'Nature seems to have already solved the problem.' Breakthroughs, discoveries, and DIY tips sent six days a week. To help figure out what makes stingrays such unique and unusual swimmers, a team of mechanical engineers at the University of California, Riverside (UCR) created a wavy robotic fin. After submerging the robot in underwater tunnels designed to mimic swimming near the sea floor, their tests indicate that different types of ray species may have evolved alternative swimming techniques that best suit their setting. Specifically, the findings suggest that some ray species swimming near the seafloor adjust the way their fins move and tilt to counter a downward force that would otherwise pull them toward the ground. It turns out that stingrays gracefully gliding along waves near seabeds aren't doing it to look cool.

Language Models (LMs) struggle with complex, interdependent instructions, particularly in high-stakes domains like finance where precision is critical. We introduce FIFE, a novel, high-difficulty benchmark designed to assess LM instruction-following capabilities for financial analysis tasks. FIFE comprises 88 human-authored prompts and employs a verification system with chainable, verifiable constraints for fine-grained reward signals. We evaluate 53 models (proprietary, open-weight, open-source) in a zero-shot setting. Our key findings reveal a clear performance hierarchy: the top open-weight model (76.1 strict / 79.5 loose) surpasses the leading proprietary system (65.9 strict / 70.5 loose), while the best open-source models lag significantly (45.5 strict / 48.9 loose). However, even top-performing models struggle with FIFE's complex requirements, failing to achieve perfect compliance. We release our dataset and code as an open-source resource to promote research in Reinforcement Learning for the financial domain.

Tensor regression has been widely studied in the literature.

Testing marine robotics systems in controlled environments before field tests is challenging, especially when acoustic-based sensors and control surfaces only function properly underwater. Deploying robots in indoor tanks and pools often faces space constraints that complicate testing of control, navigation, and perception algorithms at scale. Recent developments of high-fidelity underwater simulation tools have the potential to address these problems. We demonstrate the utility of the recently released HoloOcean 2.0 simulator with improved dynamics for torpedo AUV vehicles and a new ROS 2 interface. We have successfully demonstrated a Hardware-in-the-Loop (HIL) and Software-in-the-Loop (SIL) setup for testing and evaluating a CougUV torpedo autonomous underwater vehicle (AUV) that was built and developed in our lab. With this HIL and SIL setup, simulations are run in HoloOcean using a ROS 2 bridge such that simulated sensor data is sent to the CougUV (mimicking sensor drivers) and control surface commands are sent back to the simulation, where vehicle dynamics and sensor data are calculated. We compare our simulated results to real-world field trial results.

Transformers are deep architectures that define ``in-context maps'' which enable predicting new tokens based on a given set of tokens (such as a prompt in NLP applications or a set of patches for a vision transformer). In previous work, we studied the ability of these architectures to handle an arbitrarily large number of context tokens. To mathematically, uniformly analyze their expressivity, we considered the case that the mappings are conditioned on a context represented by a probability distribution which becomes discrete for a finite number of tokens. Modeling neural networks as maps on probability measures has multiple applications, such as studying Wasserstein regularity, proving generalization bounds and doing a mean-field limit analysis of the dynamics of interacting particles as they go through the network. In this work, we study the question what kind of maps between measures are transformers. We fully characterize the properties of maps between measures that enable these to be represented in terms of in-context maps via a push forward. On the one hand, these include transformers; on the other hand, transformers universally approximate representations with any continuous in-context map. These properties are preserving the cardinality of support and that the regular part of their Fréchet derivative is uniformly continuous. Moreover, we show that the solution map of the Vlasov equation, which is of nonlocal transport type, for interacting particle systems in the mean-field regime for the Cauchy problem satisfies the conditions on the one hand and, hence, can be approximated by a transformer; on the other hand, we prove that the measure-theoretic self-attention has the properties that ensure that the infinite depth, mean-field measure-theoretic transformer can be identified with a Vlasov flow.

