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Deep Learning · Attention Mechanisms

Max Vladymyrov, Johannes von Oswald, Mark Sandler, Rong Ge

Recent research has demonstrated that transformers, particularly linear attention models, implicitly execute gradient-descent-like algorithms on data provided in-context during their forward inference step. However, their capability in handling more complex problems remains unexplored. In this paper, we prove that each layer of a linear transformer maintains a weight vector for an implicit linear regression problem and can be interpreted as performing a variant of preconditioned gradient descent. We also investigate the use of linear transformers in a challenging scenario where the training data is corrupted with different levels of noise. Remarkably, we demonstrate that for this problem linear transformers discover an intricate and highly effective optimization algorithm, surpassing or matching in performance many reasonable baselines. We analyze this algorithm and show that it is a novel approach incorporating momentum and adaptive rescaling based on noise levels. Our findings show that even linear transformers possess the surprising ability to discover sophisticated optimization strategies.

Interpretability

Etienne Vareille, Michele Linardi, Ioannis Tsamardinos, Vassilis Christophides

We consider the problem of selecting all the minimal-size subsets of multivariate time-series (TS) variables whose past leads to an optimal predictive model for the future (forecasting) of a given target variable (multiple feature selection problem for times-series). Identifying these subsets leads to gaining insights, domain intuition,and a better understanding of the data-generating mechanism; it is often the first step in causal modeling. While identifying a single solution to the feature selection problem suffices for forecasting purposes, identifying all such minimal-size, optimally predictive subsets is necessary for knowledge discovery and important to avoid misleading a practitioner. We develop the theory of multiple feature selection for time-series data, propose the ChronoEpilogi algorithm, and prove its soundness and completeness under two mild, broad, non-parametric distributional assumptions, namely Compositionality of the distribution and Interchangeability of time-series variables in solutions. Experiments on synthetic and real datasets demonstrate the scalability of ChronoEpilogi to hundreds of TS variables and its efficacy in identifying multiple solutions. In the real datasets, ChronoEpilogi is shown to reduce the number of TS variables by 96% (on average) by conserving or even improving forecasting performance. Furthermore, it is on par with GroupLasso performance, with the added benefit of providing multiple solutions.

Interpretability

Lunjia Hu, Arun Jambulapati, Kevin Tian, Chutong Yang

In the recent literature on machine learning and decision making, calibration has emerged as a desirable and widely-studied statistical property of the outputs of binary prediction models. However, the algorithmic aspects of measuring model calibration have remained relatively less well-explored. Motivated by Blasiok et al '23, which proposed a rigorous framework for measuring distances to calibration, we initiate the algorithmic study of calibration through the lens of property testing. We define the problem of calibration testing from samples where given $n$ draws from a distribution $\mathcal{D}$ on $(\text{predictions}, \text{binary outcomes})$, our goal is to distinguish between the cases where $\mathcal{D}$ is perfectly calibrated or $\epsilon$-far from calibration. We make the simple observation that the empirical smooth calibration linear program can be reformulated as an instance of minimum-cost flow on a highly-structured graph, and design an exact dynamic programming-based solver for it which runs in time $O(n\log^2(n))$, and solves the calibration testing problem information-theoretically optimally in the same time. This improves upon state-of-the-art black-box linear program solvers requiring $\Omega(n^\omega)$ time, where $\omega > 2$ is the exponent of matrix multiplication. We also develop algorithms for tolerant variants of our testing problem improving upon black-box linear program solvers, and give sample complexity lower bounds for alternative calibration measures to the one considered in this work. Finally, we present experiments showing the testing problem we define faithfully captures standard notions of calibration, and that our algorithms scale efficiently to accommodate large sample sizes.

