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A $360^\circ$ streaming system only needs high quality where the viewer faces, so knowing when a head will turn away matters as much as where it will go. Across four public head-tracking datasets, two used to fix and validate the method and two held out for testing, three patterns emerge on the held-out sets. First, viewers facing the same region turn away within a second of one another far more often than time-shifted traces allow. That estimate is about five times the pairwise threshold for a video timing one departure in ten, mapping to roughly one and a third to over twice that one-in-ten share. The excess co-departing fraction is 0.0422, with a 90% interval from 0.0279 to 0.0565. Second, time since the last large head movement improves held-out departure prediction beyond video and viewer effects. It adds 0.0793 nats per departure, a predictive dependence rather than proof of an internal timer. Third, on the eye-tracked test set, gaze crosses the region boundary after the head starts moving, lagging head onset by 0.30 s. Because headsets record continuous angles, a departure exists only after a rule marks when a settled hold ends once the head swings past a speed and angle threshold. Before touching the test sets, we picked one primary setting for the headline estimates above and tested 18 settings on synthetic traces with planted answers, requiring at least nine passing settings for robustness. Fifteen settings passed for the clock and all 15 valid settings confirm its gain; 8 passed for synchrony and all 8 valid settings agree, one short of the nine-setting bar; and 6 of 7 dual-validated settings agree on gaze lag. Synchrony validation drops from 17 or 18 passing settings under guessed noise to 8 under measured noise because zero-tolerance rules reject a small baseline offset, consistently positive at one dataset size, as datasets grow.

At the edge of stability, the iterates of gradient descent oscillate along the sharp directions of the Hessian. This poses a significant challenge for continuous-time models as the usual continuous-time approximation -- the gradient flow -- admits no oscillations. Several continuous-time models have been proposed to capture the behavior at the edge of stability, among them central flow and rod flow. Although both models can be interpreted as performing a coarse-graining in time, the connection between them remains poorly understood. Here we show that both flows can be derived from a third object, the edge coupling: a functional on consecutive iterates whose critical points are the fixed points and period-two orbits of gradient descent. It is revealed that the two flows correspond to coarse-grainings at different time scales. Rod flow coarse-grains over only the fastest time scale, while central flow coarse-grains over both the fast and intermediate time scales. Furthermore, using the edge coupling, we derive rod flows and central flows for momentum methods such as heavy ball and Adam. We verify the derived flows experimentally on representative neural network architectures, where they track the discrete iterates throughout all phases of training -- including the transition from the stable regime to the edge of stability.

Connecting hand input in mixed reality (MR) to a nearby physical device typically requires an integration written in advance for that device, its transport and the mapping. ControlAnything defers this integration to the moment of use and assigns it to a coding agent. On a Meta Quest 3, the wearer selects an object outlined by SAM 3.1 and states what their hands should control. An agent built on Meta's Muse Spark model then writes a connector program on the wearer's laptop, tests it against the live device through hand-written MIDI, Bluetooth and key-press transports, and returns augmented-reality (AR) controls, a per-frame hand program, or both. These outputs are a form of generative UI, interfaces created by an AI model; here, the agent also generates and tests the code that binds the interface to a physical device. In a single-session technical evaluation with the author as the only wearer, nine of ten requests addressing five targets reached a ready state, and the wearer stopped one. The median time to ready was 32.5 s (range 24.9-57.8 s, excluding speech transcription); sequential model calls accounted for a median of 89.9% of this time, and 91.7% of input tokens came from the prompt cache. The system's evidence of success extends to transport acknowledgements but not to physical effects. These findings point to connector reuse and the observation of effects through the headset's own sensors as next steps for on-demand device integration in MR. A user study with first-time wearers is planned.

