We introduce NSF-SciFy, a comprehensive dataset of scientific claims and investigation proposals extracted from National Science Foundation award abstracts. While previous scientific claim verification datasets have been limited in size and scope, NSF-SciFy represents a significant advance with 2.8 million claims from 400,000 abstracts spanning all science and mathematics disciplines. We present two focused subsets: NSF-SciFy-MatSci with 114,000 claims from materials science awards, and NSF-SciFy-20K with 135,000 claims across five NSF directorates. Using zero-shot prompting, we develop a scalable approach for joint extraction of scientific claims and investigation proposals. We demonstrate the dataset’s utility through three downstream tasks: non-technical abstract generation, claim extraction, and investigation proposal extraction. Fine-tuning language models on our dataset yields substantial improvements, with relative gains often exceeding 100%, particularly for claim and proposal extraction tasks. Our error analysis reveals that extracted claims exhibit high precision but lower recall, suggesting opportunities for further methodological refinement. NSF-SciFy enables new research directions in large-scale claim verification, scientific discovery tracking, and meta-scientific analysis.

Successful communication depends on the speaker's intended style (i.e., what the speaker is trying to convey) aligning with the listener's interpreted style (i.e., what the listener perceives).However, cultural differences often lead to misalignment between the two; for example, politeness is often lost in translation.We characterize the ways that LLMs fail to translate style -biasing translations towards neutrality and performing worse in non-Western languages.We mitigate these failures with RASTA (Retrieval-Augmented STylistic Alignment), a method that leverages learned stylistic concepts to encourage LLM translation to appropriately convey cultural communication norms and align style. 1 * Equal contribution 1 Code, data, & prompts available at https://github. com/shreyahavaldar/style_alignment "After class today, I chatted with Eric, my professor." 今日の授 業の後、私は教授のエリックとお しゃべりしました。 Chat

Language model evaluations often fail to characterize consequential failure modes, forcing experts to inspect outputs and build new benchmarks.We introduce task elicitation, a method that automatically builds new evaluations to profile model behavior.Task elicitation finds hundreds of natural-language tasks-an order of magnitude more than prior work-where frontier models exhibit systematic failures, in domains ranging from forecasting to online harassment.For example, we find that Sonnet 3.5 over-associates quantum computing and AGI and that o3-mini is prone to hallucination when fabrications are repeated in-context 1 .

Prompt sensitivity, referring to the phenomenon where paraphrasing (i.e., repeating something written or spoken using different words) leads to significant changes in large language model (LLM) performance, has been widely accepted as a core limitation of LLMs.In this work, we revisit this issue and ask: Is the widely reported high prompt sensitivity truly an inherent weakness of LLMs, or is it largely an artifact of evaluation processes?To answer this question, we systematically evaluate 7 LLMs (e.g., GPT and Gemini family) across 6 benchmarks, including both multiple-choice and open-ended tasks on 12 diverse prompt templates.We find that much of the prompt sensitivity stems from heuristic evaluation methods, including log-likelihood scoring and rigid answer matching, which often overlook semantically correct responses expressed through alternative phrasings, such as synonyms or paraphrases.When we adopt LLM-as-a-Judge evaluations, we observe a substantial reduction in performance variance and a consistently higher correlation in model rankings across prompts.Our findings suggest that modern LLMs are more robust to prompt templates than previously believed, and that prompt sensitivity may be more an artifact of evaluation than a flaw in the models.

In reasoning chains generated by large language models (LLMs), initial errors often propagate and undermine the reliability of the final conclusion.Current LLM-based error detection methods often fail to detect propagated errors because earlier errors can corrupt judgments of downstream reasoning.To better detect such errors, we introduce Autoregressive Reasoning Entailment Stability (ARES), a probabilistic framework that evaluates each reasoning step based solely on previously-verified premises.This inductive method yields a nuanced score for each step and provides certified statistical guarantees of its soundness, rather than a brittle binary label.ARES achieves state-of-the-art performance across four benchmarks (72.1% Macro-F1, +8.2 points) and demonstrates superior robustness on very long synthetic reasoning chains, where it excels at detecting propagated errors (90.3% F1, +27.6 points). 1

We study how to subvert large language models (LLMs) from following prompt-specified rules. We first formalize rule-following as inference in propositional Horn logic, a mathematical system in which rules have the form "if $P$ and $Q$, then $R$" for some propositions $P$, $Q$, and $R$. Next, we prove that although small transformers can faithfully follow such rules, maliciously crafted prompts can still mislead both theoretical constructions and models learned from data. Furthermore, we demonstrate that popular attack algorithms on LLMs find adversarial prompts and induce attention patterns that align with our theory. Our novel logic-based framework provides a foundation for studying LLMs in rule-based settings, enabling a formal analysis of tasks like logical reasoning and jailbreak attacks.

