As AI models tackle increasingly complex problems, ensuring reliable human oversight becomes more challenging due to the difficulty of verifying solutions. Approaches to scaling AI supervision include debate, in which two agents engage in structured dialogue to help a judge evaluate claims; critique, in which models identify potential flaws in proposed solutions; and prover-verifier games, in which a capable 'prover' model generates solutions that must be verifiable by a less capable 'verifier'. Evaluations of the scalability of these and similar approaches to difficult problems benefit from datasets that include (1) long-form expert-verified correct solutions and (2) long-form flawed solutions with annotations highlighting specific errors, but few are available. To address this gap, we present FindTheFlaws, a group of five diverse datasets spanning medicine, mathematics, science, coding, and the Lojban language. Each dataset contains questions and long-form solutions with expert annotations validating their correctness or identifying specific error(s) in the reasoning. We evaluate frontier models' critiquing capabilities and observe a range of performance that can be leveraged for scalable oversight experiments: models performing more poorly on particular datasets can serve as judges/verifiers for more capable models. Additionally, for some task/dataset combinations, expert baselines exceed even top model performance, making them more beneficial for scalable oversight experiments.

Sparse Auto-Encoders (SAEs) are commonly employed in mechanistic interpretability to decompose the residual stream into monosemantic SAE latents. Recent work demonstrates that perturbing a model's activations at an early layer results in a step-function-like change in the model's final layer activations. Furthermore, the model's sensitivity to this perturbation differs between model-generated (real) activations and random activations. In our study, we assess model sensitivity in order to compare real activations to synthetic activations composed of SAE latents. Our findings indicate that synthetic activations closely resemble real activations when we control for the sparsity and cosine similarity of the constituent SAE latents. This suggests that real activations cannot be explained by a simple "bag of SAE latents" lacking internal structure, and instead suggests that SAE latents possess significant geometric and statistical properties. Notably, we observe that our synthetic activations exhibit less pronounced activation plateaus compared to those typically surrounding real activations.

We identify stable regions in the residual stream of Transformers, where the model's output remains insensitive to small activation changes, but exhibits high sensitivity at region boundaries. These regions emerge during training and become more defined as training progresses or model size increases. The regions appear to be much larger than previously studied polytopes. Our analysis suggests that these stable regions align with semantic distinctions, where similar prompts cluster within regions, and activations from the same region lead to similar next token predictions. This work provides a promising research direction for understanding the complexity of neural networks, shedding light on training dynamics, and advancing interpretability.