In two-tier triage a fast model decides most web requests and escalates the rest to a slow tier, so an attack the fast tier closes is never examined. We hold each of seven attack families out of training, recalibration and thresholds, splice the payloads into parameters of real browsing traffic, and compare zero-shot decision models, which return a probability for a typed question, with supervised detectors, a local language model, the OWASP Core Rule Set and an anomaly baseline. Detectors trained on the known families can give much of a held-out family a confident benign verdict: over 10 training runs, ModernBERT gives 37% to 60% of held-out path traversal a probability below 0.05 and escalates only 50% to 81% of it within a 5% benign budget, against nearly all of the same requests when traversal is known. Jev and Clef, two hosted decision models whose budget decisions do not depend on the held-out family, escalate at least 97.6% of every family within the same budget, but their undisclosed training data may contain these public families. Tests on recent exploits need controls for request shape: Jev escalates 37% of benign twins (exploit requests with the attack replaced by legitimate values), and detectors trained on older exploits learn what scanner requests look like. A search guided by Jev's probability gets 43% of held-out attacks past Jev within 300 queries, but Jev's answers vary: asked again, it escalates those requests in 60% of its answers.

We have applied a novel combination of classic relational database modeling and modern reinforcement learning to automated intrusion response to enable inductive decision agents. Unlike previous work in the area, our approach allows agents to handle variable quantities of network assets without retraining. We test the operational performance of our approach in a virtualized computer network with variable topologies, red-team automation and simulated user agents. The task of the agents is to prevent hosts in the network from being accessed by the red-team agent, while minimizing the availability costs induced from defensive measures. We test a combination of heuristic agents and policies trained using relational reinforcement learning. The reinforcement learning agents were overall more efficient at defending the system than the heuristic policy, and the closest to the performance of human operators at the task.

Monadically dependent graph classes are those in which first-order logic cannot encode all graphs. They include all nowhere dense classes and all classes of bounded twin-width. We show that first-order model checking is fixed-parameter tractable on every monadically dependent graph class. Together with the known hardness result for hereditary classes that are not monadically dependent, this gives a complete characterization of the hereditary graph classes with fixed-parameter tractable first-order model checking. This resolves a central open problem in algorithmic model theory. Our proof combines ideas from structural graph theory (graph decompositions), finite model theory (locality of first-order logic), and model theory (counting types). In particular, we show that in monadically dependent classes, tuples of fixed length have only $|U|^{O(1)}$ types of fixed quantifier rank over any set of parameters $U$.

Modern data systems often require aggregating information from multiple sources: some might be entirely untrustworthy, while the remaining presumably reliable sources may still suffer from a small amount of corruption. We study robust mean estimation under this practical scenario, which is formulated through the double corruption model: samples are divided among $N$ users, each with $n$ samples. $\varepsilon$ fraction of the users could be arbitrarily corrupted, while each of the remaining ``good'' users still have $α$-fraction ($α>0$) of corrupted samples. The goal is to estimate the unknown mean $μ$ with small $\ell_2$ error. This is a challenging scenario because we must handle two types of adversarial corruption: user-level corruption and sample-level corruption. When the unknown distribution has covariance matrix bounded by the identity matrix, we design a sum-of-squares (SoS) algorithm that achieves an $\ell_2$ error of $\sqrtα$ with probability at least $2/3$ as long as the total number of samples $nN=\widetildeΩ(d/α)$. The estimation error and sample complexity are min-max optimal under the mild condition. For comparison, treating all $nN$ samples as $(\varepsilon+α)$-corrupted and applying standard robust mean estimation only achieves an error of $\sqrt{\varepsilon+α}$. Thus, our new algorithm removes the adverse effect of untrustworthy users and achieves the optimal error as if only sample-level corruption is present. Also, our SoS algorithm extends to the heterogeneous setting where each user's local mean could be additionally shifted by $\sqrtβ$ in $\ell_2$ distance. We show that an error of $O(\sqrt{α+β})$ can be achieved with probability at least $2/3$ when $nN=\widetildeΩ(d/(α+β))$.