Neurosymbolic learning enables the integration of symbolic reasoning with deep learning but faces significant challenges in scaling to complex symbolic programs, large datasets, or both. We introduce DOLPHIN, a framework that tackles these challenges by supporting neurosymbolic programs in Python, executing complex symbolic reasoning on the CPU while vectorizing probabilistic computations and gradient propagation on the GPU. Across 13 benchmarks spanning tasks over text, image, and video data, with symbolic reasoning features like recursion and blackbox functions, DOLPHIN converges to state-of-the-art accuracies on the more complex benchmarks while existing frameworks such as Scallop, ISED, and IndeCateR+ fail to converge within the time limit. On simpler benchmarks, DOLPHIN matches their performance, while achieving these results 1.71x to 62x faster than the baselines. Overall, DOLPHIN advances the scalability of neurosymbolic frameworks, achieving state-of-the-art efficiency and convergence on difficult benchmarks where existing frameworks struggle. The code is published at https://github.com/Dolphin-NeSy/Dolphin.

Self-attributing neural networks (SANNs) present a potential path towards interpretable models for high-dimensional problems, but often face significant trade-offs in performance. In this work, we formally prove a lower bound on errors of per-feature SANNs, whereas group-based SANNs can achieve zero error and thus high performance. Motivated by these insights, we propose Sum-of-Parts (SOP), a framework that transforms any differentiable model into a group-based SANN, where feature groups are learned end-to-end without group supervision. SOP achieves state-of-the-art performance for SANNs on vision and language tasks, and we validate that the groups are interpretable on a range of quantitative and semantic metrics. We further validate the utility of SOP explanations in model debugging and cosmological scientific discovery.

Many computational tasks benefit from being formulated as the composition of neural networks followed by a discrete symbolic program. The goal of neurosymbolic learning is to train the neural networks using end-to-end input-output labels of the composite. We introduce CTSketch, a novel, scalable neurosymbolic learning algorithm. CTSketch uses two techniques to improve the scalability of neurosymbolic inference: decompose the symbolic program into sub-programs and summarize each sub-program with a sketched tensor. This strategy allows us to approximate the output distribution of the program with simple tensor operations over the input distributions and the sketches. We provide theoretical insight into the maximum approximation error. Furthermore, we evaluate CTSketch on benchmarks from the neurosymbolic learning literature, including some designed for evaluating scalability. Our results show that CTSketch pushes neurosymbolic learning to new scales that were previously unattainable, with neural predictors obtaining high accuracy on tasks with one thousand inputs, despite supervision only on the final output.

Stability guarantees have emerged as a principled way to evaluate feature attributions, but existing certification methods rely on heavily smoothed classifiers and often produce conservative guarantees. To address these limitations, we introduce soft stability and propose a simple, model-agnostic, sample-efficient stability certification algorithm (SCA) that yields non-trivial and interpretable guarantees for any attribution method. Moreover, we show that mild smoothing achieves a more favorable trade-off between accuracy and stability, avoiding the aggressive compromises made in prior certification methods. To explain this behavior, we use Boolean function analysis to derive a novel characterization of stability under smoothing. We evaluate SCA on vision and language tasks and demonstrate the effectiveness of soft stability in measuring the robustness of explanation methods.

Large language models (LLMs) excel at zero-shot inference but continue to struggle with complex, multi-step reasoning. Recent methods that augment LLMs with intermediate reasoning steps such as Chain of Thought (CoT) and Program of Thought (PoT) improve performance but often produce undesirable solutions, especially in algorithmic domains. We introduce Per-Instance Program Synthesis (PIPS), a method that generates and refines programs at the instance level using structural feedback without relying on task-specific guidance or explicit test cases. To further improve performance, PIPS incorporates a confidence metric that dynamically chooses between direct inference and program synthesis on a per-instance basis. Experiments across three frontier LLMs and 30 benchmarks including all tasks of Big Bench Extra Hard (BBEH), visual question answering tasks, relational reasoning tasks, and mathematical reasoning tasks show that PIPS improves the absolute harmonic mean accuracy by up to 8.6\% and 9.4\% compared to PoT and CoT respectively, and reduces undesirable program generations by 65.1\% on the algorithmic tasks compared to PoT with Gemini-2.0-Flash.

