, and 23 writing systems. In the non-parallel split of Global PIQA, over 50% of examples reference local foods, customs, traditions, or other culturally-specific elements. We find that state-of-the-art LLMs perform well on Global PIQA in aggregate, but they exhibit weaker performance in lower-resource languages (up to a 37% accuracy gap, despite random chance at 50%). Open models generally perform worse than proprietary models. Global PIQA highlights that in many languages and cultures, everyday knowledge remains an area for improvement, alongside more widely-discussed capabilities such as complex reasoning and expert knowledge. Beyond its uses for LLM evaluation, we hope that Global PIQA provides a glimpse into the wide diversity of cultures in which human language is embedded.

Recent advances in post-training techniques have endowed Large Language Models (LLMs) with enhanced capabilities for tackling complex, logic-intensive tasks through the generation of supplementary planning tokens. This development raises a fundamental question: Are these models aware of what they "learn" and "think"? To address this, we define three core competencies: (1) awareness of learned latent policies, (2) generalization of these policies across domains, and (3) alignment between internal reasoning traces and final outputs. We empirically evaluate these abilities on several tasks, each designed to require learning a distinct policy. Furthermore, we contrast the profiles of models post-trained via Supervised Fine-Tuning (SFT), Direct Policy Optimization (DPO), and Group Relative Policy Optimization (GRPO). Our findings indicate that RL-trained models not only demonstrate greater awareness of their learned behaviors and stronger generalizability to novel, structurally similar tasks than SFT models but also often exhibit weak alignment between their reasoning traces and final outputs, an effect most pronounced in GRPO-trained models.

Datasets and code files are publicly accessible at Link. Our dataset will be hosted on both the GitHub and cloud storage drive. Code for the TimesNet Link Code for the SAITS Link 5.2 Trajectory Prediction Codes The following are the codes for the trajectory prediction methods used in our work. The dataset is primarily created by an academic team (students and faculty). The data statistics are shown in Section 4 of the main paper.