Time series forecasting drives operational decisions in areas like finance, transportation, and energy. While supervised learning approaches achieve strong performance, they require domain-specific training, feature engineering, and ongoing maintenance. Large-scale foundation models have recently emerged as a zero-shot alternative, avoiding task-specific training much like LLMs. In this work, we evaluate foundation models against standard supervised approaches. Rather than focusing solely on aggregate accuracy, we analyze performance across four operational regimes: periodic human-centric systems, physically constrained processes, stochastic financial markets, and heterogeneous demand forecasting. Our results characterize optimal deployment areas. Foundation models perform well in domains with transferable periodic structures and are efficient for cold-start or long-tail scenarios. Conversely, supervised specialists maintain higher precision in systems governed by strict physical constraints. In financial domains, newer foundation models are rapidly closing the performance gap with supervised specialists. We further quantify trade-offs in inference latency, data drift adaptability, and deployment constraints. Finally, we propose a Complexity Router that assigns each series to the optimal model class using empirical features. We demonstrate that this selective routing achieves higher accuracy and significantly lower inference costs compared to deploying a universal foundation model, providing a practical framework for balancing generalization and efficiency.

We audit alignment-induced shifts in residual-stream activations of three open-weight instruction-tuned LLMs (Llama-3.1-8B-Instruct, Gemma-2-9B-it, Qwen-2.5-7B-Instruct) using the effective rank of the alignment modification matrix on safety-relevant inputs, rho_eps := rank_eps(M_Ds)/d, which formalizes the single-refusal-direction observation of Arditi et al. (2024) as a continuous quantity. The paper has three contributions. (1) Confound-controlled measurement: a four-variant decomposition (M_naive, M_template, M_aligned, M_DiD) separates chat-template formatting, alignment-stage shift, and the refusal-mediating direction, and recovers the Arditi refusal direction on M_DiD at |cos| in {0.77, 0.86, 0.50} (Llama/Gemma/Qwen); chat-template-controlled rho_eps is {0.0029, 0.0048, 0.0044}, and the centered SVD residual is 4-7x larger. (2) Constructive calibration on a 3-layer MLP across rho_eps in {0.008, 0.17, 0.33, 0.40} exhibits a sweet-spot vs. brittle distinction: mild rank-maximization (lambda=5) buys ablation robustness, while strong regularization at the same nominal rho_eps (lambda=50) does not. rho_eps is a diagnostic for fragility, not a target whose mechanical inflation buys robustness. (3) Limits of rank-based diagnostics: (a) not safety-specific (LRH baseline is 2-3x the safety value); (b) SVD principal ordering does not match causal ordering (Llama u_2 inert despite ranking second; cumulative ablation non-monotone at k=5); (c) the spectral-gap hypothesis required to upgrade the O(rho_eps * d) achievability bound to a matching Mirsky-route lower bound fails empirically (1/90 Llama layer-reference pairs, 0/36 MLP combinations) and structurally (kappa_lb <= 2/(eps * r)). The matching lower bound remains an open problem.

We prove that no reinforcement learning policy with confidence-gated autonomy can simultaneously achieve maximum helpfulness, optimal calibration, and full autonomy under rational oversight, whenever some tasks exceed the agent's reliable competence: the Behavioral Credibility Trilemma. The impossibility is geometric -- adding any non-affine autonomy incentive to a strictly proper scoring rule destroys strict properness, so an agent rewarded for both calibrated confidence and autonomous action systematically inflates its reported confidence on tasks below the principal's approval threshold. The Behavioral Perturbation Lemma quantifies the inflation (scaling as $w_A/(2 w_C)$ for the Brier score) and shows detection requires $Ω(1/Δ^2)$ observations. We prove the principal's optimal oversight rule is necessarily non-affine, making the impossibility unconditional and optimizer-independent across log-concave-density policy families. We formalize the Confidence-Gated Decision Problem, map existing methods onto the trilemma, and identify two constructive resolution pathways (commitment, domain separation). A 540-configuration Best-of-N experiment tests five pre-registered hypotheses, all strongly confirmed (effect sizes $d = 1.10$ to $5.32$), and adds a descriptive analysis of the achievable-$(H, C, A)$ surface geometry showing a plateau-truncated frontier consistent with the predicted inflation saturation.

