What He's Doing Now Boggles the Mind. My partner, a 36-year-old man, is being let go from his job. He was informed that his company would be cutting him and his entire department. The only person staying is his boss, who will be overseeing the new AI customer service client they are replacing the real life people with. But that's not what this is about, even if AI is going to be the death of humanity.

Ashlin McCourt clocks up 60 hours a week working as a civil servant, a waitress and a baker because life's so expensive, she says. The UK unemployment rate stands at 4.9% - however, increasing numbers of those in work are juggling more than one job. While working in multiple jobs and side hustles has long been a needs must for many households to manage the cost of living, there are now a record 1.35 million adults working at least two jobs. It is mostly Gen Z - adults aged up to 29 - driving this poly-employment trend - according to Deputy, a global workforce management platform, which analysed more than 20 million shifts done by over 300,000 UK workers. For 28-year-old Ashlin from Northern Ireland, having more than one job seems normal.

As search depth increases in autonomous reasoning and embodied planning, the candidate action space expands exponentially, heavily taxing computational budgets. While heuristic pruning is a common countermeasure, it operates without formal safety guarantees when surrogate models (like LLMs) exhibit systematic evaluation biases. This paper frames the node expansion process as a localized Best-Arm Identification (BAI) problem over dynamic frontiers, subject to a bounded systematic bias $L$. By inverting the Lambert W function, we establish an additive sample complexity of $\mathcal{O}((Δ-4L)^{-2})$, which indicates that safe node elimination is only feasible when the empirical reward gap exceeds $4L$. We complement this with an information-theoretic lower bound of $Ω((Δ-2L)^{-2})$ to confirm the structural limits of biased search. Subsequent evaluations on both synthetic trees and complex reasoning tasks demonstrate that adhering to this local safety boundary successfully preserves optimal trajectories while maximizing sample allocation efficiency.

In multi-fidelity optimization, biased approximations of varying costs of the target function are available. This paper studies the problem of optimizing a locally smooth function with a limited budget, where the learner has to make a tradeoff between the cost and the bias of these approximations. We first prove lower bounds for the simple regret under different assumptions on the fidelities, based on a cost-to-bias function. We then present the Kometo algorithm which achieves, with additional logarithmic factors, the same rates without any knowledge of the function smoothness and fidelity assumptions, and improves previously proven guarantees. We finally empirically show that our algorithm outperforms previous multi-fidelity optimization methods without the knowledge of problem-dependent parameters.

Sequential experimental design under expensive, gradient-free objectives is a central challenge in computational statistics: evaluation budgets are tightly constrained and information must be extracted efficiently from each observation. We propose \textbf{ALMAB-DC}, a GP-based sequential design framework combining active learning, multi-armed bandits (MAB), and distributed asynchronous computing for expensive black-box experimentation. A Gaussian process surrogate with uncertainty-aware acquisition identifies informative query points; a UCB or Thompson-sampling bandit controller allocates evaluations across parallel workers; and an asynchronous scheduler handles heterogeneous runtimes. We present cumulative regret bounds for the bandit components and characterize parallel scalability via Amdahl's Law. We validate ALMAB-DC on five benchmarks. On the two statistical experimental-design tasks, ALMAB-DC achieves lower simple regret than Equal Spacing, Random, and D-optimal designs in dose--response optimization, and in adaptive spatial field estimation matches the Greedy Max-Variance benchmark while outperforming Latin Hypercube Sampling; at $K=4$ the distributed setting reaches target performance in one-quarter of sequential wall-clock rounds. On three ML/engineering tasks (CIFAR-10 HPO, CFD drag minimization, MuJoCo RL), ALMAB-DC achieves 93.4\% CIFAR-10 accuracy (outperforming BOHB by 1.7\,pp and Optuna by 1.1\,pp), reduces airfoil drag to $C_D = 0.059$ (36.9\% below Grid Search), and improves RL return by 50\% over Grid Search. All advantages over non-ALMAB baselines are statistically significant under Bonferroni-corrected Mann--Whitney $U$ tests. Distributed execution achieves $7.5\times$ speedup at $K = 16$ agents, consistent with Amdahl's Law.

Modern LLMs scale at test-time, e.g. via repeated sampling, where inference cost grows with model size and the number of samples. This creates a trade-off that pretraining scaling laws, such as Chinchilla, do not address. We present Train-to-Test ($T^2$) scaling laws that jointly optimize model size, training tokens, and number of inference samples under fixed end-to-end budgets. $T^2$ modernizes pretraining scaling laws with pass@$k$ modeling used for test-time scaling, then jointly optimizes pretraining and test-time decisions. Forecasts from $T^2$ are robust over distinct modeling approaches: measuring joint scaling effect on the task loss and modeling impact on task accuracy. Across eight downstream tasks, we find that when accounting for inference cost, optimal pretraining decisions shift radically into the overtraining regime, well-outside of the range of standard pretraining scaling suites. We validate our results by pretraining heavily overtrained models in the optimal region that $T^2$ scaling forecasts, confirming their substantially stronger performance compared to pretraining scaling alone. Finally, as frontier LLMs are post-trained, we show that our findings survive the post-training stage, making $T^2$ scaling meaningful in modern deployments.

