machine learning model auditors

Abstract: Classical PAC-Bayesian generalization theory places prior distributions over Euclidean parameter space $Θ\subseteq \mathbb{R}^D$, causing relative entropy to scale with network dimension $D$. For modern overparameterized neural networks where $D \gg n$, this parameter-counting dependency yields vacuous generalization bounds ($> 1{,}000\%$). In this work, we resolve this barrier by shifting prior specification from internal parameters to the non-parametric space of data distributions $\mathcal{M}_1(\mathcal{Z})$ via a \textbf{Dirichlet Process (DP)}, $\mathcal{DP}(α, F_0)$, inducing parameter distributions through push-forward measures under the learning algorithm. By the Data Processing Inequality, parameter-space relative entropy is strictly bounded by the data-space DP divergence, which we evaluate in exact closed form using Digamma functions. The resulting PAC-Bayesian certificate is strictly invariant to network parameter count $D$, width, and depth. On intrinsic $d^*$-dimensional submanifolds, optimal partition scaling achieves the minimax non-parametric rate $\mathcal{O}(n^{-1/(d^*+2)} \sqrt{\ln n})$. Across vision architectures scaling up to 4.2 million parameters ($D = 7{,}850$ to $D = 4{,}203{,}522$) on the full MNIST benchmark, while classical weight-space bounds scale past $940\%$ (becoming vacuous), our data-space DP-PAC-Bayes certificate remains stable, non-vacuous, and certified at \textbf{$8.8\%$--$9.4\%$}.

Abstract: Fine-grained visual classification requires models to recognize subtle local traits while exposing the visual evidence behind their predictions. Class-specific attention pathways provide a natural basis for interpretable recognition, but their constrained prediction structure limits discriminative capacity and underuses intermediate representations from strong pretrained backbones. To address this problem, we propose CARE, a constrained attention refinement framework for interpretable fine-grained recognition via teacher-student distillation. CARE keeps the final prediction and explanation within a class-specific attention student, while introducing a training-only auxiliary query teacher that reads selected intermediate DINOv2 layers with learnable queries. The teacher fuses multi-level representations and transfers logit-standardized class-discriminative knowledge to the student. To further refine the explanation pathway, we design diversity and sparsity terms to regularize student attention heads, reducing redundancy and encouraging compact trait localization. Experiments on CUB, Oxford-IIIT Pet, Stanford Dogs, and Stanford Cars show that CARE achieves strong classification performance under an interpretable frozen-backbone setting, reaching 78.5% Top-1 accuracy on CUB. Faithfulness analysis with insertion and deletion metrics further indicates that the top-ranked attention regions retain class-relevant evidence for explanation.

Abstract: The corpus-mean direction of a transformer's residual stream is a component shared across all inputs, and is commonly removed by mean-centering before representational analysis. We present evidence that it is a functional component: the reference against which the MLP gate population sets its operating point. In Phi-2, an exact decomposition of resting gate pre-activations shows that at mid-stack layers the resting inhibition of >99.9% of gates is carried by the coupling $w \cdot b_L$ to the carried mean direction, at 48-56$\times$ the explicit bias parameter, and the coupling is direction-specific: a random direction at matched norm orders the population's firing rates at Spearman $ρ\leq 0.09$ where the reference reaches 0.95. (That 0.95 is near-tautological on its own; the paper derives its null.) Causally, removing the stream's projection on the reference multiplies above-threshold firing by about 9$\times$, dose-monotonically, at 23-59$\times$ a norm-matched control; a random-initialised twin is flat, and replacement tests show that the direction carries the function and the magnitude does not. A direction-matched control makes the same point: noise injected along the reference costs 8-42$\times$ the same energy along a random direction. The decomposition replicates on four further families spanning both gate types (GELU with an explicit gate bias, bias-free SwiGLU), and the dose-response on two of them. Across an eight-model scan the mechanism is present in every GELU and SiLU family and absent only in OPT, where an opposing LayerNorm bias cancels the carried reference. Gate thresholds are implemented as couplings to a constant the network builds for the distribution it is reading, with the bias parameters contributing little; how much of that constant is carried in the stream and how much in parameters depends on the architecture.

Abstract: Physics-Informed Neural Networks (PINNs) embed PDE residuals into neural network training, but their internal representations remain opaque: it is unknown what physical features their hidden layers encode or whether those features have a localized causal role. We present PhysSAE, a mechanistic interpretability framework that trains overcomplete sparse autoencoders (SAEs) on PINN penultimate-layer activations and evaluates dictionary atoms through direct causal intervention in the original frozen hidden state: $h_{\mathrm{cf}} = h - αz_k d_k$, bypassing the SAE decoder entirely. Across six PDE families, with 3 PINN seeds and 3 SAE seeds each---we show that (i) Our discovered SAE atoms align with independently-defined physical observables (max Pearson $|r|=0.951$, always $\gg$ permutation null), (ii) the causal footprint of top-aligned atom ablation is 1.2--4.2$\times$ more spatially concentrated canonical than PCA or ICA interventions, and (iii) top-aligned atoms outperform matched random controls on causal localization for structured physical concepts (ESF$_{80}$ advantage 0.04-0.44). Two-atom bilateral representations improve concept regression R$^2$ by $ΔR^2\!=\!0.05\text{-}0.15$ over single atoms, while random pairs decrease it by up to 0.60. These results demonstrate that PINNs develop sparse, physically structured latent representations that can be identified and causally interrogated post-hoc, opening a path toward interpretability-aware scientific machine learning.