Shriyash Upadhyay

Liam Dugan, Eleni Miltsakaki, Shriyash Upadhyay et al.

We conduct a feasibility study into the applicability of answer-agnostic question generation models to textbook passages. We show that a significant portion of errors in such systems arise from asking irrelevant or uninterpretable questions and that such errors can be ameliorated by providing summarized input. We find that giving these models human-written summaries instead of the original text results in a significant increase in acceptability of generated questions (33% $\rightarrow$ 83%) as determined by expert annotators. We also find that, in the absence of human-written summaries, automatic summarization can serve as a good middle ground.

Narmeen Oozeer, Shivam Raval, Philip Quirke et al.

Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention transformations without learning an explicit geometry over paths in activation space. Freshly introduced geometry-aware manifold methods do learn such a geometry, but require labelled class centroids together with prescribed cyclic or sequential structure. These assumptions restrict where manifold steering can be applied, since existing constructions require labelled centroids and compatible boundary conditions. We recast manifold steering more broadly as \textbf{Riemannian geodesic computation} on activation space, recovering linear and labelled-spline steering as geodesics under particular choices of metric. A principled metric within this framework is the output-space Hellinger distance pulled back to activations; we approximate this with a learned encoder trained on output distances over a small concept-token schema - no per-prompt labels, no topology prior, and no per-task curve fitting. Empirically, the method reliably drives the model onto the target class across all tasks in a standard four-task language-model arithmetic benchmark, while following more behaviourally natural trajectories than baselines on smaller output spaces. We thereby provide a unified Riemannian framework for manifold steering together with a schema-supervised, label-free instantiation that operates without labelled centroids or prescribed boundary conditions.

Georgi Ivanov, Narmeen Oozeer, Shivam Raval et al.

Neural networks represent more features than they have dimensions via superposition, forcing features to share representational space. Current methods decompose activations into sparse linear features but discard geometric structure. We develop a theory for studying the geometric structre of features by analyzing the spectra (eigenvalues, eigenspaces, etc.) of weight derived matrices. In particular, we introduce the frame operator $F = WW^\top$, which gives us a spectral measure that describes how each feature allocates norm across eigenspaces. While previous tools could describe the pairwise interactions between features, spectral methods capture the global geometry (``how do all features interact?''). In toy models of superposition, we use this theory to prove that capacity saturation forces spectral localization: features collapse onto single eigenspaces, organize into tight frames, and admit discrete classification via association schemes, classifying all geometries from prior work (simplices, polygons, antiprisms). The spectral measure formalism applies to arbitrary weight matrices, enabling diagnosis of feature localization beyond toy settings. These results point toward a broader program: applying operator theory to interpretability.

Shriyash Upadhyay, Chaithanya Bandi, Narmeen Oozeer et al.

Recent proposals for regulating frontier AI models have sparked concerns about the cost of safety regulation, and most such regulations have been shelved due to the safety-innovation tradeoff. This paper argues for an alternative regulatory approach that ensures AI safety while actively promoting innovation: mandating that large AI laboratories release small, openly accessible analog models (scaled-down versions) trained similarly to and distilled from their largest proprietary models. Analog models serve as public proxies, allowing broad participation in safety verification, interpretability research, and algorithmic transparency without forcing labs to disclose their full-scale models. Recent research demonstrates that safety and interpretability methods developed using these smaller models generalize effectively to frontier-scale systems. By enabling the wider research community to directly investigate and innovate upon accessible analogs, our policy substantially reduces the regulatory burden and accelerates safety advancements. This mandate promises minimal additional costs, leveraging reusable resources like data and infrastructure, while significantly contributing to the public good. Our hope is not only that this policy be adopted, but that it illustrates a broader principle supporting fundamental research in machine learning: deeper understanding of models relaxes the safety-innovation tradeoff and lets us have more of both.