Existing language model safety evaluations focus on overt attacks and low-stakes tasks. In reality, an attacker can easily subvert existing safeguards by requesting help on small, benign-seeming tasks across many independent queries. Because the individual queries do not appear harmful, the attack is hard to detect. However, when combined, these fragments uplift misuse by helping the attacker complete hard and dangerous tasks. Toward identifying defenses against such strategies, we develop Benchmarks for Stateful Defenses (BSD), a data generation pipeline that automates evaluations of covert attacks and corresponding defenses. Using this pipeline, we curate two new datasets that are consistently refused by frontier models and are too difficult for weaker open-weight models. This enables us to evaluate decomposition attacks, which are found to be effective misuse enablers, and to highlight stateful defenses as a promising countermeasure.
Emilie Purvine, Davis Brown, Brett Jefferson et al.
Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of parameters associated with a series of transformations defined by the model architecture, resulting in high-dimensional, difficult-to-interpret internal representations of input data. As DNNs become more ubiquitous across multiple sectors of our society, there is increasing recognition that mathematical methods are needed to aid analysts, researchers, and practitioners in understanding and interpreting how these models' internal representations relate to the final classification. In this paper, we apply cutting edge techniques from TDA with the goal of gaining insight into the interpretability of convolutional neural networks used for image classification. We use two common TDA approaches to explore several methods for modeling hidden-layer activations as high-dimensional point clouds, and provide experimental evidence that these point clouds capture valuable structural information about the model's process. First, we demonstrate that a distance metric based on persistent homology can be used to quantify meaningful differences between layers, and we discuss these distances in the broader context of existing representational similarity metrics for neural network interpretability. Second, we show that a mapper graph can provide semantic insight into how these models organize hierarchical class knowledge at each layer. These observations demonstrate that TDA is a useful tool to help deep learning practitioners unlock the hidden structures of their models.
Charles Godfrey, Davis Brown, Tegan Emerson et al.
Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of a family of models with the symmetries of that family's internal representation of data. We do this by calculating a set of fundamental symmetry groups, which we call the intertwiner groups of the model. We connect intertwiner groups to a model's internal representations of data through a range of experiments that probe similarities between hidden states across models with the same architecture. Our work suggests that the symmetries of a network are propagated into the symmetries in that network's representation of data, providing us with a better understanding of how architecture affects the learning and prediction process. Finally, we speculate that for ReLU networks, the intertwiner groups may provide a justification for the common practice of concentrating model interpretability exploration on the activation basis in hidden layers rather than arbitrary linear combinations thereof.
Brenda Praggastis, Davis Brown, Carlos Ortiz Marrero et al.
Deep neural networks used for image classification often use convolutional filters to extract distinguishing features before passing them to a linear classifier. Most interpretability literature focuses on providing semantic meaning to convolutional filters to explain a model's reasoning process and confirm its use of relevant information from the input domain. Fully connected layers can be studied by decomposing their weight matrices using a singular value decomposition, in effect studying the correlations between the rows in each matrix to discover the dynamics of the map. In this work we define a singular value decomposition for the weight tensor of a convolutional layer, which provides an analogous understanding of the correlations between filters, exposing the dynamics of the convolutional map. We validate our definition using recent results in random matrix theory. By applying the decomposition across the linear layers of an image classification network we suggest a framework against which interpretability methods might be applied using hypergraphs to model class separation. Rather than looking to the activations to explain the network, we use the singular vectors with the greatest corresponding singular values for each linear layer to identify those features most important to the network. We illustrate our approach with examples and introduce the DeepDataProfiler library, the analysis tool used for this study.
Charles Godfrey, Henry Kvinge, Elise Bishoff et al.
Past work exploring adversarial vulnerability have focused on situations where an adversary can perturb all dimensions of model input. On the other hand, a range of recent works consider the case where either (i) an adversary can perturb a limited number of input parameters or (ii) a subset of modalities in a multimodal problem. In both of these cases, adversarial examples are effectively constrained to a subspace $V$ in the ambient input space $\mathcal{X}$. Motivated by this, in this work we investigate how adversarial vulnerability depends on $\dim(V)$. In particular, we show that the adversarial success of standard PGD attacks with $\ell^p$ norm constraints behaves like a monotonically increasing function of $ε(\frac{\dim(V)}{\dim \mathcal{X}})^{\frac{1}{q}}$ where $ε$ is the perturbation budget and $\frac{1}{p} + \frac{1}{q} =1$, provided $p > 1$ (the case $p=1$ presents additional subtleties which we analyze in some detail). This functional form can be easily derived from a simple toy linear model, and as such our results land further credence to arguments that adversarial examples are endemic to locally linear models on high dimensional spaces.
