Robostral Navigate

Deploying navigation systems at scale requires a recipe that minimizes sensor assumptions, generalizes across robot embodiments, and trains efficiently. Yet, today's best systems depend on depth sensors, multi-camera rigs, or pre-built maps, limiting the hardware they support and increasing deployment cost. We introduce Robostral Navigate, an 8B vision-language model built around this scalability objective. The model consumes only a stream of monocular RGB images - the most ubiquitous sensor across robotic platforms and predicts waypoints by pointing to the next target location in the current camera view. Operating purely in image space, rather than robot-specific coordinates, makes the policy naturally robust to changes in camera intrinsics and scene scale, enabling deployment across wheeled, legged, and aerial robots without recalibration. We generate 2.4 million trajectories across 350k simulated scenes to reduce the reliance on real-world data collection and scale easily. We further introduce a prefix-caching training recipe that packs entire episodes into single training sequences, reducing training tokens by 22x and cutting training time from months to days. A tree-based attention mask prevents conditioning on previous ground-truth actions, encouraging visually grounded action prediction, and reinforcement learning is used to further improve exploration and recovery capabilities. On the Room-to-Room and Room-Across-Room in Continuous Environments (R2R-CE and RxR-CE) benchmarks, Robostral Navigate sets a new state of the art. On R2R-CE, it achieves a 77.4% success rate, surpassing the best monocular method by 10.5 points and the strongest depth- or multi-camera system by 5.3 points despite using only a single RGB camera. On RxR-CE, it reaches 75.1% success rate, outperforming all monocular baselines.

Estimation of Simultaneously Sparse and Low Rank Matrices

The paper introduces a penalized matrix estimation procedure aiming at solutions which are sparse and low-rank at the same time. Such structures arise in the context of social networks or protein interactions where underlying graphs have adjacency matrices which are block-diagonal in the appropriate basis. We introduce a convex mixed penalty which involves $\ell_1$-norm and trace norm simultaneously. We obtain an oracle inequality which indicates how the two effects interact according to the nature of the target matrix. We bound generalization error in the link prediction problem. We also develop proximal descent strategies to solve the optimization problem efficiently and evaluate performance on synthetic and real data sets.

Graph Prediction in a Low-Rank and Autoregressive Setting

We study the problem of prediction for evolving graph data. We formulate the problem as the minimization of a convex objective encouraging sparsity and low-rank of the solution, that reflect natural graph properties. The convex formulation allows to obtain oracle inequalities and efficient solvers. We provide empirical results for our algorithm and comparison with competing methods, and point out two open questions related to compressed sensing and algebra of low-rank and sparse matrices.