#01Jul 21, 2026
cs.LG
Riemannian Deep Learning:Modules, Networks, and Geometries
Chen Ziheng
Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations. This thesis develops a unified framework for Riemannian deep learning from three complementary perspectives: reusable neural modules, manifold-specific network architectures, and the design of underlying geometries. It generalizes batch normalization from Euclidean spaces and individual manifolds to broad classes of Lie groups and gyrogroups, and extends multinomial logistic regression from Euclidean space to SPD manifolds and then to general Riemannian manifolds. It further develops neural networks for several important geometric representations, including an unconstrained model of hyperbolic space, Busemann-based hyperbolic learning, and full-rank correlation matrices. Finally, it introduces adaptive and computationally efficient Riemannian metrics on SPD manifolds, including learnable Log-Euclidean geometries and fast, stable Cholesky-based geometries. The proposed methods are supported by theoretical analysis and validated through numerical experiments and applications in vision, signal processing, graph learning, and genomics.
#02Jul 21, 2026
cs.LG
GUIDED Network-Agnostic Feature Initialization for Spatial Transferability in GNN-based Models
Alessandro Scalese, Santhanakrishnan Narayanan, Constantinos Antoniou
The Traffic Assignment Problem is a fundamental but computationally expensive component of transportation planning. While Graph Neural Networks have emerged as fast, data-driven surrogates, their practical deployment is severely constrained by a spatial generalization gap. Standard models rely on transductive feature initializations that tie travel demand to fixed network topologies, preventing seamless transfer to new urban environments. To overcome this structural limitation, this research proposes a network-agnostic initialization layer, termed Geometrically Unconstrained Inductive Demand EmbeDding (GUIDED). By injecting travel demand as a scalar attribute on auxiliary virtual links rather than as specific node features, this modular framework standardizes the input space regardless of network scale. Extensive experimental evaluation across multiple urban topologies demonstrates that a Heterogeneous Graph Attention Network (HetGAT) model integrated with the proposed GUIDED layer maintains state-of-the-art predictive accuracy on single-network tasks, while demonstrating superior robustness to out-of-distribution demand patterns and maintaining a distinct performance advantage over the baseline even under severe data scarcity. Notably, the proposed feature initialization enables highly parameter-efficient domain adaptation for inter-network transfer learning without artificial input homogenization, establishing a robust foundation for truly inductive models. At the same time, the optimized scatter operations of the initialization layer yield an approximate 50% reduction in training time per epoch compared to the baseline approach. Furthermore, while demonstrated on vehicular traffic, this fundamental abstraction of spatial topology provides a versatile blueprint for generalized origin-destination spatial problems, such as freight logistics and multimodal network optimization.
#03Jul 21, 2026
cs.RO
From Distances to Trajectories: Real-Time Signed Distance Function Mapping and Distance-Accelerated Motion Planning for UAVs
Jason Stanley, Zhirui Dai, Qihao Qian and 6 more
Autonomous flight in cluttered environments requires a robot to build a geometric map of its surroundings and plan safe, dynamically feasible trajectories, all onboard and in real time. Conventional approaches treat mapping and planning as separate stages and often rely on binary occupancy for collision checking. We argue that these two stages should be co-designed around a single representation: a signed distance function (SDF). By encoding distance to the nearest obstacle, an SDF provides richer information for planning and trajectory optimization than occupancy alone. We develop an Octree REsidual Network (OREN) that pairs an explicit octree prior with an implicit neural residual to reconstruct SDFs online from point cloud observations with the efficiency of volumetric methods and the accuracy and differentiability of neural methods. In tandem, we develop Bubble$^\star$, a search-based planner that exploits the distance information to grow maximal collision-free balls, which we call bubbles, with formal guarantees of termination, completeness, and failure detection. Planning over a graph of bubbles significantly reduces collision checks compared to a grid-based A$^\star$ search and returns a bubble sequence that forms a safe corridor for trajectory optimization. We demonstrate the integrated OREN-Bubble$^\star$ approach onboard a quadrotor, navigating unseen indoor environments in real time under tight compute constraints. OREN improves SDF estimation by $22$% compared to baselines, while Bubble$^\star$ finds trajectories spanning $\approx 90$ m through a cluttered environment in $1$-$3$ sec., whereas baselines take up to $10$ sec. in the same environment.
#04Jul 21, 2026
cs.AI
LLM Detection as an Intervention: Downstream Impact under Strategic User Behavior
Meena Jagadeesan, Tatsunori Hashimoto, Jon Kleinberg
As LLM adoption becomes more widespread, there is a growing interest in detecting LLM-generated content, for example through LLM detection tools and through heuristics based on language patterns. Detectors operate as an intervention that steers not only the detected attribute itself, but also downstream metrics such as LLM usage and output quality. In this work, we demonstrate how imperfect LLM detectors lead to counterintuitive impacts on these downstream metrics, by distorting how users are incentivized to use LLMs in their workflow. We develop a stylized model which captures how users strategically choose how much to use the LLM and how to post-process content to reduce the detected attribute. Using this model, we show that LLM detection can counterintuitively lead humans to increase their LLM usage. Moreover, even when reducing the detected attribute improves output quality, we find that introducing an LLM detector can lead users to produce lower quality outputs. In contrast, we show that detectors result in a clean "rise-then-fall" pattern for the detected attribute, which we empirically reproduce for word frequencies on arXiv abstracts. Altogether, our work illustrates how LLM detection can distort LLM usage and output quality, uncovering failure modes when LLM detectors operate as an intervention on these downstream metrics.
#05Jul 21, 2026
cs.LG
Real-time optimal control with shallow recurrent decoder networks
Matteo Tomasetto, Francesco Braghin, J. Nathan Kutz and 1 more
Controlling dynamical systems in real-time across multiple scenarios is critical to enabling adaptive control strategies, ensuring stability and efficiency. However, to tailor control actions in response to varying scenarios, traditional optimal control problems typically require several system simulations, which are often computationally demanding due to the high-dimensionality of the underlying spatio-temporal dynamics. In this work, we exploit SHallow REcurrent Decoder networks-based Reduced Order Modeling (SHRED-ROM) to synthesize a real-time closed-loop controller for high-dimensional and parametric dynamics, relying solely on limited state sensor readings. After training the model on a few optimal examples given by an expert demonstrator, SHRED-ROM mimics the expert behavior with effective distributed control actions in new scenarios, alleviating the curse of dimensionality. Moreover, a sensor forecaster is synthesized and used to close the loop at the latent level, thus efficiently mitigating possible sensor failures or delays. The performance of the proposed optimal control strategy is finally assessed on three challenging high-dimensional cases dealing with either parametric density control or fluid flow control.