Charles Godfrey, Michael G. Rawson, Davis Brown et al.
Linear neural network layers that are either equivariant or invariant to permutations of their inputs form core building blocks of modern deep learning architectures. Examples include the layers of DeepSets, as well as linear layers occurring in attention blocks of transformers and some graph neural networks. The space of permutation equivariant linear layers can be identified as the invariant subspace of a certain symmetric group representation, and recent work parameterized this space by exhibiting a basis whose vectors are sums over orbits of standard basis elements with respect to the symmetric group action. A parameterization opens up the possibility of learning the weights of permutation equivariant linear layers via gradient descent. The space of permutation equivariant linear layers is a generalization of the partition algebra, an object first discovered in statistical physics with deep connections to the representation theory of the symmetric group, and the basis described above generalizes the so-called orbit basis of the partition algebra. We exhibit an alternative basis, generalizing the diagram basis of the partition algebra, with computational benefits stemming from the fact that the tensors making up the basis are low rank in the sense that they naturally factorize into Kronecker products. Just as multiplication by a rank one matrix is far less expensive than multiplication by an arbitrary matrix, multiplication with these low rank tensors is far less expensive than multiplication with elements of the orbit basis. Finally, we describe an algorithm implementing multiplication with these basis elements.
Davis Brown, Charles Godfrey, Cody Nizinski et al.
The current trend toward ever-larger models makes standard retraining procedures an ever-more expensive burden. For this reason, there is growing interest in model editing, which enables computationally inexpensive, interpretable, post-hoc model modifications. While many model editing techniques are promising, research on the properties of edited models is largely limited to evaluation of validation accuracy. The robustness of edited models is an important and yet mostly unexplored topic. In this paper, we employ recently developed techniques from the field of deep learning robustness to investigate both how model editing affects the general robustness of a model, as well as the robustness of the specific behavior targeted by the edit. We find that edits tend to reduce general robustness, but that the degree of degradation depends on the editing algorithm and layers chosen. Motivated by these observations we introduce a new model editing algorithm, 1-layer interpolation (1-LI), which uses weight-space interpolation to navigate the trade-off between editing task accuracy and general robustness.
Prompting has become an important mechanism by which users can more effectively interact with many flavors of foundation model. Indeed, the last several years have shown that well-honed prompts can sometimes unlock emergent capabilities within such models. While there has been a substantial amount of empirical exploration of prompting within the community, relatively few works have studied prompting at a mathematical level. In this work we aim to take a first step towards understanding basic geometric properties induced by prompts in Stable Diffusion, focusing on the intrinsic dimension of internal representations within the model. We find that choice of prompt has a substantial impact on the intrinsic dimension of representations at both layers of the model which we explored, but that the nature of this impact depends on the layer being considered. For example, in certain bottleneck layers of the model, intrinsic dimension of representations is correlated with prompt perplexity (measured using a surrogate model), while this correlation is not apparent in the latent layers. Our evidence suggests that intrinsic dimension could be a useful tool for future studies of the impact of different prompts on text-to-image models.
Nicholas Konz, Charles Godfrey, Madelyn Shapiro et al.
By now there is substantial evidence that deep learning models learn certain human-interpretable features as part of their internal representations of data. As having the right (or wrong) concepts is critical to trustworthy machine learning systems, it is natural to ask which inputs from the model's original training set were most important for learning a concept at a given layer. To answer this, we combine data attribution methods with methods for probing the concepts learned by a model. Training network and probe ensembles for two concept datasets on a range of network layers, we use the recently developed TRAK method for large-scale data attribution. We find some evidence for convergence, where removing the 10,000 top attributing images for a concept and retraining the model does not change the location of the concept in the network nor the probing sparsity of the concept. This suggests that rather than being highly dependent on a few specific examples, the features that inform the development of a concept are spread in a more diffuse manner across its exemplars, implying robustness in concept formation.
Henry Kvinge, Grayson Jorgenson, Davis Brown et al.
While the last five years have seen considerable progress in understanding the internal representations of deep learning models, many questions remain. This is especially true when trying to understand the impact of model design choices, such as model architecture or training algorithm, on hidden representation geometry and dynamics. In this work we present a new approach to studying such representations inspired by the idea of a frame on the tangent bundle of a manifold. Our construction, which we call a neural frame, is formed by assembling a set of vectors representing specific types of perturbations of a data point, for example infinitesimal augmentations, noise perturbations, or perturbations produced by a generative model, and studying how these change as they pass through a network. Using neural frames, we make observations about the way that models process, layer-by-layer, specific modes of variation within a small neighborhood of a datapoint. Our results provide new perspectives on a number of phenomena, such as the manner in which training with augmentation produces model invariance or the proposed trade-off between adversarial training and model generalization.