Neuroscience, Cognitive Science

Hadi Vafaii, Dekel Galor, Jacob Yates

Variational autoencoders (VAE) employ Bayesian inference to interpret sensory inputs, mirroring processes that occur in primate vision across both ventral (Higgins et al., 2021) and dorsal (Vafaii et al., 2023) pathways. Despite their success, traditional VAEs rely on continuous latent variables, which significantly deviates from the discrete nature of biological neurons. Here, we developed the Poisson VAE (P-VAE), a novel architecture that combines principles of predictive coding with a VAE that encodes inputs into discrete spike counts. Combining Poisson-distributed latent variables with predictive coding introduces a metabolic cost term in the model loss function, suggesting a relationship with sparse coding which we verify empirically. Additionally, we analyze the geometry of learned representations, contrasting the P-VAE to alternative VAE models. We find that the P-VAE encodes its inputs in relatively higher dimensions, facilitating linear separability of categories in a downstream classification task with a much better (5x) sample efficiency. Our work provides an interpretable computational framework to study brain-like sensory processing and paves the way for a deeper understanding of perception as an inferential process.

Reinforcement Learning · Planning

Andrew Li, Zizhao Chen, Toryn Klassen, Pashootan Vaezipoor, Rodrigo Toro Icarte, Sheila McIlraith

Reward Machines provide an automaton-inspired structure for specifying instructions, safety constraints, and other temporally extended reward-worthy behaviour. By exposing the underlying structure of a reward function, they enable the decomposition of an RL task, leading to impressive gains in sample efficiency. Although Reward Machines and similar formal specifications have a rich history of application towards sequential decision-making problems, prior frameworks have traditionally ignored ambiguity and uncertainty when interpreting the domain-specific vocabulary forming the building blocks of the reward function. Such uncertainty critically arises in many real-world settings due to factors like partial observability or noisy sensors. In this work, we explore the use of Reward Machines for Deep RL in noisy and uncertain environments. We characterize this problem as a POMDP and propose a suite of RL algorithms that exploit task structure under uncertain interpretation of the domain-specific vocabulary. Through theory and experiments, we expose pitfalls in naive approaches to this problem while simultaneously demonstrating how task structure can be successfully leveraged under noisy interpretations of the vocabulary.

Theory · Probabilistic Methods

Javier Maass, Joaquin Fontbona

We develop a Mean-Field (MF) view of the learning dynamics of overparametrized Artificial Neural Networks (NN) under distributional symmetries of the data w.r.t. the action of a general compact group $G$. We consider for this a class of generalized shallow NNs given by an ensemble of $N$ multi-layer units, jointly trained using stochastic gradient descent (SGD) and possibly symmetry-leveraging (SL) techniques, such as Data Augmentation (DA), Feature Averaging (FA) or Equivariant Architectures (EA). We introduce the notions of weakly and strongly invariant laws (WI and SI) on the parameter space of each single unit, corresponding, respectively, to $G$-invariant distributions, and to distributions supported on parameters fixed by the group action (which encode EA). This allows us to define symmetric models compatible with taking $N\to\infty$ and give an interpretation of the asymptotic dynamics of DA, FA and EA in terms of Wasserstein Gradient Flows describing their MF limits. When activations respect the group action, we show that, for symmetric data, DA, FA and freely-trained models obey the exact same MF dynamic, which stays in the space of WI parameter laws and attains therein the population risk's minimizer. We also provide a counterexample to the general attainability of such an optimum over SI laws.Despite this, and quite remarkably, we show that the space of SI laws is also preserved by these MF distributional dynamics even when freely trained. This sharply contrasts the finite-$N$ setting, in which EAs are generally not preserved by unconstrained SGD. We illustrate the validity of our findings as $N$ gets larger, in a teacher-student experimental setting, training a student NN to learn from a WI, SI or arbitrary teacher model through various SL schemes. We lastly deduce a data-driven heuristic to discover the largest subspace of parameters supporting SI distributions for a problem, that could be used for designing EA with minimal generalization error.

