One Sequential Recommendation Model Pretrained from Synthetic Priors Predicts Multiple Datasets

Existing sequential recommendation models rely on dataset-specific training, where the learned parameters are fitted to the item catalog and the observed interaction distribution of the training data. This limits generalization to new domains, typically requiring retraining from scratch. In this work, we propose SRPFN, a Prior-data Fitted Network for sequential recommendation -- predicting the next item in a single forward pass without any gradient-based parameter updates in the target domain. SRPFN is pretrained offline on 25.6M sequences sampled from a synthetic prior that spans diverse item-to-item transition patterns, learning to produce posterior predictive next-item distributions. At inference time, SRPFN generates recommendations by conditioning on a support set of item-item transition examples from the target domain, adapting to domain-specific patterns without retraining. Extensive experiments on five benchmarks across 10 baselines show that SRPFN achieves the best or second-best performance across nearly all metrics and datasets, while being substantially more computationally efficient than trained baselines. These results establish that a single model pretrained on synthetic priors can generalize across diverse real-world domains, offering a framework for update-free sequential recommendation.

How Much Memory Do We Need? Adaptive Memory Gate for Neural Operators

Neural operators have emerged as a powerful data-driven approach for solving time-dependent PDEs. Among recent advances, memory-augmented neural operators explicitly incorporate past states and have achieved remarkable performance under low-resolution observation settings. However, existing approaches apply a fixed memory weight regardless of observation conditions, such as resolution or physical parameters, limiting their adaptability. Our preliminary experiments reveal that optimal memory weight varies with resolution and viscosity, implying that a fixed memory weight cannot simultaneously optimize performance across diverse settings. We propose AMGFNO, which dynamically modulates memory weight through a learnable gate. On the Kuramoto-Sivashinsky and Burgers' equations, AMGFNO achieves 55-79% nRMSE reduction over at low resolution, with the learned gate value automatically decreasing from $\bar{g} \approx 0.7$ to near-zero as resolution increases.

Q-Delta: Beyond Key-Value Associative State Evolution

Linear attention reformulates sequence modeling as recurrent state evolution, enabling efficient linear-time inference. Under the key-value associative paradigm, existing approaches restrict the role of the query to the readout operation, decoupling it from state evolution. We show that query-conditioned state readout induces a structured value prediction over accumulated memory that complements key-based retrieval. Based on this insight, we propose Q-Delta, a query-aware delta rule that integrates mixed key-query prediction errors into state evolution, enabling jointly corrective dynamics while preserving delta-rule efficiency. We establish stability guarantees for the resulting dynamics and derive a hardware-efficient chunkwise-parallel formulation with a custom Triton implementation. Empirical results demonstrate stable optimization, competitive throughput, and consistent improvements over strong baselines on language modeling and long-context retrieval tasks.

STAR: Rethinking MoE Routing as Structure-Aware Subspace Learning

Mixture-of-Experts (MoE) scales model capacity efficiently by selectively routing inputs to a specialized subset of experts. However, input-expert specialization, the core motivation of MoE, critically depends on whether the router is actually aware of input structure. In practice, MoE routing is typically implemented as a shallow linear projection with limited awareness of input representation, which often leads to unstable routing. We propose STAR, a Structure Aware Routing that rethinks MoE routing as a subspace learning problem by augmenting standard learnable routing with an evolving principal subspace that tracks dominant input structure via Generalized Hebbian Algorithm (GHA). By aligning routing decisions directly with input structure, STAR enables stable expert specialization. We evaluate STAR on controlled synthetic setup and large-scale language and vision tasks, where it consistently improves routing quality and downstream performance over strong MoE baselines. Moreover, optional test-time subspace updates further enhance routing robustness and generalization under input distribution shifts.

Learning Posterior Predictive Distributions for Node Classification from Synthetic Graph Priors

One of the most challenging problems in graph machine learning is generalizing across graphs with diverse properties. Graph neural networks (GNNs) face a fundamental limitation: they require separate training for each new graph, preventing universal generalization across diverse graph datasets. A critical challenge facing GNNs lies in their reliance on labeled training data for each individual graph, a requirement that hinders the capacity for universal node classification due to the heterogeneity inherent in graphs -- differences in homophily levels, community structures, and feature distributions across datasets. Inspired by the success of large language models (LLMs) that achieve in-context learning through massive-scale pre-training on diverse datasets, we introduce NodePFN. This universal node classification method generalizes to arbitrary graphs without graph-specific training. NodePFN learns posterior predictive distributions (PPDs) by training only on thousands of synthetic graphs generated from carefully designed priors. Our synthetic graph generation covers real-world graphs through the use of random networks with controllable homophily levels and structural causal models for complex feature-label relationships. We develop a dual-branch architecture combining context-query attention mechanisms with local message passing to enable graph-aware in-context learning. Extensive evaluation on 23 benchmarks demonstrates that a single pre-trained NodePFN achieves 71.27 average accuracy. These results validate that universal graph learning patterns can be effectively learned from synthetic priors, establishing a new paradigm for generalization in node classification.

