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1. Consistent Counterfactuals for Deep Models

   Emily Black; Zifan Wang; Matt Fredrikson; Anupam Datta (May 2021, Ninth International Conference on Learning Representations)

   Counterfactual examples are one of the most commonly-cited methods for explaining the predictions of machine learning models in key areas such as finance and medical diagnosis. Counterfactuals are often discussed under the assumption that the model on which they will be used is static, but in deployment models may be periodically retrained or fine-tuned. This paper studies the consistency of model prediction on counterfactual examples in deep networks under small changes to initial training conditions, such as weight initialization and leave-one-out variations in data, as often occurs during model deployment. We demonstrate experimentally that counterfactual examples for deep models are often inconsistent across such small changes, and that increasing the cost of the counterfactual, a stability-enhancing mitigation suggested by prior work in the context of simpler models, is not a reliable heuristic in deep networks. Rather, our analysis shows that a model's local Lipschitz continuity around the counterfactual is key to its consistency across related models. To this end, we propose Stable Neighbor Search as a way to generate more consistent counterfactual explanations, and illustrate the effectiveness of this approach on several benchmark datasets. 

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2. Towards Unifying Feature Attribution and Counterfactual Explanations: Different Means to the Same End

   https://doi.org/10.1145/3461702.3462597  

   Kommiya Mothilal, Ramaravind; Mahajan, Divyat; Tan, Chenhao; Sharma, Amit (May 2021, Proceedings of the 2021 AAAI/ACM Conference on AI, Ethics, and Society)

   null (Ed.)

   Feature attributions and counterfactual explanations are popular approaches to explain a ML model. The former assigns an importance score to each input feature, while the latter provides input examples with minimal changes to alter the model's predictions. To unify these approaches, we provide an interpretation based on the actual causality framework and present two key results in terms of their use. First, we present a method to generate feature attribution explanations from a set of counterfactual examples. These feature attributions convey how important a feature is to changing the classification outcome of a model, especially on whether a subset of features is necessary and/or sufficient for that change, which attribution-based methods are unable to provide. Second, we show how counterfactual examples can be used to evaluate the goodness of an attribution-based explanation in terms of its necessity and sufficiency. As a result, we highlight the complimentary of these two approaches. Our evaluation on three benchmark datasets --- Adult-Income, LendingClub, and German-Credit --- confirms the complimentary. Feature attribution methods like LIME and SHAP and counterfactual explanation methods like Wachter et al. and DiCE often do not agree on feature importance rankings. In addition, by restricting the features that can be modified for generating counterfactual examples, we find that the top-k features from LIME or SHAP are often neither necessary nor sufficient explanations of a model's prediction. Finally, we present a case study of different explanation methods on a real-world hospital triage problem. 

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3. Wide and deep neural networks achieve consistency for classification

   https://doi.org/10.1073/pnas.2208779120  

   Radhakrishnan, Adityanarayanan; Belkin, Mikhail; Uhler, Caroline (April 2023, Proceedings of the National Academy of Sciences)

   While neural networks are used for classification tasks across domains, a long-standing open problem in machine learning is determining whether neural networks trained using standard procedures are consistent for classification, i.e., whether such models minimize the probability of misclassification for arbitrary data distributions. In this work, we identify and construct an explicit set of neural network classifiers that are consistent. Since effective neural networks in practice are typically both wide and deep, we analyze infinitely wide networks that are also infinitely deep. In particular, using the recent connection between infinitely wide neural networks and neural tangent kernels, we provide explicit activation functions that can be used to construct networks that achieve consistency. Interestingly, these activation functions are simple and easy to implement, yet differ from commonly used activations such as ReLU or sigmoid. More generally, we create a taxonomy of infinitely wide and deep networks and show that these models implement one of three well-known classifiers depending on the activation function used: 1) 1-nearest neighbor (model predictions are given by the label of the nearest training example); 2) majority vote (model predictions are given by the label of the class with the greatest representation in the training set); or 3) singular kernel classifiers (a set of classifiers containing those that achieve consistency). Our results highlight the benefit of using deep networks for classification tasks, in contrast to regression tasks, where excessive depth is harmful. 

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4. On the Need for Topology-Aware Generative Models for Manifold-Based Defenses

   Jang, Uyeong; Jha, Susmit; Jha, Somesh (April 2020, 8th International Conference on Learning Representations (ICLR) 2020)

   ML algorithms or models, especially deep neural networks (DNNs), have shown significant promise in several areas. However, recently researchers have demonstrated that ML algorithms, especially DNNs, are vulnerable to adversarial examples (slightly perturbed samples that cause mis-classification). Existence of adversarial examples has hindered deployment of ML algorithms in safety-critical sectors, such as security. Several defenses for adversarial examples exist in the literature. One of the important classes of defenses are manifold-based defenses, where a sample is “pulled back” into the data manifold before classifying. These defenses rely on the manifold assumption (data lie in a manifold of lower dimension than the input space). These defenses use a generative model to approximate the input distribution. This paper asks the following question: do the generative models used in manifold-based defenses need to be topology-aware? Our paper suggests the answer is yes. We provide theoretical and empirical evidence to support our claim. 

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5. Learning Dynamics of Deep Matrix Factorization Beyond the Edge of Stability

   Ghosh, Avrajit; Kwon, Soo Min; Wang, Rongrong; Ravishankar, Saiprasad; Qu, Qing (March 2025, International Conference on Learning Representations)

   Deep neural networks trained using gradient descent with a fixed learning rate eta often operate in the regime of ``edge of stability'' (EOS), where the largest eigenvalue of the Hessian equilibrates about the stability threshold 2/eta. In this work, we present a fine-grained analysis of the learning dynamics of (deep) linear networks (DLNs) within the deep matrix factorization loss beyond EOS. For DLNs, loss oscillations beyond EOS follow a period-doubling route to chaos. We theoretically analyze the regime of the 2-period orbit and show that the loss oscillations occur within a small subspace, with the dimension of the subspace precisely characterized by the learning rate. The crux of our analysis lies in showing that the symmetry-induced conservation law for gradient flow, defined as the balancing gap among the singular values across layers, breaks at EOS and decays monotonically to zero. Overall, our results contribute to explaining two key phenomena in deep networks: (i) shallow models and simple tasks do not always exhibit EOS; and (ii) oscillations occur within top features}. We present experiments to support our theory, along with examples demonstrating how these phenomena occur in nonlinear networks and how they differ from those which have benign landscapes such as in DLNs. 

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