Trustworthy Machine Learning

Tri Nguyen, Shahana Ibrahim, Xiao Fu

The generation of label noise is often modeled as a process involving a probability transition matrix (also interpreted as the _annotator confusion matrix_) imposed onto the label distribution. Under this model, learning the ``ground-truth classifier''---i.e., the classifier that can be learned if no noise was present---and the confusion matrix boils down to a model identification problem. Prior works along this line demonstrated appealing empirical performance, yet identifiability of the model was mostly established by assuming an instance-invariant confusion matrix. Having an (occasionally) instance-dependent confusion matrix across data samples is apparently more realistic, but inevitably introduces outliers to the model. Our interest lies in confusion matrix-based noisy label learning with such outliers taken into consideration. We begin with pointing out that under the model of interest, using labels produced by only one annotator is fundamentally insufficient to detect the outliers or identify the ground-truth classifier. Then, we prove that by employing a crowdsourcing strategy involving multiple annotators, a carefully designed loss function can establish the desired model identifiability under reasonable conditions. Our development builds upon a link between the noisy label model and a column-corrupted matrix factorization mode---based on which we show that crowdsourced annotations distinguish nominal data and instance-dependent outliers using a low-dimensional subspace. Experiments show that our learning scheme substantially improves outlier detection and the classifier's testing accuracy.

Interpretability

Hayden McTavish, Jon Donnelly, Margo Seltzer, Cynthia Rudin

Many important datasets contain samples that are missing one or more feature values. Maintaining the interpretability of machine learning models in the presence of such missing data is challenging. Singly or multiply imputing missing values complicates the model’s mapping from features to labels. On the other hand, reasoning on indicator variables that represent missingness introduces a potentially large number of additional terms, sacrificing sparsity. We solve these problems with M-GAM, a sparse, generalized, additive modeling approach that incorporates missingness indicators and their interaction terms while maintaining sparsity through $\ell_0$ regularization. We show that M-GAM provides similar or superior accuracy to prior methods while significantly improving sparsity relative to either imputation or naïve inclusion of indicator variables.

Generative Models · In Context Learning

Aniket Didolkar, Anirudh Goyal, Nan Rosemary Ke, Siyuan Guo, Michal Valko, Timothy Lillicrap, Danilo Jimenez Rezende, Yoshua Bengio, Michael Mozer, Sanjeev Arora

\emph{Metacognitive knowledge} refers to humans' intuitive knowledge of their own thinking and reasoning processes. Today's best LLMs clearly possess some reasoning processes. The paper gives evidence that they also have metacognitive knowledge, including ability to name skills and procedures to apply given a task. We explore this primarily in context of math reasoning, developing a prompt-guided interaction procedure to get a powerful LLM to assign sensible skill labels to math questions, followed by having it perform semantic clustering to obtain coarser families of skill labels. These coarse skill labels look interpretable to humans.To validate that these skill labels are meaningful and relevant to the LLM's reasoning processes we perform the following experiments. (a) We ask GPT-4 to assign skill labels to training questions in math datasets GSM8K and MATH. (b) When using an LLM to solve the test questions, we present it with the full list of skill labels and ask it to identify the skill needed. Then it is presented with randomly selected exemplar solved questions associated with that skill label. This improves accuracy on GSM8k and MATH for several strong LLMs, including code-assisted models. The methodology presented is domain-agnostic, even though this article applies it to math problems.

Graph Neural Networks

Burouj Armgaan, Manthan Dalmia, Sourav Medya, Sayan Ranu

Instance-level explanation of graph neural networks (GNNs) is a well-studied area. These explainers, however, only explain an instance (e.g., a graph) and fail to uncover the combinatorial reasoning learned by a GNN from the training data towards making its predictions. In this work, we introduce GraphTrail, the first end-to-end, global, post-hoc GNN explainer that translates the functioning of a black-box GNN model to a boolean formula over the (sub)graph level concepts without relying on local explainers. GraphTrail is unique in automatically mining the discriminative subgraph-level concepts using Shapley values. Subsequently, the GNN predictions are mapped to a human-interpretable boolean formula over these concepts through symbolic regression. Extensive experiments across diverse datasets and GNN architectures demonstrate significant improvement over existing global explainers in mapping GNN predictions to faithful logical formulae. The robust and accurate performance of GraphTrail makes it invaluable for improving GNNs and facilitates adoption in domains with strict transparency requirements.

