The Fisher Information Matrix (FIM) is the canonical local measure of the curvature of a statistical model's log-likelihood surface, and its dominant eigenvalue λmax quantifies the worst-case sensitivity of the model's output distribution to infinitesimal parameter perturbation [1, 2]. The spectral properties of the FIM of neural networks have been studied directly in the random matrix theory literature. Pennington and Worah [4] derive the limiting spectral density of the FIM of a single-hidden-layer network in the high-dimensional asymptotic regime, building on the broader programme of analysing neural network Hessian and kernel spectra via random matrix methods [5, 6], with subsequent work extending these techniques to deeper architectures and non-asymptotic regimes [7, 8]. These results characterize the typical (bulk and edge) spectral behaviour of the FIM for a fixed network and a random or structured input ensemble. This paper studies a complementary question, posed as a perturbation problem rather than an asymptotic-spectrum problem: how does the dominant eigenvalue of a fixed, evaluated empirical FIM change under two specific structured perturbations of the underlying distribution? The first perturbation is a change in the conditioning input away from a reference (in-distribution) ensemble. The second is a structured additive perturbation of the model's own parameters by finite-precision quantization noise -- a perturbation of independent mathematical interest, since it falls outside the i.i.d.-input asymptotic regime treated in the random matrix literature cited above, and instead concerns a fixed network whose parameters, not its input distribution, are perturbed by a noise process with a specific, analytically tractable structure (Definition 4.1). To our knowledge, this parameterperturbation question for the FIM's dominant eigenvalue, under either source of departure, has not been previously formalized.

A recurring data mining task in complex networks is to determine how individual nodes contribute to system behavior. Existing approaches rely on either static-graph centralities or control-theoretic quantities such as controllability Gramians, which assume linear, time-invariant dynamics. Estimated systems, however, are typically nonlinear and time-varying. We define "emergent contribution (EC)," a finite-horizon measure of a node's dynamical leverage: the metric-weighted energy of its impulse response accumulated along the system trajectory. Computed from the Jacobians of any differentiable model, EC is estimator-agnostic and reduces exactly to average controllability in the linear, time-invariant limit. Our contribution is a characterization of when the two measures agree and diverge. Using a controlled synthetic family with known ground-truth contribution, we construct a phase diagram spanning nonlinearity, regime structure, persistence, and perturbation amplitude. EC and average controllability agree under static or smoothly drifting dynamics and both track ground truth. Divergence emerges under persistent regime switching, is strongest under persistent sign reversal, and disappears when the sign reversal is removed. At extreme perturbation amplitudes, both measures degrade, identifying the limits of local linearization. We place five estimated real systems from several domains within this phase space. Their placement serves as a diagnostic of when EC provides information beyond static controllability and therefore justifies its additional computational cost. On one panel examined in depth, a twenty-seed retraining ensemble reveals a robust variance--leverage dissociation: nodes whose perturbations propagate widely despite low within-system variance, which is not recovered by static centralities nor variance-based summaries.

We study true self-avoiding walk (TSAW) as a mechanism for improving empirical integral estimation via Markov chain Monte Carlo (MCMC). We consider finite-state adaptive sampling dynamics associated with an irreducible Markov kernel $P$ on a finite set, with stationary distribution $π$, in which the transition probabilities are penalized according to empirical overuse. Our main result is that the empirical occupation counts $L_t(i)$ and transition counts $N_t(i,j)$ of the resulting TSAW-based walk satisfy \[ L_t(i)-tπ_i = O(\sqrt{\log t}) \quad\text{and}\quad N_t(i,j)-tπ_iP_{ij}=O(\sqrt{\log t}) \qquad\text{almost surely} \] for every state $i$ and every edge $(i,j)$ with $P_{ij}>0$. Consequently, for every bounded function $f:V\to\mathbb R$, the error of our integral estimator converges as \[ \left|\frac1t\sum_{s=0}^{t-1} f(X_s)-\sum_{i\in V}π_i f(i)\right| = O\left(\frac{\sqrt{\log t}}{t}\right) \qquad\text{almost surely}. \] These results show that, in contrast with the usual $t^{-1/2}$ error scaling for empirical averages under standard random-walk-based methods, TSAW-based estimator yields empirical integral errors of order $O(\sqrt{\log t}/t)$ almost surely, thereby achieving a substantially sharper dependence on the sample size $t$.

Ritzy Bay Area town torn apart after teacher's daughter, 16, was behind wheel when four friends died in high-speed crash... then she posted a TikTok video that poured fuel on the flames Two CIA officers killed in Mexico when their car skidded off ravine and exploded after meeting about bust of'largest ever drug lab' Nancy Guthrie sheriff's appalling past revealed: Beat handcuffed suspect so badly he needed intensive care, used VILE language about woman and lied in sworn statement Trump confronts Xi as US forces seize Chinese ship carrying mysterious'gift' to Iran New'Hollywood dose' pill: A-listers hooked on'youth elixir' that dermatologists say is anti-ageing, shrinks pores, smooths wrinkles... and even banishes rosacea Days after we got engaged, the love of my life told me he'd killed a man and buried him in a bog. I reported him to police... but then I made this irreversible mistake Ark of the Covenant's final resting place pinpointed by archaeologists as fresh search begins Fury as murderer marries pen pal behind bars... as teenage victim's mom says: 'I'm serving a life sentence without my son' Insiders claim failed AI rollout could be to blame for Tim Cook's departure from Apple - as one says'the AI era requires a different kind of leadership' Life-threatening cantaloupe recall in four states upgraded to FDA's highest risk level... 'reasonable probability of death' AMANDA PLATELL: Why Sarah Ferguson - with the ghost of Princess Diana at her side - is ready to sensationally blow up the Royal Family. She knows ALL their secrets... Team USA Olympics star Noah Lyles slammed for'horrible' reaction to his wife's wedding dress reveal In honour of the Queen's (purple!) reign: Kate mirrors late monarch's colourful wardrobe and wears her pearl earrings and necklace US troops board second tanker as Iran is accused of breaking ceasefire'numerous times' How to lose weight when perimenopause sabotages your metabolism: I'm a trainer but when I hit 46, I piled on the pounds overnight. The new'posh' drug that's easier to order than Uber Eats - and why all my middle-class friends have ditched booze and cocaine for it: JANA HOCKING Autistic woman, 24, worked hard to build independent life for herself... now she's PARALYZED thanks to selfishness of stranger Insiders claim failed AI rollout could be to blame for Tim Cook's departure from Apple - as one says'the AI era requires a different kind of leadership' Industry insiders have revealed what they claim is the real reason for Tim Cook's departure from Apple . After 15 years in the top spot, the CEO will make way for John Ternus, the current head of hardware engineering, who has been at the company for 25 years.

