Critical Percolation as a Synthetic Data Model for Interpretability

Neural networks learn features that reflect the hierarchical, multi-scale structure of natural data. Synthetic datasets used to evaluate interpretability methods typically lack this structure, limiting their value as realistic toy models. To close this gap, we introduce a family of synthetic datasets consisting of hierarchical functions defined on critical mean-field percolation clusters embedded in a high-dimensional data space. The percolation data consists of sparse, low-dimensional fractal clusters with a power-law size distribution. Latent variables modeling a taxonomic hierarchy generate each data point's target value. The data model is analytically tractable with known critical exponents that fix its properties without requiring hyperparameter tuning. We leverage a mapping between percolation clusters, random trees, and additive coalescence to propose an almost linear-time algorithm to jointly sample a random tree and its hierarchical latent decomposition, enabling data generation at arbitrary scale. Using probing experiments, we find that the model's ground-truth latent variables can be linearly decoded from neural network activations. Together, sparsity, self-similarity, power-law statistics, and analytical tractability make critical percolation a principled testbed for interpretability research.

Towards Worst-Case Guarantees with Scale-Aware Interpretability

Neural networks organize information according to the hierarchical, multi-scale structure of natural data. Methods to interpret model internals should be similarly scale-aware, explicitly tracking how features compose across resolutions and guaranteeing bounds on the influence of fine-grained structure that is discarded as irrelevant noise. We posit that the renormalisation framework from physics can meet this need by offering technical tools that can overcome limitations of current methods. Moreover, relevant work from adjacent fields has now matured to a point where scattered research threads can be synthesized into practical, theory-informed tools. To combine these threads in an AI safety context, we propose a unifying research agenda -- \emph{scale-aware interpretability} -- to develop formal machinery and interpretability tools that have robustness and faithfulness properties supported by statistical physics.

Representation Learning on a Random Lattice

Decomposing a deep neural network's learned representations into interpretable features could greatly enhance its safety and reliability. To better understand features, we adopt a geometric perspective, viewing them as a learned coordinate system for mapping an embedded data distribution. We motivate a model of a generic data distribution as a random lattice and analyze its properties using percolation theory. Learned features are categorized into context, component, and surface features. The model is qualitatively consistent with recent findings in mechanistic interpretability and suggests directions for future research.

Self-Supervised Learning for Modeling Gamma-ray Variability in Blazars

Blazars are active galactic nuclei with relativistic jets pointed almost directly at Earth. Blazars are characterized by strong, apparently stochastic flux variability at virtually all observed wavelengths and timescales, from minutes to years, the physical origin of which is still poorly understood. In the high-energy gamma-ray band, the Large Area Telescope aboard the Fermi space telescope (Fermi-LAT) has conducted regular monitoring of thousands of blazars since 2008. Deep learning can help uncover structure in gamma-ray blazars' complex variability patterns that traditional methods based on parametric statistical modeling or manual feature engineering may miss. In this work, we propose using a self-supervised Transformer encoder architecture to construct an effective representation of blazar gamma-ray variability. Measurement errors, upper limits, and missing data are accommodated using learned encodings. The model predicts a set of quantiles for the flux probability distribution at each time step, an architecture naturally suited for describing data generated by a stochastic process. As a proof of concept for how the model output can be analyzed to extract scientifically relevant information, a preliminary search for weekly-timescale time-reversal asymmetry in gamma-ray blazar light curves was conducted, finding no significant evidence for asymmetry.