Language

Ge Gao, Alexey Taymanov, Eduardo Salinas, Paul Mineiro, Dipendra Misra

We study interactive learning of language agents based on user edits made to the agent's output. In a typical setting such as writing assistants, the user interacts with a language agent to generate a response given a context, and may optionally edit the agent response to personalize it based on their latent preference, in addition to improving the correctness. The edit feedback is naturally generated, making it a suitable candidate for improving the agent's alignment with the user's preference, and for reducing the cost of user edits over time. We propose a learning framework, PRELUDE that infers a description of the user's latent preference based on historic edit data and using it to define a prompt policy that drives future response generation. This avoids fine-tuning the agent, which is costly, challenging to scale with the number of users, and may even degrade its performance on other tasks. Furthermore, learning descriptive preference improves interpretability, allowing the user to view and modify the learned preference. However, user preference can be complex and vary based on context, making it challenging to learn. To address this, we propose a simple yet effective algorithm named CIPHER that leverages a large language model (LLM) to infer the user preference for a given context based on user edits. In the future, CIPHER retrieves inferred preferences from the k-closest contexts in the history, and forms an aggregate preference for response generation. We introduce two interactive environments -- summarization and email writing, for evaluation using a GPT-4 simulated user. We compare with algorithms that directly retrieve user edits but do not learn descriptive preference, and algorithms that learn context-agnostic preference. On both tasks, CIPHER outperforms baselines by achieving the lowest edit distance cost. Meanwhile, CIPHER has a lower computational expense, as using learned preference results in a shorter prompt than directly using user edits. Our further analysis reports that the user preference learned by CIPHER shows significant similarity to the ground truth latent preference.

Optimization · Optimization and Learning under Uncertainty

Michael Huang, Vishal Gupta

We propose a novel family of decision-aware surrogate losses, called Perturbation Gradient (PG) losses, for the predict-then-optimize framework. These losses directly approximate the downstream decision loss and can be optimized using off-the-shelf gradient-based methods. Importantly, unlike existing surrogate losses, the approximation error of our PG losses vanishes as the number of samples grows. This implies that optimizing our surrogate loss yields a best-in-class policy asymptotically, even in misspecified settings. This is the first such result in misspecified settings and we provide numerical evidence confirming our PG losses substantively outperform existing proposals when the underlying model is misspecified and the noise is not centrally symmetric. Insofar as misspecification is commonplace in practice -- especially when we might prefer a simpler, more interpretable model -- PG losses offer a novel, theoretically justified, method for computationally tractable decision-aware learning.

Interpretability

Xingyi Yang, Xinchao Wang

In this paper, we present Language Model as Visual Explainer (\texttt{LVX}), a systematic approach for interpreting the internal workings of vision models using a tree-structured linguistic explanation, without the need for model training. Central to our strategy is the collaboration between vision models and LLM to craft explanations. On one hand, the LLM is harnessed to delineate hierarchical visual attributes, while concurrently, a text-to-image API retrieves images that are most aligned with these textual concepts. By mapping the collected texts and images to the vision model's embedding space, we construct a hierarchy-structured visual embedding tree. This tree is dynamically pruned and grown by querying the LLM using language templates, tailoring the explanation to the model. Such a scheme allows us to seamlessly incorporate new attributes while eliminating undesired concepts based on the model's representations. When applied to testing samples, our method provides human-understandable explanations in the form of attribute-laden trees. Beyond explanation, we retrained the vision model by calibrating it on the generated concept hierarchy, allowing the model to incorporate the refined knowledge of visual attributes. To access the effectiveness of our approach, we introduce new benchmarks and conduct rigorous evaluations, demonstrating its plausibility, faithfulness, and stability.