Recent works have shown that physics-inspired architectures allow the training of deep graph neural networks (GNNs) without oversmoothing. The role of these physics is unclear, however, with successful examples of both reversible (e.g., Hamiltonian) and irreversible (e.g., diffusion) phenomena producing comparable results despite diametrically opposed mechanisms, and further complications arising due to empirical departures from mathematical theory. This work presents a series of novel GNN architectures based upon structure-preserving bracket-based dynamical systems, which are provably guaranteed to either conserve energy or generate positive dissipation with increasing depth. It is shown that the theoretically principled framework employed here allows for inherently explainable constructions, which contextualize departures from theory in current architectures and better elucidate the roles of reversibility and irreversibility in network performance.

Spatial boundaries, such as ecological transitions or climatic regime interfaces, capture steep environmental gradients, and shifts in their structure can signal emerging environmental changes. Quantifying uncertainty in spatial boundary locations and formally testing for temporal shifts remains challenging, especially when boundaries are derived from noisy, gridded environmental data. We present a unified framework that combines heteroskedastic Gaussian process (GP) regression with a scaled Maximum Absolute Difference (MAD) Global Envelope Test (GET) to estimate spatial boundary curves and assess whether they evolve over time. The heteroskedastic GP provides a flexible probabilistic reconstruction of boundary lines, capturing spatially varying mean structure and location specific variability, while the test offers a rigorous hypothesis testing tool for detecting departures from expected boundary behaviors. Simulation studies show that the proposed method achieves the correct size under the null and high power for detecting local boundary shifts. Applying our framework to the Sahel Sahara transition zone, using annual Koppen Trewartha climate classifications from 1960 to 1989, we find no statistically significant decade scale changes in the arid and semi arid or semi arid and non arid interfaces. However, the method successfully identifies localized boundary shifts during the extreme drought years of 1983 and 1984, consistent with climate studies documenting regional anomalies in these interfaces during that period.

Electric vehicles (EVs) are key to sustainable mobility, yet their lithium-ion batteries (LIBs) degrade more rapidly under prolonged high states of charge (SOC). This can be mitigated by delaying full charging \ours until just before departure, which requires accurate prediction of user departure times. In this work, we propose Transformer-based real-time-to-event (TTE) model for accurate EV departure prediction. Our approach represents each day as a TTE sequence by discretizing time into grid-based tokens. Unlike previous methods primarily dependent on temporal dependency from historical patterns, our method leverages streaming contextual information to predict departures. Evaluation on a real-world study involving 93 users and passive smartphone data demonstrates that our method effectively captures irregular departure patterns within individual routines, outperforming baseline models. These results highlight the potential for practical deployment of the \ours algorithm and its contribution to sustainable transportation systems.

A memo obtained by WIRED confirms Denise Dresser's departure from Slack. She is now headed to OpenAI. Slack CEO Denise Dresser is leaving the company and joining OpenAI as the company's chief revenue officer, multiple sources tell WIRED. Marc Benioff, the chief executive of Salesforce, which owns Slack, shared news of Dresser's departure in a message to staff on Monday evening. At OpenAI, Dresser will manage the company's enterprise unit, which has been growing rapidly this year.

A Research Leader Behind ChatGPT's Mental Health Work Is Leaving OpenAI The model policy team leads core parts of AI safety research, including how ChatGPT responds to users in crisis. An OpenAI safety research leader who helped shape ChatGPT's responses to users experiencing mental health crises announced her departure from the company internally last month, WIRED has learned. Andrea Vallone, the head of a safety research team known as model policy, is slated to leave OpenAI at the end of the year. Wood said OpenAI is actively looking for a replacement and that, in the interim, Vallone's team will report directly to Johannes Heidecke, the company's head of safety systems. Vallone's departure comes as OpenAI faces growing scrutiny over how its flagship product responds to users in distress .

Why an AI'godfather' is quitting Meta after 12 years Just a couple of weeks ago, one of the godfathers of artificial intelligence was in St James's Palace being handed an award from King Charles for his work in artificial intelligence (AI). Professor Yann LeCun was being honoured along with six other recipients for his contributions to the field, which have been credited as advancing deep learning. But Mr LeCun is at odds with some of the AI world over the future of the generation-defining technology. And now he is going all-in on his idea of advanced machine intelligence after announcing he is leaving his role as Meta's chief AI scientist to start a new firm. During his 12 years at the company, Prof LeCun won the prestigious Turing Award and witnessed several flurries of excitement around AI - not least the most recent boom in generative AI accelerated by rival OpenAI's launch of ChatGPT in late 2022.