Intrinsic Structure: Spectral Identifiability for Mechanistic Interpretability

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.

ITNet: A Learnable Integral Transform That Subsumes Convolution, Attention, and Recurrence

Convolutional networks, recurrent networks, and transformers each encode different inductive biases -- locality, sequential memory, and content-dependent pairwise interaction -- and have remained mathematically distinct since their inception. We show that this fragmentation reflects not a fundamental diversity in how signals should be processed, but rather incomplete views of a single underlying mathematical object: a learnable integral transform. We introduce the Integral Transform Network (ITNet), a unified architecture built around a learnable kernel that depends jointly on positions and features. This kernel is implemented as a small neural network, specifically an MLP, that models pairwise interactions, enabling the model to adapt its behavior from data. We show that convolution, self-attention (including multi-head), and autoregressive recurrence (including LSTM, GRU, S4, and Mamba) arise as special cases under appropriate parameterizations, and that ITNet is a universal approximator of continuous operators. To make this practical, we develop tiled kernel fusion, importance-weighted Monte Carlo integration, and learned low-rank factorization, enabling efficient and scalable computation. A single ITNet architecture with a shared operator and lightweight modality-specific encoders matches or exceeds specialized baselines on ImageNet-1K , GLUE, ModelNet40, VQA\,v2 and NLVR2. The results demonstrate that a single learned interaction mechanism can recover the behavior of all three architectural families from data.

Hierarchical Pedagogical Oversight: A Multi-Agent Adversarial Framework for Reliable AI Tutoring

Large Language Models (LLMs) are increasingly deployed as automated tutors to address educator shortages; however, they often fail at pedagogical reasoning, frequently validating incorrect student solutions (sycophancy) or providing overly direct answers that hinder learning. We introduce Hierarchical Pedagogical Oversight (HPO), a framework that adapts structured adversarial synthesis to educational assessment. Unlike cooperative multi-agent systems that often drift toward superficial consensus, HPO enforces a dialectical separation of concerns: specialist agents first distill dialogue context, which then grounds a moderated, five-act debate between opposing pedagogical critics. We evaluate this framework on the MRBench dataset of 1,214 middle-school mathematics dialogues. Our 8B-parameter model achieves a Macro F1 of 0.845, outperforming GPT-4o (0.812) by 3.3% while using 20 times fewer parameters. These results establish adversarial reasoning as a critical mechanism for deploying reliable, low-compute pedagogical oversight in resource-constrained environments.

Financial Fraud Detection using Quantum Graph Neural Networks

Financial fraud detection is essential for preventing significant financial losses and maintaining the reputation of financial institutions. However, conventional methods of detecting financial fraud have limited effectiveness, necessitating the need for new approaches to improve detection rates. In this paper, we propose a novel approach for detecting financial fraud using Quantum Graph Neural Networks (QGNNs). QGNNs are a type of neural network that can process graph-structured data and leverage the power of Quantum Computing (QC) to perform computations more efficiently than classical neural networks. Our approach uses Variational Quantum Circuits (VQC) to enhance the performance of the QGNN. In order to evaluate the efficiency of our proposed method, we compared the performance of QGNNs to Classical Graph Neural Networks using a real-world financial fraud detection dataset. The results of our experiments showed that QGNNs achieved an AUC of $0.85$, which outperformed classical GNNs. Our research highlights the potential of QGNNs and suggests that QGNNs are a promising new approach for improving financial fraud detection.