We test whether the optimal learning-rate schedule depends on bit-width during from-initialisation quantisation-aware training (QAT) for sub-100M decoder language models. A 720-run factorial grid (Phase 2) over bit-width x warmdown fraction x LR magnitude x model size x seed (FP16/INT8/INT6, 15M-100M, 5 seeds) finds the optimal warmdown is 33% at every (bit-width, size) cell. The primary hypothesis -- that INT6 QAT requires a different schedule than higher-precision training -- is falsified at FP16/INT8/INT6. A 625-run follow-up (Phase 5) probes the null along five axes: optimiser (AdamW), schedule shape (cosine), training length (up to 9x more iterations), an extended size sweep (5M-350M), and an INT4 sweep from 3M to 100M. The null is robust under all three setup changes. The INT6 penalty follows a log-linear scaling law whose fit on Phase 2 predicts the five held-out Phase 5 sizes (5M, 8M, 175M, 250M, 350M) within their 95% prediction intervals (5/5). For INT4 the picture is sharper than the higher precisions: at 50M and 100M, wd33 is decisively optimal (paired z ~ 12-15, 10/10 seeds); below 50M, across the six tested sizes from 3M to 30M, no individual size shows a statistically significant schedule preference and the per-size mean penalty oscillates within seed-level noise. The boundary is therefore a transition between a noise-dominated regime below 50M and a decisive wd33 regime at and above 50M, not a clean wd10 region. A weight-to-grid-distance probe falsifies the simplest mechanism for the FP16/INT8/INT6 null result (rapid grid-snapping): pre-warmdown, INT6-QAT weights sit at essentially the same distance from the INT6 grid as FP16 weights (ratio ~ 1.04). Practical recommendation: at sub-100M scale, tune the LR schedule once at FP16 and apply unchanged to INT8/INT6 QAT; for INT4 at 50M+ use wd33; for INT4 below 50M the schedule choice is in the noise.

Frontier LLMs now perform strongly across a wide range of physics evaluations, but it is hard to disentangle genuine reasoning from recall of established science. We introduce DiscoverPhysics, an interactive benchmark that asks a LLM agent to discover the laws of motion of a simulated world whose physics deliberately deviates from our own. We construct 22 worlds governed by, among others, screened and fractional-power gravity, multi-species couplings, hidden dark-matter-like particles, non-coordinate-free physics, and time-varying interactions. Each world is generated on demand by an N-body simulator, for which the agent proposes several rounds of experiments, observes raw trajectory data, and ultimately submits both a natural-language explanation of the world's physics and a Python implementation of the inferred law. Because solving a world requires the agent to design informative experiments and revise its hypotheses, the benchmark probes long-horizon reasoning over an experimental history. We evaluate submissions along two complementary axes: trajectory MSE on held-out particles and an LLM-judged explanation score following an expert-written rubric assessing conceptual understanding of each world. Across eleven frontier models, we find that the strongest agents pass only half of the worlds and consistently fail on those where latent structure must be uncovered. Open-source models lag substantially behind commercial models, both in their ability to design informative experiments and in extracting conclusions from the data. We further find that good predictive accuracy does not guarantee high explanation quality and that conceptual understanding depends on hypothesis refinement through well-chosen experiments.

As attackers ramp up their AI exploit development, the search for software vulnerabilities is changing rapidly. A decade ago, programs to reward researchers for submitting software vulnerability findings were just starting to go mainstream. Vulnerability disclosure and "bug bounty" programs represented a paradigm shift years in the making--moving institutions from hostility and defensiveness about security research findings to acknowledgement that receiving input and releasing fixes was necessary. When Apple finally announced a bug bounty in 2016, the top reward was $200,000. It rose to $1 million in 2019 and $2 million last year .

