Manifold Steering Reveals the Shared Geometry of Neural Network Representation and Behavior

Neural representations carry rich geometric structure; but does that structure causally shape behavior? To address this question, we intervene along paths through activation space defined by different geometries, and measure the behavioral trajectories they induce. In particular, we test whether interventions that respect the geometry of activation space will yield behaviors close to those the model exhibits naturally. Concretely, we first fit an activation manifold $M_h$ to representations and a behavior manifold $M_y$ to output probability distributions. We then test the link $M_h \leftrightarrow M_y$ via interventions: we find that steering along $M_h$, which we term manifold steering, yields behavioral trajectories that follow $M_y$, while linear steering -- which assumes a Euclidean geometry -- cuts through off-manifold regions and hence produces unnatural outputs. Moreover, optimizing interventions in activation space to produce paths along $M_y$ recovers activation trajectories that trace the curvature of $M_h$. We demonstrate this bidirectional relationship between the geometry of representation and behavior across tasks and modalities. In language models, we use reasoning tasks with cyclic and sequential geometries as well as in-context learning tasks with more complex graph geometries. In a video world model, we use a task with geometry corresponding to physical dynamics. Overall, our work shows that geometry in neural representation is not merely incidental, but is in fact the proper object for enabling principled control via intervention on internals. This recasts the core problem of steering from finding the right direction to finding the right geometry.

Reasoning Theater: Disentangling Model Beliefs from Chain-of-Thought

We provide evidence of performative chain-of-thought (CoT) in reasoning models, where a model becomes strongly confident in its final answer, but continues generating tokens without revealing its internal belief. Our analysis compares activation probing, early forced answering, and a CoT monitor across two large models (DeepSeek-R1 671B & GPT-OSS 120B) and find task difficulty-specific differences: The model's final answer is decodable from activations far earlier in CoT than a monitor is able to say, especially for easy recall-based MMLU questions. We contrast this with genuine reasoning in difficult multihop GPQA-Diamond questions. Despite this, inflection points (e.g., backtracking, 'aha' moments) occur almost exclusively in responses where probes show large belief shifts, suggesting these behaviors track genuine uncertainty rather than learned "reasoning theater." Finally, probe-guided early exit reduces tokens by up to 80% on MMLU and 30% on GPQA-Diamond with similar accuracy, positioning attention probing as an efficient tool for detecting performative reasoning and enabling adaptive computation.

Tracking and triangulating firefly flashes in field recordings

Identifying firefly flashes from other bright features in nature images is complicated. I provide a training dataset and trained neural networks for reliable flash classification. The training set consists of thousands of cropped images (patches) extracted by manual labeling from video recordings of fireflies in their natural habitat. The trained network appears as considerably more reliable to differentiate flashes from other sources of light compared to traditional methods relying solely on intensity thresholding. This robust tracking enables a new calibration-free method for the 3D reconstruction of flash occurrences from stereoscopic 360-degree videos, which I also present here.