Probabilistic Methods · Bayesian Models and Methods

Amber Hu, David Zoltowski, Aditya Nair, David Anderson, Lea Duncker, Scott Linderman

Understanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience. To this end, statistical methods which describe high-dimensional neural time series in terms of low-dimensional latent dynamics have played a fundamental role in characterizing neural systems. Yet, what constitutes a successful method involves two opposing criteria: (1) methods should be expressive enough to capture complex nonlinear dynamics, and (2) they should maintain a notion of interpretability often only warranted by simpler linear models. In this paper, we develop an approach that balances these two objectives: the Gaussian Process Switching Linear Dynamical System (gpSLDS). Our method builds on previous work modeling the latent state evolution via a stochastic differential equation whose nonlinear dynamics are described by a Gaussian process (GP-SDEs). We propose a novel kernel function which enforces smoothly interpolated locally linear dynamics, and therefore expresses flexible -- yet interpretable -- dynamics akin to those of recurrent switching linear dynamical systems (rSLDS). Our approach resolves key limitations of the rSLDS such as artifactual oscillations in dynamics near discrete state boundaries, while also providing posterior uncertainty estimates of the dynamics. To fit our models, we leverage a modified learning objective which improves the estimation accuracy of kernel hyperparameters compared to previous GP-SDE fitting approaches. We apply our method to synthetic data and data recorded in two neuroscience experiments and demonstrate favorable performance in comparison to the rSLDS.

Neuroscience, Cognitive Science

Yash Mehta, Danil Tyulmankov, Adithya Rajagopalan, Glenn Turner, James Fitzgerald, Jan Funke

Inferring the synaptic plasticity rules that govern learning in the brain is a key challenge in neuroscience. We present a novel computational method to infer these rules from experimental data, applicable to both neural and behavioral data. Our approach approximates plasticity rules using a parameterized function, employing either truncated Taylor series for theoretical interpretability or multilayer perceptrons. These plasticity parameters are optimized via gradient descent over entire trajectories to align closely with observed neural activity or behavioral learning dynamics. This method can uncover complex rules that induce long nonlinear time dependencies, particularly involving factors like postsynaptic activity and current synaptic weights. We validate our approach through simulations, successfully recovering established rules such as Oja's, as well as more intricate plasticity rules with reward-modulated terms. We assess the robustness of our technique to noise and apply it to behavioral data from \textit{Drosophila} in a probabilistic reward-learning experiment. Notably, our findings reveal an active forgetting component in reward learning in flies, improving predictive accuracy over previous models. This modeling framework offers a promising new avenue for elucidating the computational principles of synaptic plasticity and learning in the brain.

Interpretability

Adithya Bhaskar, Alexander Wettig, Dan Friedman, Danqi Chen

The path to interpreting a language model often proceeds via analysis of circuits---sparse computational subgraphs of the model that capture specific aspects of its behavior. Recent work has automated the task of discovering circuits. Yet, these methods have practical limitations, as they either rely on inefficient search algorithms or inaccurate approximations. In this paper, we frame circuit discovery as an optimization problem and propose _Edge Pruning_ as an effective and scalable solution. Edge Pruning leverages gradient-based pruning techniques, but instead of removing neurons or components, prunes the _edges_ between components. Our method finds circuits in GPT-2 that use less than half the number of edges than circuits found by previous methods while being equally faithful to the full model predictions on standard circuit-finding tasks. Edge Pruning is efficient on tasks involving up to 100,000 examples, outperforming previous methods in speed and producing substantially better circuits. It also perfectly recovers the ground-truth circuits in two models compiled with Tracr. Thanks to its efficiency, we scale Edge Pruning to CodeLlama-13B, a model over 100x the size of GPT-2.We use this setting for a case study, where we compare the mechanisms behind instruction prompting and in-context learning.We find two circuits with more than 99.96% sparsity that match the performance of the full model. Further analysis reveals that the mechanisms in the two settings overlap substantially. This shows that Edge Pruning is a practical and scalable tool for interpretability, which can shed light on behaviors that only emerge in large models.

Theory · Domain Adaptation and Transfer Learning

Zhaorui Tan, Xi Yang, Qiufeng Wang, Anh Nguyen, Kaizhu Huang

Vision models excel in image classification but struggle to generalize to unseen data, such as classifying images from unseen domains or discovering novel categories. In this paper, we explore the relationship between logical reasoning and deep learning generalization in visual classification. A logical regularization termed L-Reg is derived which bridges a logical analysis framework to image classification. Our work reveals that L-Reg reduces the complexity of the model in terms of the feature distribution and classifier weights. Specifically, we unveil the interpretability brought by L-Reg, as it enables the model to extract the salient features, such as faces to persons, for classification. Theoretical analysis and experiments demonstrate that L-Reg enhances generalization across various scenarios, including multi-domain generalization and generalized category discovery. In complex real-world scenarios where images span unknown classes and unseen domains, L-Reg consistently improves generalization, highlighting its practical efficacy.

