The Blessing of Dimensionality in LLM Fine-tuning: A Variance-Curvature Perspective

Weight-perturbation evolution strategies (ES) can fine-tune billion-parameter language models with surprisingly small populations (e.g., $N\!\approx\!30$), contradicting classical zeroth-order curse-of-dimensionality intuition. We also observe a second seemingly separate phenomenon: under fixed hyperparameters, the stochastic fine-tuning reward often rises, peaks, and then degrades in both ES and GRPO. We argue that both effects reflect a shared geometric property of fine-tuning landscapes: they are low-dimensional in curvature. A small set of high-curvature dimensions dominates improvement, producing (i) heterogeneous time scales that yield rise-then-decay under fixed stochasticity, as captured by a minimal quadratic stochastic-ascent model, and (ii) degenerate improving updates, where many random perturbations share similar components along these directions. Using ES as a geometric probe on fine-tuning reward landscapes of GSM8K, ARC-C, and WinoGrande across Qwen2.5-Instruct models (0.5B--7B), we show that reward-improving perturbations remain empirically accessible with small populations across scales. Together, these results reconcile ES scalability with non-monotonic training dynamics and suggest that high-dimensional fine-tuning may admit a broader class of viable optimization methods than worst-case theory implies.

Estimating the Empowerment of Language Model Agents

As language model (LM) agents become more capable and gain broader access to real-world tools, there is a growing need for scalable evaluation frameworks of agentic capability. However, conventional benchmark-centric evaluations are costly to design and require human designers to come up with valid tasks that translate into insights about general model capabilities. In this work, we propose information-theoretic evaluation based on empowerment, the mutual information between an agent's actions and future states, as an open-ended method for evaluating LM agents. We introduce EELMA (Estimating Empowerment of Language Model Agents), an algorithm for approximating effective empowerment from multi-turn text interactions. We validate EELMA on both language games and scaled-up realistic web-browsing scenarios. We find that empowerment strongly correlates with average task performance, characterize the impact of environmental complexity and agentic factors such as chain-of-thought, model scale, and memory length on estimated empowerment, and that high empowerment states and actions are often pivotal moments for general capabilities. Together, these results demonstrate empowerment as an appealing general-purpose metric for evaluating and monitoring LM agents in complex, open-ended settings.

When AI Co-Scientists Fail: SPOT-a Benchmark for Automated Verification of Scientific Research

Recent advances in large language models (LLMs) have fueled the vision of automated scientific discovery, often called AI Co-Scientists. To date, prior work casts these systems as generative co-authors responsible for crafting hypotheses, synthesizing code, or drafting manuscripts. In this work, we explore a complementary application: using LLMs as verifiers to automate the \textbf{academic verification of scientific manuscripts}. To that end, we introduce SPOT, a dataset of 83 published papers paired with 91 errors significant enough to prompt errata or retraction, cross-validated with actual authors and human annotators. Evaluating state-of-the-art LLMs on SPOT, we find that none surpasses 21.1\% recall or 6.1\% precision (o3 achieves the best scores, with all others near zero). Furthermore, confidence estimates are uniformly low, and across eight independent runs, models rarely rediscover the same errors, undermining their reliability. Finally, qualitative analysis with domain experts reveals that even the strongest models make mistakes resembling student-level misconceptions derived from misunderstandings. These findings highlight the substantial gap between current LLM capabilities and the requirements for dependable AI-assisted academic verification.

Emergence of Abstractions: Concept Encoding and Decoding Mechanism for In-Context Learning in Transformers

Humans distill complex experiences into fundamental abstractions that enable rapid learning and adaptation. Similarly, autoregressive transformers exhibit adaptive learning through in-context learning (ICL), which begs the question of how. In this paper, we propose \textbf{concept encoding-decoding mechanism} to explain ICL by studying how transformers form and use internal abstractions in their representations. On synthetic ICL tasks, we analyze the training dynamics of a small transformer and report the coupled emergence of concept encoding and decoding. As the model learns to encode different latent concepts (e.g., ``Finding the first noun in a sentence.") into distinct, separable representations, it concureently builds conditional decoding algorithms and improve its ICL performance. We validate the existence of this mechanism across pretrained models of varying scales (Gemma-2 2B/9B/27B, Llama-3.1 8B/70B). Further, through mechanistic interventions and controlled finetuning, we demonstrate that the quality of concept encoding is causally related and predictive of ICL performance. Our empirical insights shed light into better understanding the success and failure modes of large language models via their representations.

Reconciling Kaplan and Chinchilla Scaling Laws

Kaplan et al. [2020] (`Kaplan') and Hoffmann et al. [2022] (`Chinchilla') studied the scaling behavior of transformers trained on next-token language prediction. These studies produced different estimates for how the number of parameters ($N$) and training tokens ($D$) should be set to achieve the lowest possible loss for a given compute budget ($C$). Kaplan: $N_\text{optimal} \propto C^{0.73}$, Chinchilla: $N_\text{optimal} \propto C^{0.50}$. This note finds that much of this discrepancy can be attributed to Kaplan counting non-embedding rather than total parameters, combined with their analysis being performed at small scale. Simulating the Chinchilla study under these conditions produces biased scaling coefficients close to Kaplan's. Hence, this note reaffirms Chinchilla's scaling coefficients, by explaining the cause of Kaplan's original overestimation.

A Resource Model For Neural Scaling Law

Neural scaling laws characterize how model performance improves as the model size scales up. Inspired by empirical observations, we introduce a resource model of neural scaling. A task is usually composite hence can be decomposed into many subtasks, which compete for resources (measured by the number of neurons allocated to subtasks). On toy problems, we empirically find that: (1) The loss of a subtask is inversely proportional to its allocated neurons. (2) When multiple subtasks are present in a composite task, the resources acquired by each subtask uniformly grow as models get larger, keeping the ratios of acquired resources constants. We hypothesize these findings to be generally true and build a model to predict neural scaling laws for general composite tasks, which successfully replicates the neural scaling law of Chinchilla models reported in arXiv:2203.15556. We believe that the notion of resource used in this paper will be a useful tool for characterizing and diagnosing neural networks.