In practice, many models from a function class can fit a dataset almost equally well. This collection of near-optimal models is known as the Rashomon set. Prior work has shown that the Rashomon set offers flexibility in choosing models aligned with secondary objectives like interpretability or fairness. However, it is unclear how far this flexibility extends to different trustworthy criteria, especially given that most trustworthy machine learning systems today still rely on complex specialized optimization procedures. Is the Rashomon set all you need for trustworthy model selection?

Accurately modeling complex dynamic spatio-temporal systems requires capturing flow-mediated interdependencies and context-sensitive interaction dynamics. Existing methods, predominantly graph-based or attention-driven, rely on similaritydriven connectivity assumptions, neglecting asymmetric flow exchanges that govern system evolution. We propose Spatio-Temporal Flow, a physics-inspired paradigm that explicitly models dynamic node couplings through quantifiable flow transfers governed by conservation principles. Building on this, we design FlowNet, a novel architecture leveraging flow tokens as information carriers to simulate source-todestination transfers via Flow Allocation Modules, ensuring state redistribution aligns with conservation laws. FlowNet dynamically adjusts the interaction radius through an Adaptive Spatial Masking module, suppressing irrelevant noise while enabling context-aware propagation. A cascaded architecture enhances scalability and nonlinear representation capacity. Experiments demonstrate that FlowNet significantly outperforms existing state-of-the-art approaches on seven metrics in the modeling of three real-world systems, validating its efficiency and physical interpretability. We establish a principled methodology for modeling complex systems through spatio-temporal flow interactions.

Steering cooperative multi-agent reinforcement learning (MARL) towards desired outcomes is challenging, particularly when the global guidance from a human on the whole multi-agent system is impractical in a large-scale MARL. On the other hand, designing external mechanisms (e.g., intrinsic rewards and human feedback) to coordinate agents mostly relies on empirical studies, lacking a easy-to-use research tool. In this work, we employ multi-agent influence diagrams (MAIDs) as a graphical framework to address the above issues. First, we introduce the concept of MARL interaction paradigms (orthogonal to MARL learning paradigms), using MAIDs to analyze and visualize both unguided self-organization and global guidance mechanisms in MARL. Then, we design a new MARL interaction paradigm, referred to as the targeted intervention paradigm that is applied to only a single targeted agent, so the problem of global guidance can be mitigated. In implementation, we introduce a causal inference technique--referred to as Pre-Strategy Intervention (PSI)--to realize the targeted intervention paradigm. Since MAIDs can be regarded as a special class of causal diagrams, a composite desired outcome that integrates the primary task goal and an additional desired outcome can be achieved by maximizing the corresponding causal effect through the PSI. Moreover, the bundled relevance graph analysis of MAIDs provides a tool to identify whether an MARL learning paradigm is workable under the design of an MARL interaction paradigm. In experiments, we demonstrate the effectiveness of our proposed targeted intervention, and verify the result of relevance graph analysis.

Understanding the geometry of neural network loss landscapes is a central question in deep learning, with implications for generalization and optimization. A striking phenomenon is linear mode connectivity (LMC), where independently trained models can be connected by low-or zero-barrier paths, despite appearing to lie in separate loss basins. However, this is often obscured by symmetries in parameter space--such as neuron permutations--which make functionally equivalent models appear dissimilar. Prior work has predominantly focused on neuron reordering through permutations, but such approaches are limited in scope and fail to capture the richer symmetries exhibited by modern architectures such as Transformers. In this work, we introduce a unified framework that captures four symmetry classes--permutations, semi-permutations, orthogonal transformations, and general invertible maps--broadening the set of valid reparameterizations and subsuming many previous approaches as special cases. Crucially, this generalization enables, for the first time, the discovery of low-and zero-barrier linear interpolation paths between independently trained Vision Transformers and GPT-2 models. Furthermore, our framework extends beyond pairwise alignment, to multi-model and width-heterogeneous settings, enabling alignment across architectures of different sizes. These results reveal deeper structure in the loss landscape and underscore the importance of symmetry-aware analysis for understanding model space geometry. Our code is available here.

ChebNet, one of the earliest spectral GNNs, has largely been overshadowed by Message Passing Neural Networks (MPNNs), which gained popularity for their simplicity and effectiveness in capturing local graph structure. Despite their success, MPNNs are limited in their ability to capture long-range dependencies between nodes. This has led researchers to adapt MPNNs through rewiring or make use of Graph Transformers, which compromises the computational efficiency that characterized early spatial message-passing architectures, and typically disregards the graph structure. Almost a decade after its original introduction, we revisit ChebNet to shed light on its ability to model distant node interactions. We find that out-of-box, ChebNet already shows competitive advantages relative to classical MPNNs and GTs on long-range benchmarks, while maintaining good scalability properties for high-order polynomials. However, we uncover that this polynomial expansion leads ChebNet to an unstable regime during training. To address this limitation, we cast ChebNet as a stable and non-dissipative dynamical system, which we coin Stable-ChebNet. Our Stable-ChebNetmodel allows for stable information propagation, and has controllable dynamics which do not require the use of eigendecompositions, positional encodings, or graph rewiring.