Motile nanosized particles, or "nanobots", promise more effective and less toxic targeted drug delivery because of their unique scale and precision. We consider the case in which the cancer is "diffuse", dispersed such that there are multiple distinct cancer sites. We investigate the problem of a swarm of nanobots locating these sites and treating them by dropping drug payloads at the sites. To improve the success of the treatment, the drug payloads must be allocated between sites according to their "demands"; this requires extra nanobot coordination. We present a mathematical model of the behavior of the nanobot agents and of their colloidal environment. This includes a movement model for agents based upon experimental findings from actual nanoparticles in which bots noisily ascend and descend chemical gradients. We present three algorithms: The first algorithm, called KM, is the most representative of reality, with agents simply following naturally existing chemical signals that surround each cancer site. The second algorithm, KMA, includes an additional chemical payload which amplifies the existing natural signals. The third algorithm, KMAR, includes another additional chemical payload which counteracts the other signals, instead inducing negative chemotaxis in agents such that they are repelled from sites that are already sufficiently treated. We present simulation results for all algorithms across different types of cancer arrangements. For KM, we show that the treatment is generally successful unless the natural chemical signals are weak, in which case the treatment progresses too slowly. For KMA, we demonstrate a significant improvement in treatment speed but a drop in eventual success, except for concentrated cancer patterns. For KMAR, our results show great performance across all types of cancer patterns, demonstrating robustness and adaptability.

Understanding how language models develop their internal computational structure is a central problem in the science of deep learning. While susceptibilities, drawn from statistical physics, offer a promising analytical tool, their full potential for visualizing network organization remains untapped. In this work, we introduce an embryological approach, applying UMAP to the susceptibility matrix to visualize the model's structural development over training. Our visualizations reveal the emergence of a clear ``body plan,'' charting the formation of known features like the induction circuit and discovering previously unknown structures, such as a ``spacing fin'' dedicated to counting space tokens. This work demonstrates that susceptibility analysis can move beyond validation to uncover novel mechanisms, providing a powerful, holistic lens for studying the developmental principles of complex neural networks.

We introduce DeepSeek-Prover-V2, an open-source large language model designed for formal theorem proving in Lean 4, with initialization data collected through a recursive theorem proving pipeline powered by DeepSeek-V3. The cold-start training procedure begins by prompting DeepSeek-V3 to decompose complex problems into a series of subgoals. The proofs of resolved subgoals are synthesized into a chain-of-thought process, combined with DeepSeek-V3's step-by-step reasoning, to create an initial cold start for reinforcement learning. This process enables us to integrate both informal and formal mathematical reasoning into a unified model. The resulting model, DeepSeek-Prover-V2-671B, achieves state-of-the-art performance in neural theorem proving, reaching 88.9% pass ratio on the MiniF2F-test and solving 49 out of 658 problems from PutnamBench. In addition to standard benchmarks, we introduce ProverBench, a collection of 325 formalized problems, to enrich our evaluation, including 15 selected problems from the recent AIME competitions (years 24-25). Further evaluation on these 15 AIME problems shows that the model successfully solves 6 of them. In comparison, DeepSeek-V3 solves 8 of these problems using majority voting, highlighting that the gap between formal and informal mathematical reasoning in large language models is substantially narrowing.

Financial institutions are required by regulation to report suspicious financial transactions related to money laundering. Therefore, they need to constantly monitor vast amounts of incoming and outgoing transactions. A particular challenge in detecting money laundering is that money launderers continuously adapt their tactics to evade detection. Hence, detection methods need constant fine-tuning. Traditional machine learning models suffer from catastrophic forgetting when fine-tuning the model on new data, thereby limiting their effectiveness in dynamic environments. Continual learning methods may address this issue and enhance current anti-money laundering (AML) practices, by allowing models to incorporate new information while retaining prior knowledge. Research on continual graph learning for AML, however, is still scarce. In this review, we critically evaluate state-of-the-art continual graph learning approaches for AML applications. We categorise methods into replay-based, regularization-based, and architecture-based strategies within the graph neural network (GNN) framework, and we provide in-depth experimental evaluations on both synthetic and real-world AML data sets that showcase the effect of the different hyperparameters. Our analysis demonstrates that continual learning improves model adaptability and robustness in the face of extreme class imbalances and evolving fraud patterns. Finally, we outline key challenges and propose directions for future research.