Chinchilla Approach 2 is among the most widely used methods for fitting neural scaling laws. Its parabolic approximation introduces systematic biases in compute-optimal allocation estimates, even on noise-free synthetic data. Applied to published Llama 3 IsoFLOP data at open frontier compute scales, these biases imply a parameter underallocation corresponding to 6.5% of the $3.8\times10^{25}$ FLOP training budget and \$1.4M (90% CI: \$412K-\$2.9M) in unnecessary compute at 50% H100 MFU. Simulated multimodal model misallocations show even greater opportunity costs due to higher loss surface asymmetry. Three sources of this error are examined: IsoFLOP sampling grid width (Taylor approximation accuracy), uncentered IsoFLOP sampling, and loss surface asymmetry ($α\neq β$). Chinchilla Approach 3 largely eliminates these biases but is often regarded as less data-efficient, numerically unstable, prone to local minima, and harder to implement. Each concern is shown to be unfounded or addressable, especially when the partially linear structure of the objective is exploited via Variable Projection, enabling unbiased inference on all five loss surface parameters through a two-dimensional optimization that is well-conditioned, analytically differentiable, and amenable to dense, or even exhaustive, grid search. It may serve as a more convenient replacement for Approach 2 or a more scalable alternative for adaptations of Approach 3 to richer scaling law formulations. See https://github.com/Open-Athena/vpnls for details and https://openathena.ai/scaling-law-analysis for other results from this study.

We study stochastic multi-armed bandits under simultaneous constraints on space and adaptivity: the learner interacts with the environment in $B$ batches and has only $W$ bits of persistent memory. Prior work shows that each constraint alone is surprisingly mild: near-minimax regret $\widetilde{O}(\sqrt{KT})$ is achievable with $O(\log T)$ bits of memory under fully adaptive interaction, and with a $K$-independent $O(\log\log T)$-type number of batches when memory is unrestricted. We show that this picture breaks down in the simultaneously constrained regime. We prove that any algorithm with a $W$-bit memory constraint must use at least $Ω(K/W)$ batches to achieve near-minimax regret $\widetilde{O}(\sqrt{KT})$, even under adaptive grids. In particular, logarithmic memory rules out $O(K^{1-\varepsilon})$ batch complexity. Our proof is based on an information bottleneck. We show that near-minimax regret forces the learner to acquire $Ω(K)$ bits of information about the hidden set of good arms under a suitable hard prior, whereas an algorithm with $B$ batches and $W$ bits of memory allows only $O(BW)$ bits of information. A key ingredient is a localized change-of-measure lemma that yields probability-level arm exploration guarantees, which is of independent interest. We also give an algorithm that, for any bit budget $W$ with $Ω(\log T) \le W \le O(K\log T)$, uses at most $W$ bits of memory and $\widetilde{O}(K/W)$ batches while achieving regret $\widetilde{O}(\sqrt{KT})$, nearly matching our lower bound up to polylogarithmic factors.

Deploying neural networks on microcontrollers is constrained by kilobytes of flash and SRAM, where 1x1 pointwise (PW) mixers often dominate memory even after INT8 quantization across vision, audio, and wearable sensing. We present HYPER-TINYPW, a compression-as-generation approach that replaces most stored PW weights with generated weights: a shared micro-MLP synthesizes PW kernels once at load time from tiny per-layer codes, caches them, and executes them with standard integer operators. This preserves commodity MCU runtimes and adds only a one-off synthesis cost; steady-state latency and energy match INT8 separable CNN baselines. Enforcing a shared latent basis across layers removes cross-layer redundancy, while keeping PW1 in INT8 stabilizes early, morphology-sensitive mixing. We contribute (i) TinyML-faithful packed-byte accounting covering generator, heads/factorization, codes, kept PW1, and backbone; (ii) a unified evaluation with validation-tuned t* and bootstrap confidence intervals; and (iii) a deployability analysis covering integer-only inference and boot versus lazy synthesis. On three ECG benchmarks (Apnea-ECG, PTB-XL, MIT-BIH), HYPER-TINYPW shifts the macro-F1 versus flash Pareto frontier: at about 225 kB it matches a roughly 1.4 MB CNN while being 6.31x smaller (84.15% fewer bytes), retaining at least 95% of large-model macro-F1. Under 32-64 kB budgets it sustains balanced detection where compact baselines degrade. The mechanism applies broadly to other 1D biosignals, on-device speech, and embedded sensing tasks where per-layer redundancy dominates, indicating a wider role for compression-as-generation in resource-constrained ML systems. Beyond ECG, HYPER-TINYPW transfers to TinyML audio: on Speech Commands it reaches 96.2% test accuracy (98.2% best validation), supporting broader applicability to embedded sensing workloads where repeated linear mixers dominate memory.

Model-based design of experiments (MBDOE) is essential for efficient parameter estimation in nonlinear dynamical systems. However, conventional adaptive MBDOE requires costly posterior inference and design optimization between each experimental step, precluding real-time applications. We address this by combining Deep Adaptive Design (DAD), which amortizes sequential design into a neural network policy trained offline, with differentiable mechanistic models. For dynamical systems with known governing equations but uncertain parameters, we extend sequential contrastive training objectives to handle nuisance parameters and propose a transformer-based policy architecture that respects the temporal structure of dynamical systems. We demonstrate the approach on four systems of increasing complexity: a fed-batch bioreactor with Monod kinetics, a Haldane bioreactor with uncertain substrate inhibition, a two-compartment pharmacokinetic model with nuisance clearance parameters, and a DC motor for real-time deployment.