HINTS: Extraction of Human Insights from Time-Series Without External Sources

Human decision-making, emotions, and collective psychology are complex factors that shape the temporal dynamics observed in financial and economic systems. Many recent time series forecasting models leverage external sources (e.g., news and social media) to capture human factors, but these approaches incur high data dependency costs in terms of financial, computational, and practical implications. In this study, we propose HINTS, a self-supervised learning framework that extracts these latent factors endogenously from time series residuals without external data. HINTS leverages the Friedkin-Johnsen (FJ) opinion dynamics model as a structural inductive bias to model evolving social influence, memory, and bias patterns. The extracted human factors are integrated into a state-of-the-art backbone model as an attention map. Experimental results using nine real-world and benchmark datasets demonstrate that HINTS consistently improves forecasting accuracy. Furthermore, multiple case studies and ablation studies validate the interpretability of HINTS, demonstrating strong semantic alignment between the extracted factors and real-world events, demonstrating the practical utility of HINTS.

How Many Experts Are Enough? Towards Optimal Semantic Specialization for Mixture-of-Experts

Finding the optimal configuration of Sparse Mixture-ofExperts (SMoE) that maximizes semantic differentiation among experts is essential for exploiting the full potential of MoE architectures. However, existing SMoE frameworks either heavily rely on hyperparameter tuning or overlook the importance of diversifying semantic roles across experts when adapting the expert pool size. We propose Mixture-of-Experts for Adaptive Semantic Specialization (MASS), a semanticaware MoE framework for adaptive expert expansion and dynamic routing. MASS introduces two key advancements: (i) a gradient-based semantic drift detector that prompts targeted expert expansion when the existing expert pool lacks capacity to capture the full semantic diversity of the data, and (ii) an integration of adaptive routing strategy that dynamically adjusts expert usage based on token-level routing confidence mass. We first demonstrate that MASS reliably converges to the point of optimal balance between cost-performance trade-off with notably improved sematic specialization in a highly controlled synthetic setup. Further empirical results on real-world datasets across language and vision domains show that MASS consistently outperforms a range of strong MoE baselines, demonstrating its domain robustness and enhanced expert specialization.

Can TabPFN Compete with GNNs for Node Classification via Graph Tabularization?

Foundation models pretrained on large data have demonstrated remarkable zero-shot generalization capabilities across domains. Building on the success of TabPFN for tabular data and its recent extension to time series, we investigate whether graph node classification can be effectively reformulated as a tabular learning problem. We introduce TabPFN-GN, which transforms graph data into tabular features by extracting node attributes, structural properties, positional encodings, and optionally smoothed neighborhood features. This enables TabPFN to perform direct node classification without any graph-specific training or language model dependencies. Our experiments on 12 benchmark datasets reveal that TabPFN-GN achieves competitive performance with GNNs on homophilous graphs and consistently outperforms them on heterophilous graphs. These results demonstrate that principled feature engineering can bridge the gap between tabular and graph domains, providing a practical alternative to task-specific GNN training and LLM-dependent graph foundation models.

Are Graph Transformers Necessary? Efficient Long-Range Message Passing with Fractal Nodes in MPNNs

Graph Neural Networks (GNNs) have emerged as powerful tools for learning on graph-structured data, but often struggle to balance local and global information. While graph Transformers aim to address this by enabling long-range interactions, they often overlook the inherent locality and efficiency of Message Passing Neural Networks (MPNNs). We propose a new concept called fractal nodes, inspired by the fractal structure observed in real-world networks. Our approach is based on the intuition that graph partitioning naturally induces fractal structure, where subgraphs often reflect the connectivity patterns of the full graph. Fractal nodes are designed to coexist with the original nodes and adaptively aggregate subgraph-level feature representations, thereby enforcing feature similarity within each subgraph. We show that fractal nodes alleviate the over-squashing problem by providing direct shortcut connections that enable long-range propagation of subgraph-level representations. Experiment results show that our method improves the expressive power of MPNNs and achieves comparable or better performance to graph Transformers while maintaining the computational efficiency of MPNN by improving the long-range dependencies of MPNN.

PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling

Scientific machine learning often involves representing complex solution fields that exhibit high-frequency features such as sharp transitions, fine-scale oscillations, and localized structures. While implicit neural representations (INRs) have shown promise for continuous function modeling, capturing such high-frequency behavior remains a challenge-especially when modeling multiple solution fields with a shared network. Prior work addressing spectral bias in INRs has primarily focused on single-instance settings, limiting scalability and generalization. In this work, we propose Global Fourier Modulation (GFM), a novel modulation technique that injects high-frequency information at each layer of the INR through Fourier-based reparameterization. This enables compact and accurate representation of multiple solution fields using low-dimensional latent vectors. Building upon GFM, we introduce PDEfuncta, a meta-learning framework designed to learn multi-modal solution fields and support generalization to new tasks. Through empirical studies on diverse scientific problems, we demonstrate that our method not only improves representational quality but also shows potential for forward and inverse inference tasks without the need for retraining.