Summary: Neural networks are a commonly used prediction tool in computer science and statistics. However, the barrier to entry of this interesting field remains high, particularly for classical statisticians trained in a frequentist perspective. In this letter, we demystify neural networks by describing networks that approximate a linear regression and describe common customizations that provide a foundation for further study.

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.

Scorio.jl is a Julia package for evaluating and ranking systems from repeated responses to shared tasks. It provides a common tensor-based interface for direct score-based, pairwise, psychometric, voting, graph, and listwise methods, so the same benchmark can be analyzed under multiple ranking assumptions. We describe the package design, position it relative to existing Julia tools, and report pilot experiments on synthetic rank recovery, stability under limited trials, and runtime scaling.

Diffusion language models (DLMs) have recently emerged as a promising alternative to autoregressive (AR) approaches, enabling parallel token generation beyond a rigid left-to-right order. Despite growing empirical success, the theoretical understanding of how unmasking schedules -- which specify the order and size of unmasked tokens during sampling -- affect generation quality remains limited. In this work, we introduce a distribution-agnostic unmasking schedule for DLMs that adapts to the (unknown) dependence structure of the target data distribution, without requiring any prior knowledge or hyperparameter tuning. In contrast to prior deterministic procedures that fix unmasking sizes, our method randomizes the number of tokens revealed at each iteration. We show that, for two specific parameter choices, the sampling convergence guarantees -- measured by Kullback-Leibler (KL) divergence -- scale as $\widetilde O(\mathsf{TC}/K)$ and $\widetilde O(\mathsf{DTC}/K)$ respectively. Here, $K$ is the number of iterations, and $\mathsf{TC}$ and $\mathsf{DTC}$ are the total correlation and dual total correlation of the target distribution, capturing the intrinsic dependence structure underlying the data. Importantly, our guarantees hold in the practically relevant parallel-sampling regime $K

We can only see the exact value realized in a box if we open it and pay the opening cost.