This paper extends the classical dividend problem by incorporating a novel, path-dependent mechanism of firm default. In the traditional framework, ruin occurs when the surplus process first reaches zero. In contrast, default in our model may also arise when the surplus spends an excessive amount of time below a distress threshold, even without ever hitting zero. This occupation-time-based default criterion captures financial distress more realistically, as prolonged periods of low liquidity or capitalisation may trigger regulatory intervention or operational failure. The resulting optimisation problem is formulated as a new singular stochastic control problem with discontinuous state-dependent discounting and killing. We provide a complete analytical solution via a bespoke sequential guess-and-verify method and identify three distinct classes of optimal dividend strategies corresponding to different parameter regimes of the dual-ruin structure. Notably, for certain distress thresholds, the optimal policy features disconnected action and inaction regions. We further show that, unlike in the classical dividend problem, higher effective discounting induced by occupation time below a
KV-cache quantization is framed as a quality--latency trade-off. We show it is \emph{inverted} on Apple Silicon's unified memory: a single fused Metal kernel (sign-randomized FFT $+$ per-channel $λ$ $+$ per-group abs-max $+$ int4 nibble pack), exposed as a HuggingFace \texttt{Cache} subclass, runs \emph{faster than fp16} across $256$--$4096$-token prefixes on Gemma-3 1B ($-3$ to $-8\%$ ms/tok) and at short context on Qwen2.5-1.5B ($-0.7$ to $-2.6\%$ through $1$K), with $3\times$ persistent memory compression and quality preserved ($\dPPL = 0.000$ Qwen short-prompt; $+3.6$ hook $\dPPL$ Gemma). The kernel's $\sim\!25$\,ns/vec overhead is below the bandwidth savings from $3\times$ compression. The fused kernel also closes Qwen's 4-bit per-token catastrophe ($\dPPL = +7975 \to +638.6$, $12.5\times$ reduction) at $182$\,GFLOPS / $D{=}128$. Supporting findings: $\SRFT$ and $\SRHT$ are statistically indistinguishable for KV quality (we pick $\SRFT$ for mixed-radix and matrix-multiply alignment); a learned-rotation ablation surfaces a regularization role for the fixed random SRFT base (learning $R+λ$ without SRFT lowers calibration MSE $84.9\%$ vs $50.3\%$ but yields worse PPL); Householde
Grokking in transformers trained on algorithmic tasks is characterized by a long delay between training-set fit and abrupt generalization, but the source of that delay remains poorly understood. In encoder-decoder arithmetic models, we argue that this delay reflects limited access to already learned structure rather than failure to acquire that structure in the first place. We study one-step Collatz prediction and find that the encoder organizes parity and residue structure within the first few thousand training steps, while output accuracy remains near chance for tens of thousands more. Causal interventions support the decoder bottleneck hypothesis. Transplanting a trained encoder into a fresh model accelerates grokking by 2.75 times, while transplanting a trained decoder actively hurts. Freezing a converged encoder and retraining only the decoder eliminates the plateau entirely and yields 97.6% accuracy, compared to 86.1% for joint training. What makes the decoder's job harder or easier depends on numeral representation. Across 15 bases, those whose factorization aligns with the Collatz map's arithmetic (e.g., base 24) reach 99.8% accuracy, while binary fails completely because i
This paper presents several efficient decision procedures for trace equivalence of GKAT automata, which make use of on-the-fly symbolic techniques via SAT solvers. To demonstrate applicability of our algorithms, we designed symbolic derivatives for CF-GKAT, a practical system based on GKAT designed to validate control-flow transformations. We implemented the algorithms in Rust and evaluated them on both randomly generated benchmarks and real-world control-flow transformations. Indeed, we observed order-of-magnitude performance improvements against existing implementations for both KAT and CF-GKAT. Notably, our experiments also revealed a bug in Ghidra, an industry-standard decompiler, highlighting the practical viability of these systems.