Davis Brown, Cody Nizinski, Madelyn Shapiro et al.
Deep learning still struggles with certain kinds of scientific data. Notably, pretraining data may not provide coverage of relevant distribution shifts (e.g., shifts induced via the use of different measurement instruments). We consider deep learning models trained to classify the synthesis conditions of uranium ore concentrates (UOCs) and show that model editing is particularly effective for improving generalization to distribution shifts common in this domain. In particular, model editing outperforms finetuning on two curated datasets comprising of micrographs taken of U$_{3}$O$_{8}$ aged in humidity chambers and micrographs acquired with different scanning electron microscopes, respectively.
Charles Godfrey, Elise Bishoff, Myles Mckay et al.
It is widely acknowledged that trained convolutional neural networks (CNNs) have different levels of sensitivity to signals of different frequency. In particular, a number of empirical studies have documented CNNs sensitivity to low-frequency signals. In this work we show with theory and experiments that this observed sensitivity is a consequence of the frequency distribution of natural images, which is known to have most of its power concentrated in low-to-mid frequencies. Our theoretical analysis relies on representations of the layers of a CNN in frequency space, an idea that has previously been used to accelerate computations and study implicit bias of network training algorithms, but to the best of our knowledge has not been applied in the domain of model robustness.
Machine learning is becoming an increasingly valuable tool in mathematics, enabling one to identify subtle patterns across collections of examples so vast that they would be impossible for a single researcher to feasibly review and analyze. In this work, we use graph neural networks to investigate \emph{quiver mutation} -- an operation that transforms one quiver (or directed multigraph) into another -- which is central to the theory of cluster algebras with deep connections to geometry, topology, and physics. In the study of cluster algebras, the question of \emph{mutation equivalence} is of fundamental concern: given two quivers, can one efficiently determine if one quiver can be transformed into the other through a sequence of mutations? In this paper, we use graph neural networks and AI explainability techniques to independently discover mutation equivalence criteria for quivers of type $\tilde{D}$. Along the way, we also show that even without explicit training to do so, our model captures structure within its hidden representation that allows us to reconstruct known criteria from type $D$, adding to the growing evidence that modern machine learning models are capable of learning abstract and parsimonious rules from mathematical data.
Characteristic classes, which are abstract topological invariants associated with vector bundles, have become an important notion in modern physics with surprising real-world consequences. As a representative example, the incredible properties of topological insulators, which are insulators in their bulk but conductors on their surface, can be completely characterized by a specific characteristic class associated with their electronic band structure, the first Chern class. Given their importance to next generation computing and the computational challenge of calculating them using first-principles approaches, there is a need to develop machine learning approaches to predict the characteristic classes associated with a material system. To aid in this program we introduce the {\emph{Haldane bundle dataset}}, which consists of synthetically generated complex line bundles on the $2$-torus. We envision this dataset, which is not as challenging as noisy and sparsely measured real-world datasets but (as we show) still difficult for off-the-shelf architectures, to be a testing ground for architectures that incorporate the rich topological and geometric priors underlying characteristic classes.
In this study, we investigate whether the representations learned by neural networks possess a privileged and convergent basis. Specifically, we examine the significance of feature directions represented by individual neurons. First, we establish that arbitrary rotations of neural representations cannot be inverted (unlike linear networks), indicating that they do not exhibit complete rotational invariance. Subsequently, we explore the possibility of multiple bases achieving identical performance. To do this, we compare the bases of networks trained with the same parameters but with varying random initializations. Our study reveals two findings: (1) Even in wide networks such as WideResNets, neural networks do not converge to a unique basis; (2) Basis correlation increases significantly when a few early layers of the network are frozen identically. Furthermore, we analyze Linear Mode Connectivity, which has been studied as a measure of basis correlation. Our findings give evidence that while Linear Mode Connectivity improves with increased network width, this improvement is not due to an increase in basis correlation.
Methods for model explainability have become increasingly critical for testing the fairness and soundness of deep learning. Concept-based interpretability techniques, which use a small set of human-interpretable concept exemplars in order to measure the influence of a concept on a model's internal representation of input, are an important thread in this line of research. In this work we show that these explainability methods can suffer the same vulnerability to adversarial attacks as the models they are meant to analyze. We demonstrate this phenomenon on two well-known concept-based interpretability methods: TCAV and faceted feature visualization. We show that by carefully perturbing the examples of the concept that is being investigated, we can radically change the output of the interpretability method. The attacks that we propose can either induce positive interpretations (polka dots are an important concept for a model when classifying zebras) or negative interpretations (stripes are not an important factor in identifying images of a zebra). Our work highlights the fact that in safety-critical applications, there is need for security around not only the machine learning pipeline but also the model interpretation process.