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AI agents are playing an increasingly important role in physics research. However, existing physics benchmarks only evaluate fixed questions, isolated sub-tasks, or paper reproduction with given solutions, and rarely check research quality alongside correctness. We introduce FrontierPhysics, an end-to-end benchmark with 56 tasks made by 42 physicists based on their own research, covering nine domains across theoretical, computational, and experimental physics. Each task requires agents to review the literature, develop a research plan, conduct research and experiments, and produce structured outputs and scientific manuscripts. Combining deterministic verifiers with expert-authored rubrics, FrontierPhysics evaluates whether agents' research is correct and publishable. Across 22 models in 26 configurations, no configuration passes more than 46 of its 168 rollouts. Manual review of agent trajectories shows that frontier agents' main weaknesses are insufficiently rigorous reasoning and limited expert intuition, rather than gaps in physics knowledge or execution errors.

Recursive self-improvement requires AI systems to improve the models and infrastructure used by subsequent systems. LLM compression offers a concrete efficiency objective: retain a pretrained model's behavior within a smaller model storage budget. We study whether coding agents can carry out this step autonomously. We formulate compression as a terminal task in which an agent receives a source checkpoint, storage limit, inference environment, and time budget, then constructs compressed weights and executable inference code. The agent controls its algorithm and experiments; perplexity feedback guides search, and independent verification checks the final model. Across six agents and six model--size settings, 29 of 36 submissions pass verification. Selecting the lowest-perplexity agent design per task yields an average 3.4% perplexity increase over BF16 and 77.33% downstream accuracy, compared with 79.56% for BF16. Recorded experiments reveal how agents achieve these outcomes and where improvement breaks down. Agents lower PPL in 21 of 24 revisions at nearly fixed storage; complete-model feedback reverses 17 of 79 prior local rankings; and generation and inference tests expose failures that likelihood alone misses. The results identify representation design, experimental judgment, and capability validation as central to agent-driven model compression, a measurable component of efficiency-oriented self-improvement.

End-to-end digital twins can be constructed by fitting separate stage models and connecting them after inference. We investigate the Frequentist prediction properties of a commonly used Monte Carlo simulation scheme that forwards complete predictive draws through such a chain when measured stage outputs contain independent normal errors, but the latent stage means are deterministic. Analytical two-stage examples show persistent asymptotic interval and coverage inflation and, with quadratic propagation, mean bias dependent on the parameters to be estimated. Simulations of four- and eight-stage linear-quadratic univariate chains with 7, 15 or 30 training runs demonstrate pronounced input-dependent distortions. A diagnostic using error-free latent training predictors shows that the effect is mainly not attributable to errors in variables, but to the MCSim approach even showing underestimation of coverage. We propose a model-based bootstrap: an initial chain forwards fitted means, bootstrap chains are refitted on fixed-center bootstrap data while forwarding their mean prediction, and a target-stage future error enters a studentized prediction root. Across the investigated scenarios, relative mean bias is substantially reduced, and coverage is closer to the nominal 90%. At sample size 30, the eight-stage bootstrap has mean width ratios of 1.16-1.42 relative to the known-parameter normal reference, compared with 4.11-4.97 for observed-to-observed MCSim. These results support improved endpoint prediction in the tested setting. Further investigations of the bootstrap scheme in the supplement for a bivariate 6-stage process show similar satisfactory results.

Large language models (LLMs) are increasingly used as computational models of human language processing, yet it remains unclear which components of their representations drive alignment with neural activity. Here, we use ridge reduced-rank regression to identify the brain-predictive subspace of LLM representations: the representational directions that support linear prediction of neural responses. Across three naturalistic language-listening datasets spanning intracranial electrophysiology and fMRI, and six model conditions spanning autoregressive, bidirectional masked, and randomly initialized language models, we find that full linear encoding performance can be recovered using only 1-3% of the original embedding dimensionality. These low-dimensional subspaces generalize across held-out participants and, to a lesser extent, across datasets, suggesting that neural predictivity is concentrated in a compact and partially shared representational space. We next compare these brain-predictive directions with the principal axes of variation in the embeddings. Principal component analysis requires substantially more dimensions to recover neural prediction, demonstrating that the directions most useful for predicting neural activity are distinct from those capturing the most overall variance within LLM representations themselves. Finally, characterizing the learned subspaces allows us to surface interpretable features that are overrepresented in neural activity above and beyond the LLM representations. Together, these results show that LLM-brain alignment is supported by a small, structured subset of model representations and provides a framework for better understanding exactly why these representations align. Code can be found at: https://github.com/thefinnlab/low-rank-alignment