With the prevalence of the Pretraining-Finetuning paradigm in transfer learning, the robustness of down-stream tasks has become a critical concern. In this work, we delve into adversarial robustness in transfer learning and reveal the critical role of initialization, including both the pretrained model and the linear head. First, we discover the necessity of an adversarially robust pre-trained model. Specifically, we reveal that with a standard pretrained model, Parameter-Efficient Finetuning (PEFT) methods either fail to be adversarially robust or continue to exhibit significantly degraded adversarial robustness on downstream tasks, even with adversarial training during finetuning. Leveraging a robust pretrained model, surprisingly, we observe that a simple linear probing can outper-form full finetuning and other PEFT methods with random initialization on certain datasets. We further identify that linear probing excels in preserving robustness from the robust pretraining. Based on this, we propose Robust Linear Initialization (RoLl) for adversarial finetuning, which initializes the linear head with the weights obtained by ad-versarial linear probing to maximally inherit the robust-ness from pretraining. Across five different image classification datasets, we demonstrate the effectiveness of RoLI and achieve new state-of-the-art results. Our code is available at https://github.com/DongXzz/RoLI.

With evolving data regulations, machine unlearning (MU) has become an important tool for fostering trust and safety in today's AI models. However, existing MU methods focusing on data and/or weight perspectives often suffer limitations in unlearning accuracy, stability, and cross-domain applicability. To address these challenges, we introduce the concept of 'weight saliency' for MU, drawing parallels with input saliency in model explanation. This innovation directs MU's attention toward specific model weights rather than the entire model, improving effectiveness and efficiency. The resultant method that we call saliency unlearning (SalUn) narrows the performance gap with 'exact' unlearning (model retraining from scratch after removing the forgetting data points). To the best of our knowledge, SalUn is the first principled MU approach that can effectively erase the influence of forgetting data, classes, or concepts in both image classification and generation tasks. As highlighted below, For example, SalUn yields a stability advantage in high-variance random data forgetting, e.g., with a 0.2% gap compared to exact unlearning on the CIFAR-10 dataset. Moreover, in preventing conditional diffusion models from generating harmful images, SalUn achieves nearly 100% unlearning accuracy, outperforming current state-of-the-art baselines like Erased Stable Diffusion and Forget-Me-Not. Codes are available at https://github.com/OPTML-Group/Unlearn-Saliency. **WARNING**: This paper contains model outputs that may be offensive in nature.

Concept-based interpretability methods offer a lens into the internals of foundation models by decomposing their embeddings into high-level concepts. These concept representations are most useful when they are *compositional*, meaning that the individual concepts compose to explain the full sample. We show that existing unsupervised concept extraction methods find concepts which are not compositional. To automatically discover compositional concept representations, we identify two salient properties of such representations, and propose Compositional Concept Extraction (CCE) for finding concepts which obey these properties. We evaluate CCE on five different datasets over image and text data. Our evaluation shows that CCE finds more compositional concept representations than baselines and yields better accuracy on four downstream classification tasks.

Designing faithful yet accurate AI models is challenging, particularly in the field of individual treatment effect estimation (ITE). ITE prediction models deployed in critical settings such as healthcare should ideally be (i) accurate, and (ii) provide faithful explanations. However, current solutions are inadequate: state-of-the-art black-box models do not supply explanations, post-hoc explainers for black-box models lack faithfulness guarantees, and self-interpretable models greatly compromise accuracy. To address these issues, we propose DISCRET, a self-interpretable ITE framework that synthesizes faithful, rule-based explanations for each sample. A key insight behind DISCRET is that explanations can serve dually as database queries to identify similar subgroups of samples. We provide a novel RL algorithm to efficiently synthesize these explanations from a large search space. We evaluate DISCRET on diverse tasks involving tabular, image, and text data. DISCRET outperforms the best self-interpretable models and has accuracy comparable to the best black-box models while providing faithful explanations. DISCRET is available at https://github.com/wuyinjun-1993/DISCRET-ICML2024.

