Mechanistic interpretability explains models by identifying circuits inside them, but has no way to tell whether a circuit is a property of the model or an artifact of the method that found it. Sparse autoencoders illustrate the problem: different seeds and widths recover materially different features from the same activations, and no theory says whether that variability is incidental or structural. We put dictionary learning for interpretability on an identifiability footing. Treating the forward pass as a controlled dynamical system with depth as time and lifting it with the Koopman operator yields a finite linear realisation whose \emph{spectrum} is a coordinate-free property of the model. We prove the spectrum is recoverable from $M$ calibration samples at rate $M^{-1/2}$ up to permutation - to our knowledge the first identifiability theorem for a mechanistic-interpretability primitive, with a matching minimax lower bound, a median-of-means variant for heavy-tailed activations, and a dissociation theorem: whenever the realisation is non-normal, the directions carrying activation variance and the directions carrying information across depth cannot coincide. The identifiable object and the legible object are not the same object. On GPT-2 small, Gemma-2-2B and Qwen3-8B-Base the spectrum converges everywhere and attains the predicted exponent on Qwen3-8B-Base ($0.506 \pm 0.031$); shortfalls collapse onto one curve against each cell's sample threshold. Koopman modes beat random directions but lose to principal components on indirect-object identification, with the gap decaying $4.1\times$ in depth-distance, as the theorem predicts. The Koopman spectrum is an identifiable, model-intrinsic fingerprint with a stated error bar, not a legible decomposition.
Detection and localization of AI-tampered images are critical for trustworthy AI, yet modern generative models have made such manipulations increasingly difficult to identify. While traditional binary classifiers can detect image tampering, they lack interpretability and generalization. Vision-Language Models (VLMs) offer a promising alternative due to their strong visual understanding and reasoning capabilities; however, existing approaches typically rely on supervised finetuning with curated explanations rather than exploiting their inherent reasoning capabilities. In this work, we investigate whether VLMs can be trained to reason about AI-generated image edits using reinforcement learning (RL) rather than explicit reasoning supervision. Motivated by the success in Group Relative Policy Optimization (GRPO), an RL technique that incentivizes the model to reason by generating thinking traces prior to giving the final answer, we propose a GRPO-based training framework that utilizes simple accuracy and format rewards. Given an input image, the model produces a structured reasoning trace and predicts whether the image has been tampered with. A lightweight segmentation model is then guided by the reasoning output to generate pixel-level localization masks. Experiments across multiple image manipulation datasets demonstrate that our approach achieves competitive detection and localization performance compared to state-of-the-art image forgery detectors, despite requiring substantially weaker supervision. We introduce effective intersection over union (eff-IoU), a unified metric to jointly evaluate detection and localization. These results suggest that reinforcement learning provides an effective and scalable mechanism for teaching VLMs to reason about AI-generated content.
Darsha Udayanga, Pin-Yu Chen, Payel Das et al.· 0 citations