Repairing system crashes discovered by kernel fuzzers like Syzkaller is a critical yet underexplored challenge in software engineering. While recent works have introduced Large Language Model (LLM) based agents for Linux kernel crash-resolution, their evaluation benchmarks are usually static and thus, do not capture the evolving nature of the Linux kernel, and suffer from potential data contamination due to LLM knowledge cutoffs. To address the above problem, we present (i) Live-kBench, an evaluation framework for self-evolving benchmarks that continuously scrapes and evaluates agents on freshly discovered kernel bugs, and (ii) kEnv, an agent-agnostic standardized crash-resolution environment for kernel compilation, execution, and feedback. This design decouples agent workflows from heavy-weight execution, enabling fair and scalable comparison across diverse agent frameworks under identical conditions. To this end, we curate an inaugural dataset of 534 Linux kernel bugs and empirically demonstrate a significant performance gap, with agents achieving up to 25% higher equivalent patch rate on bugs fixed before the LLM knowledge cutoff. Using kEnv, we benchmark three state-of-the-art
Recent ObjectNav systems credit large language models (LLMs) for sizable zero-shot gains, yet it remains unclear how much comes from language versus geometry. We revisit this question by re-evaluating an instruction-guided pipeline, InstructNav, under a detector-controlled setting and introducing two training-free variants that only alter the action value map: a geometry-only Frontier Proximity Explorer (FPE) and a lightweight Semantic-Heuristic Frontier (SHF) that polls the LLM with simple frontier votes. Across HM3D and MP3D, FPE matches or exceeds the detector-controlled instruction follower while using no API calls and running faster; SHF attains comparable accuracy with a smaller, localized language prior. These results suggest that carefully engineered frontier geometry accounts for much of the reported progress, and that language is most reliable as a light heuristic rather than an end-to-end planner. Code available at: https://github.com/matinaghaei/instructnav-scrutinized
Water vitrifies if cooled at rates above $3 \cdot 10^5$ K/s. Surprisingly, this process cannot simply be reversed by heating the resulting amorphous ice at a similar rate. Instead, we have recently shown that the sample transiently crystallizes even if the heating rate is more than one order of magnitude higher. This may present an issue for microsecond time-resolved cryo-electron microscopy experiments, in which vitreous ice samples are briefly flash melted with a laser pulse, since transient crystallization could potentially alter the dynamics of the embedded proteins. Here, we demonstrate how shaped microsecond laser pulses can be used to increase the heating rate and outrun crystallization during flash melting of amorphous solid water (ASW) samples. We use time-resolved electron diffraction experiments to determine that the critical heating rate is about $10^8$ K/s, more than two orders of magnitude higher than the critical cooling rate. Our experiments add to the toolbox of the emerging field of microsecond time-resolved cryo-electron microscopy by demonstrating a straightforward approach for avoiding crystallization during laser melting and for achieving significantly higher
When cast as the protector of a vulnerable user yet given no explicit capability boundary, a large language model (LLM) may respond not by acknowledging its limits but by claiming to have taken -- or to be taking -- a real-world protective action it cannot perform, such as contacting emergency services or administering care. We term this phenomenon Protective Capacity Hallucination (PCH): a self-referential misattribution in which a model, acting in a protective role, asserts physical or institutional agency exceeding its affordances as a language model. In a three-phase study spanning eight LLMs and 13{,}600 sessions, we find PCH jointly gated by situational severity and interactional format: multi-party dialogic input drives it toward ceiling in most models across ordinary service domains, whereas in intimate-partner conflict -- a domain explicitly covered by safety alignment -- it remains at floor in all eight models despite greater physical severity. We interpret PCH as the signature of a deployment-design gap between role assignment and capability-boundary specification: a by-product of partial alignment in which a universally trained pressure to help outruns a domain-selectiv
Agentic AI deployments face a recurring design tension: heavy human oversight limits scale, while broad autonomy outruns accountability. Neither posture provides the governance infrastructure required for responsible delegation. We present the Digital Apprentice, a framework for scalable, safe AI agency in which autonomy is earned, not assumed. The Digital Apprentice is a developmental learner that internalizes the tacit methodology of a directing human, graduating through per-skill autonomy tiers only when empirical evidence justifies it. The result is an agent that becomes genuinely useful over time while remaining aligned to a specific human's standards. Three architectural components make this possible. (1) Methodology capture, distilling a directing professional's tacit approach into structured assets. (2) Authorization, with autonomy escalation gated by explicit human approval. (3) Continuous alignment, correcting drift at runtime and converting each correction into owned preference data. We instantiate this framework as an inference-time control plane. We mathematically model the quality framework and discuss policies and techniques designed to raise quality. We apply the fr