Probabilistic Methods · Bayesian Models and Methods

Tristan Cinquin, Marvin Pförtner, Vincent Fortuin, Philipp Hennig, Robert Bamler

Laplace approximations are popular techniques for endowing deep networks with epistemic uncertainty estimates as they can be applied without altering the predictions of the trained network, and they scale to large models and datasets. While the choice of prior strongly affects the resulting posterior distribution, computational tractability and lack of interpretability of the weight space typically limit the Laplace approximation to isotropic Gaussian priors, which are known to cause pathological behavior as depth increases. As a remedy, we directly place a prior on function space. More precisely, since Lebesgue densities do not exist on infinite-dimensional function spaces, we recast training as finding the so-called weak mode of the posterior measure under a Gaussian process (GP) prior restricted to the space of functions representable by the neural network. Through the GP prior, one can express structured and interpretable inductive biases, such as regularity or periodicity, directly in function space, while still exploiting the implicit inductive biases that allow deep networks to generalize. After model linearization, the training objective induces a negative log-posterior density to which we apply a Laplace approximation, leveraging highly scalable methods from matrix-free linear algebra. Our method provides improved results where prior knowledge is abundant (as is the case in many scientific inference tasks). At the same time, it stays competitive for black-box supervised learning problems, where neural networks typically excel.

Computer Vision

Yanping Fu, Wenbin Liao, Xinyuan Liu, Hang Xu, Yike Ma, Yucheng Zhang, Feng Dai

As an emerging task that integrates perception and reasoning, topology reasoning in autonomous driving scenes has recently garnered widespread attention. However, existing work often emphasizes "perception over reasoning": they typically boost reasoning performance by enhancing the perception of lanes and directly adopt vanilla MLPs to learn lane topology from lane query. This paradigm overlooks the geometric features intrinsic to the lanes themselves and are prone to being influenced by inherent endpoint shifts in lane detection. To tackle this issue, we propose an interpretable method for lane topology reasoning based on lane geometric distance and lane query similarity, named TopoLogic. This method mitigates the impact of endpoint shifts in geometric space, and introduces explicit similarity calculation in semantic space as a complement. By integrating results from both spaces, our methods provides more comprehensive information for lane topology. Ultimately, our approach significantly outperforms the existing state-of-the-art methods on the mainstream benchmark OpenLane-V2 (23.9 v.s. 10.9 in TOP$_{ll}$ and 44.1 v.s. 39.8 in OLS on subsetA). Additionally, our proposed geometric distance topology reasoning method can be incorporated into well-trained models without re-training, significantly enhancing the performance of lane topology reasoning. The code is released at https://github.com/Franpin/TopoLogic.

Interpretability

Shuai Liu, Boyang Li, Zhiyu Fang, Mingyue Cui, Kai Huang

LiDAR-based 3D object detection has made impressive progress recently, yet most existing models are black-box, lacking interpretability. Previous explanation approaches primarily focus on analyzing image-based models and are not readily applicable to LiDAR-based 3D detectors. In this paper, we propose a feature factorization activation map (FFAM) to generate high-quality visual explanations for 3D detectors. FFAM employs non-negative matrix factorization to generate concept activation maps and subsequently aggregates these maps to obtain a global visual explanation. To achieve object-specific visual explanations, we refine the global visual explanation using the feature gradient of a target object. Additionally, we introduce a voxel upsampling strategy to align the scale between the activation map and input point cloud. We qualitatively and quantitatively analyze FFAM with multiple detectors on several datasets. Experimental results validate the high-quality visual explanations produced by FFAM. The code is available at \url{https://anonymous.4open.science/r/FFAM-B9AF}.