We introduce a novel hypergraph message passing framework inspired by interacting particle systems, where hyperedges act as fields inducing shared node dynamics. By incorporating attraction, repulsion, and Allen-Cahn forcing terms, particles of varying classes and features achieve class-dependent equilibrium, enabling separability through the particle-driven message passing. We investigate both first-order and secondorder particle system equations for modeling these dynamics, which mitigate over-smoothing and heterophily thus can capture complete interactions. The more stable second-order system permits deeper message passing. Furthermore, we enhance deterministic message passing with stochastic element to account for interaction uncertainties. We prove theoretically that our approach mitigates oversmoothing by maintaining a positive lower bound on the hypergraph Dirichlet energy during propagation and thus to enable hypergraph message passing to go deep. Empirically, our models demonstrate competitive performance on diverse real-world hypergraph node classification tasks, excelling on both homophilic and heterophilic datasets. Source code is available at the link.

Solving bilevel optimization (BLO) problems to global optimality is generally intractable. A common surrogate is to compute a hyper-stationary point--a stationary point of the hyper-objective function obtained by minimizing or maximizing the upper-level objective over the lower-level solution set. Existing methods, however, either provide weak notions of stationarity or require restrictive assumptions to guarantee the smoothness of hyper-objective functions. In this paper, we eliminate these impractical assumptions and show that strong (Clarke) hyper-stationarity remains computable even when the hyper-objective is nonsmooth. Our key ingredient is a new structural property, called set smoothness, which captures the variational dependence of the lower-level solution set on the upper-level variable. We prove that this property holds for a broad class of BLO problems and ensures weak convexity (resp.

Large Language Models (LLMs) enable a new form of digital experimentation where treatments combine human and model-generated content in increasingly sophisticated ways. The main methodological challenge in this setting is representing these high-dimensional treatments without losing their semantic meaning or rendering analysis intractable. Here we address this problem by focusing on learning low-dimensional representations that capture the underlying structure of such treatments. These representations enable downstream applications such as guiding generative models to produce meaningful treatment variants and facilitating adaptive assignment in online experiments. We propose double kernel representation learning, which models the causal effect through the inner product of kernel-based representations of treatments and user covariates. We develop an alternating-minimization algorithm that learns these representations efficiently from data and provide convergence guarantees under a low-rank factor model. As an application of this framework, we introduce an adaptive design strategy for online experimentation and demonstrate the method's effectiveness through numerical experiments.

Deep neural networks using state space models as layers are well suited for longrange sequence tasks but can be challenging to compress after training. We use that regularizing the sum of Hankel singular values of state space models leads to a fast decay of these singular values and thus to compressible models. To make the proposed Hankel singular value regularization scalable, we develop an algorithm to efficiently compute the Hankel singular values during training iterations by exploiting the specific block-diagonal structure of the system matrices that we use in our state space model parametrization. Experiments on Long Range Arena benchmarks demonstrate that the regularized state space layers are up to 10 more compressible than standard state space layers while maintaining high accuracy.

Composed Video Retrieval (CoVR) retrieves a target video given a query video and a modification text describing the intended change. Existing CoVR benchmarks emphasize appearance shifts or coarse event changes and therefore do not test the ability to capture subtle, fast-paced temporal differences. We introduce TFCoVR, the first large-scale benchmark dedicated to temporally fine-grained CoVR. TF-CoVR focuses on gymnastics and diving, and provides 180K triplets drawn from FineGym and FineDiving datasets. Previous CoVR benchmarks, focusing on temporal aspect, link each query to a single target segment taken from the same video, limiting practical usefulness. In TF-CoVR, we instead construct each pair by prompting an LLM with the label differences between clips drawn from different videos; every pair is thus associated with multiple valid target videos (3.9 on average), reflecting real-world tasks such as sports-highlight generation. To model these temporal dynamics, we propose TF-CoVR-Base, a concise two-stage training framework: (i) pre-train a video encoder on fine-grained action classification to obtain temporally discriminative embeddings; (ii) align the composed query with candidate videos using contrastive learning. We conduct the first comprehensive study of image, video, and general multimodal embedding (GME) models on temporally fine-grained composed retrieval in both zero-shot and fine-tuning regimes. On TF-CoVR, TF-CoVR-Base improves zero-shot mAP@50 from 5.92 (LanguageBind) to 7.51, and after fine-tuning raises the state-of-the-art from 19.83 to 27.22.