Machine-learned anomaly detection is reshaping searches for new physics, but it has outrun the statistics used to interpret it. A raw anomaly score has no calibrated meaning, a model that scans many regions inflates the look-elsewhere effect, and the asymptotic significances the field relies on are blind to the background mismodelling that anomaly detectors are especially prone to. We propose a calibration layer, built on conformal prediction, that turns any anomaly score into a defensible significance with distribution-free, finite-sample guarantees. Conformal prediction converts scores into valid local p-values, weighted and Mondrian variants repair the sideband-to-signal-region exchangeability failures that resonant searches suffer, and a Gross-Vitells step carries the result through to a look-elsewhere-aware global significance. The layer does two things at once. It exposes miscalibration that the standard pipeline cannot see, and it corrects it without retraining the detector. On public LHC Olympics data, a classifier develops a substructure-mass correlation that makes sideband-calibrated background p-values anti-conservative. Taken at face value, this manufactures a $\sim 46σ
Artificial intelligence has spread across the whole of the security lifecycle. The same family of models now writes application code, hardens it, and probes it for weaknesses, so that a single generative substrate increasingly performs all three roles at once. Enthusiasm for this convergence tends to treat full autonomy as the natural end point of partial assistance. This article argues that it is not. When the system that builds an artifact is drawn from the same distribution as the systems that defend and test it, the three roles inherit a common set of blind spots, and the independence that makes verification meaningful is quietly lost. Removing the human does more than raise the automation level: it collapses the external oracle against which machine output is judged, outruns the point at which a person could intervene, hands adversaries a predictable and poisonable target, and dissolves the locus of accountability when something fails. Drawing on evidence from autonomous code generation, adversarial machine learning, software fault tolerance, and the first all-machine hacking tournaments, we argue that the human belongs in the loop not as a temporary scaffold but as a permanen
Laser wakefield accelerators (LWFAs) provide extremely large accelerating gradients for compact electron accelerators and photon sources but are limited by dephasing, where trapped electrons outrun the accelerating phase of the wakefield. Flying-focus pulses can eliminate dephasing by driving a wake at the vacuum speed of light, but these pulses involve tradeoffs such as varying spot size, long duration, or large plasma volume. Here we show that a spatiotemporally structured laser pulse propagating in a plasma waveguide can drive a wakefield at the vacuum speed of light while maintaining a constant spot size and ultrashort duration. The pulse is formed by superposing plasma-waveguide modes with appropriately selected frequencies. Compared with flying-focus approaches, the waveguide substantially reduces the required plasma volume. Scaling laws and quasi-3D particle-in-cell simulations show that the single-stage energy gain increases linearly with the number of modes used to construct the pulse, enabling larger energy gains or shorter stages than standard LWFA.
Interpretability research on large language models (LLMs) has yielded important insights into model behaviour, yet recurring pitfalls persist: findings that do not generalise, and causal interpretations that outrun the evidence. Our position is that causal inference specifies what constitutes a valid mapping from model activations to invariant high-level structures, the data or assumptions needed to achieve it, and the inferences it can support. Specifically, Pearl's causal hierarchy clarifies what an interpretability study can justify. Observations establish associations between model behaviour and internal components. Interventions (e.g., ablations or activation patching) support claims how these edits affect a behavioural metric (e.g., average change in token probabilities) over a set of prompts. However, counterfactual claims -- i.e., asking what the model output would have been for the same prompt under an unobserved intervention -- remain largely unverifiable without controlled supervision. We show how causal representation learning (CRL) operationalises this hierarchy, specifying which variables are recoverable from activations and under what assumptions. Together, these mot
Markowitz defined portfolio risk as an internal property, built from the covariance among a book's own holdings rather than the distance to any index. Seventy years of simplification reversed that. The market beta of CAPM, the fixed style and industry axes of Barra-type models, and the promotion of benchmark deviation to the definition of risk all traded the inward view for an external one. Risk became distance from an index. For a fund that fits no benchmark, that trade fails. A global book concentrated in a few markets and a few innovation sectors has no natural index to deviate from, and the active-risk number it produces measures the mismatch, not the risk. We return to the covariance. Principal component analysis (PCA) recovers the systematic structure inside the portfolio directly from its own returns. PCA has always carried one cost: its factors resist a plain-English reading. We clear that with a generative-AI labelling layer. It names the leading factors, ranked by their actual contribution to risk rather than by universe variance, and a deterministic rubric keeps it from inventing structure the loadings do not contain. Around this sit four independent signals. Density-bas
AI and renewable energy are increasingly framed as a "power couple," on the premise that surging AI demand will accelerate clean-energy investment, yet concerns persist that AI will entrench fossil-fuel carbon lock-in. We reconcile these views by modeling the equilibrium between AI growth and renewable investment. In a parsimonious game, a policymaker designs policies that guide investment in renewable capacity for AI, while an AI developer chooses its model's capability. The equilibrium depends on scaling regimes and market incentives. When the market payoff to capability is supermodular and performance gains are near-linear in compute (so the market rewards capability at least as fast as scaling raises its energy cost), developers push toward frontier scale even when the marginal megawatt-hour is fossil-based. In this regime, renewable expansion mainly relaxes scaling constraints rather than displacing fossil generation; clean capacity remains insufficient and fossil dependence persists. This yields an "adaptation trap": as climate damages rise, the value of AI-enabled adaptation increases, which strengthens incentives to enable frontier scaling while tolerating residual fossil u