Large language models (LLMs) offer a scalable mechanism to elicit domain-informed prior information for high-dimensional variable selection. However, existing methods such as LLM-Lasso are sensitive to weight quality, with performance degrading substantially when LLM-generated weights are inaccurate. To address this challenge, we first introduce a framework for quantifying the quality of LLM-generated weights, enabling rigorous evaluation of LLM-informed methods across varying weight regimes. We then propose the LLM Sparsity Prior (LSP), which integrates LLM-generated weights into the prior inclusion probabilities of Spike-and-Slab and Spike-and-Slab Lasso models via two interpretable hyperparameters governing global sparsity and weight concentration. Hierarchical hyperpriors on these parameters allow the model to dynamically discount uninformative or misleading weights, improving robustness without sacrificing gains when weights are accurate. Finally, we develop principled prompt engineering strategies and validate the method on a private medical dataset studying Acute Kidney Injury. LSP improves prediction accuracy and identifies clinically relevant features missed by the baselines, with robustness to prompt variation and particular effectiveness in low-data regimes.

Language models trained on observed sequences are often described as learning the conditional distribution of the next token given previous tokens. This description is only conditionally correct. A model trained on realized token trajectories does not observe full conditional laws; it receives sampled continuations. Moreover, real language generation is conditioned not only on previous words but also on non-textual circumstances: facts, events, intentions, goals, beliefs, social context, and task-specific constraints. This paper distinguishes three objects that are often conflated: the full conditional language process conditioned on latent circumstances, the marginal text-only process obtained by integrating those circumstances out, and the model-induced distribution learned from finite observed corpora. The paper argues that interpreting model training as estimating the marginal text-only law requires strong assumptions of stationarity, representativeness, and ergodicity, assumptions that are standard in statistical estimation but problematic when applied to heterogeneous language corpora. Even if these assumptions hold, the marginal text-only law is useful only when the observed prefix is an approximately sufficient statistic for the latent circumstances relevant to continuation. In information-theoretic terms, usefulness requires that the residual conditional mutual information between the next token and the omitted circumstances, given the observed text, be small. The paper then extends this argument to heterogeneous training corpora. Finally, the paper interprets Retrieval Augmented Generation (RAG) and tool use as conditional sufficiency devices.

Evaluating large language models increasingly relies on LLM-as-a-judge protocols, but such evaluations remain costly: different judges have different prices and reliabilities, and the difficulty of each prompt-response pair can vary substantially. This raises a basic allocation question: under a fixed budget, how should one distribute evaluation queries across heterogeneous judges and instances to obtain the most accurate score estimates? We formalize this question as *budgeted heteroskedastic multi-judge estimation*. Given $K$ prompt-response pairs, $J$ judges with known costs, and unknown query-judge variances, the goal is to estimate a bounded score vector while minimizing an $\ell_p$-error. Our first contribution is to analyze the inverse-variance weighted estimator (IVWE) and to derive the oracle allocation that minimizes its error rate. Since this allocation depends on the unknown variances, we then address the practical unknown-variance setting by proposing EST-IVWE, an adaptive algorithm that constructs and leverages *optimistically biased* variance estimates to stabilize the empirical allocation. We prove that EST-IVWE matches the oracle IVWE rate up to lower-order terms in the budget. Our second and central theoretical contribution is a matching *local* minimax lower bound, which establishes the instance-optimality of the proposed algorithms. A key technical insight is that Fano-type high-probability arguments are too coarse for this problem: their packing construction loses the local variance structure that governs the optimal allocation. We instead use an Assouad-type in-expectation argument, based on local perturbations, which preserves this structure and yields the sharp allocation-dependent lower bound. Finally, we numerically validate the superiority of our approach over naïve uniform allocation on synthetic and HelpSteer2 datasets.

We introduce training-free looped transformers, in which a lightweight inference-time wrapper loops a contiguous mid-stack block of layers of a frozen checkpoint without additional fine-tuning, continued training, or architectural changes. Unlike prior looped transformer methods that train with the looped structure end-to-end, we retrofit recurrence onto pretrained models at test time. We show that naive block reapplication usually degrades performance, highlighting the importance of the loop application strategy. Motivated by viewing a pre-norm transformer block as a forward Euler step on an ODE, we instead treat looping as a refinement of the same approximation, replacing one large update with smaller damped sub-steps. Across seven dense, sparse MoE, and MLA+MoE model families, our method improves Qwen3-4B-Instruct by +2.64 pp on MMLU-Pro, Qwen3-30B-A3B-Instruct by +1.14 pp on CommonsenseQA, and Moonlight-16B-A3B-Instruct by +1.20 pp on OpenBookQA.