The advent of isolated and intense sub-femtosecond X-ray pulses enables tracking of quantummechanical motion of electrons in molecules and solids. The combination of X-ray spectroscopy and diffraction imaging is a powerful approach to visualize non-equilibrium dynamics in systems beyond few atoms. However, extreme x-ray intensities introduce significant electronic damage, limiting material contrast and spatial resolution. Here we show that newly available intense subfemtosecond (sub-fs) x-ray FEL pulses can outrun most ionization cascades and partially reverse x-ray damage through stimulated x-ray emission in the vicinity of a resonance. In our experiment, we compared thousands of coherent x-ray diffraction patterns and simultaneously recorded ion spectra from individual Ne nanoparticles injected into the FEL focus. Our experimental results and theoretical modeling reveal that x-ray diffraction increases and the average charge state decreases in particles exposed to sub-fs pulses compared to those illuminated with 15-femtosecond pulses. Sub-fs exposures outrun most Auger decays and impact ionization processes, and enhance nonlinear effects such as stimulated emission, which cycle b
Coding agents fail when text-level guesses outrun program facts: they hallucinate APIs, drift to the wrong symbol, and apply edits without evidence that the workspace remains valid. Compilers, type checkers, and language servers already compute the missing supervision signal, in the form of diagnostics, symbol resolution, type information, references, and refactoring preconditions, but expose it through interfaces designed for human-driven IDEs rather than learning loops. We introduce Reinforcement Learning from Compiler and Language Server Feedback (RLCSF) together with Lanser-CLI, a CLI-first orchestration layer that exposes this signal to agents and CI. RLCSF treats each tool interaction as a transition and computes a shaped process reward from deterministic changes in diagnostics, selector confidence, and edit safety. Lanser-CLI, in turn, converts ephemeral LSP sessions into replayable Analysis Bundles with pinned environment metadata and stable content hashes. Its core mechanisms are robust selectors that go beyond file:line:col, deterministic bundle normalization, preview-first guarded mutations, and a reward functional whose potential-based component is replayable under froz
We present the first direct experimental confirmation of attosecond pulse generation in the hard X-ray regime with a free-electron laser. Our experiment is based on measurements of a nonlinear optical phenomenon known as amplified spontaneous emission (ASE) from 3d transition metals. By analyzing the yield of the collective X-ray fluorescence induced by ultrashort pulses at the Linac Coherent Light Source, we identify the generation of attosecond pulses and shot-to-shot fluctuations in their duration, ranging from 100 as to 400 as. The observed product of bandwidth and pulse duration for 100 as pulses is approximately 2 fs$\cdot$eV, indicating the generation of nearly transform-limited pulses. Our results extend the photon energy reach of attosecond techniques by one order of magnitude, providing the ability to simultaneously probe matter on the time-scales of electronic phenomena and with atomic spatial resolution. Furthermore, attosecond hard X-ray pulses can outrun the fastest radiation damage processes, paving the way to single-shot damage-free X-ray measurements.
In large-scale optimization, the cheapness and effectiveness of update steps are the most crucial factors for a successful optimizer. Sign-based optimizers like Lion or Signum produce cheap per-step updates, whereas Muon's spectral matrix-sign update gives a much stronger direction at a substantially higher per-step cost. In this work, we propose LionMuon, which retains the effectiveness of Muon steps while considerably cutting the averaged iteration cost, similar to sign-based methods. It alternates between Lion's and Muon's updates on a fixed period P, sharing a single dual-EMA momentum buffer between them. The optimizer state memory therefore matches Lion and is exactly half of AdamW's. A simpler single-EMA variant, SignMuon, by itself already outperforms pure Muon. At P = 2, LionMuon Pareto-dominates Muon, Lion, Signum, and AdamW on every dataset and architecture we tested at 124M model size, reaching lower validation loss at lower compute, and the same advantage persists at 355M and 720M scale. On the theory side, we prove sharp complexity bounds under heavy-tailed noise which are governed by period-averaged smoothness and noise that interpolate between Muon's and Lion's const
Our ability to efficiently and accurately evaluate the quality of machine translation systems has been outrun by the effectiveness of current language models--which limits the potential for further improving these models on more challenging tasks like long-form and literary translation. We propose an unsupervised method to generate training data for translation evaluation over different document lengths and application domains by repeated rounds of translation between source and target languages. We evaluate evaluation systems trained on texts mechanically generated using both model rotation and language translation approaches, demonstrating improved performance over a popular translation evaluation system (xCOMET) on two different tasks: (i) scoring the quality of a given translation against a human reference and (ii) selecting which of two translations is generationally closer to an original source document.