Jailbreak attacks cause large language models (LLMs) to generate harmful, unethical, or otherwise objectionable content. Evaluating these attacks presents a number of challenges, which the current collection of benchmarks and evaluation techniques do not adequately address. First, there is no clear standard of practice regarding jailbreaking evaluation. Second, existing works compute costs and success rates in incomparable ways. And third, numerous works are not reproducible, as they withhold adversarial prompts, involve closed-source code, or rely on evolving proprietary APIs. To address these challenges, we introduce JailbreakBench, an open-sourced benchmark with the following components: (1) an evolving repository of state-of-the-art adversarial prompts, which we refer to as jailbreak artifacts; (2) a jailbreaking dataset comprising 100 behaviors---both original and sourced from prior work---which align with OpenAI's usage policies; (3) a standardized evaluation framework at https://github.com/JailbreakBench/jailbreakbench that includes a clearly defined threat model, system prompts, chat templates, and scoring functions; and (4) a leaderboard at https://jailbreakbench.github.io/ that tracks the performance of attacks and defenses for various LLMs. We have carefully considered the potential ethical implications of releasing this benchmark, and believe that it will be a net positive for the community.

Anomaly detection is widely used for identifying critical errors and suspicious behaviors, but current methods lack interpretability. We leverage common properties of existing methods and recent advances in generative models to introduce counterfactual explanations for anomaly detection. Given an input, we generate its counterfactual as a diffusion-based repair that shows what a non-anomalous version $\textit{should have looked like}$. A key advantage of this approach is that it enables a domain-independent formal specification of explainability desiderata, offering a unified framework for generating and evaluating explanations. We demonstrate the effectiveness of our anomaly explainability framework, AR-Pro, on vision (MVTec, VisA) and time-series (SWaT, WADI, HAI) anomaly datasets. The code used for the experiments is accessible at: https://github.com/xjiae/arpro.

Many computational tasks can be naturally expressed as a composition of a DNN followed by a program written in a traditional programming language or an API call to an LLM. We call such composites "neural programs" and focus on the problem of learning the DNN parameters when the training data consist of end-to-end input-output labels for the composite. When the program is written in a differentiable logic programming language, techniques from neurosymbolic learning are applicable, but in general, the learning for neural programs requires estimating the gradients of black-box components. We present an algorithm for learning neural programs, called ISED, that only relies on input-output samples of black-box components. For evaluation, we introduce new benchmarks that involve calls to modern LLMs such as GPT-4 and also consider benchmarks from the neurosymbolic learning literature. Our evaluation shows that for the latter benchmarks, ISED has comparable performance to state-of-the-art neurosymbolic frameworks. For the former, we use adaptations of prior work on gradient approximations of black-box components as a baseline, and show that ISED achieves comparable accuracy but in a more data- and sample-efficient manner.

Finding errors in machine learning applications requires a thorough exploration of their behavior over data. Existing approaches used by practitioners are often ad-hoc and lack the abstractions needed to scale this process. We present TorchQL, a programming framework to evaluate and improve the correctness of machine learning applications. TorchQL allows users to write queries to specify and check integrity constraints over machine learning models and datasets. It seamlessly integrates relational algebra with functional programming to allow for highly expressive queries using only eight intuitive operators. We evaluate TorchQL on diverse use-cases including finding critical temporal inconsistencies in objects detected across video frames in autonomous driving, finding data imputation errors in time-series medical records, finding data labeling errors in real-world images, and evaluating biases and constraining outputs of language models. Our experiments show that TorchQL enables up to 13x faster query executions than baselines like Pandas and MongoDB, and up to 40% shorter queries than native Python. We also conduct a user study and find that TorchQL is natural enough for developers familiar with Python to specify complex integrity constraints.

It is commonly believed that in transfer learning including more pre-training data translates into better performance. However, recent evidence suggests that removing data from the source dataset can actually help too. In this work, we take a closer look at the role of the source dataset's composition in transfer learning and present a framework for probing its impact on downstream performance. Our framework gives rise to new capabilities such as pinpointing transfer learning brittleness as well as detecting pathologies such as data-leakage and the presence of misleading examples in the source dataset. In particular, we demonstrate that removing detrimental datapoints identified by our framework indeed improves transfer learning performance from ImageNet on a variety of target tasks.11Code is available at https://github.com/MadryLab/data-transfer

Understanding how styles differ across languages is advantageous for training both humans and computers to generate culturally appropriate text.We introduce an explanation framework to extract stylistic differences from multilingual LMs and compare styles across languages.Our framework (1) generates comprehensive style lexica in any language and (2) consolidates feature importances from LMs into comparable lexical categories.We apply this framework to compare politeness, creating the first holistic multilingual politeness dataset and exploring how politeness varies across four languages.Our approach enables an effective evaluation of how distinct linguistic categories contribute to stylistic variations and provides interpretable insights into how people communicate differently around the world.

Machine learning models can make critical errors that are easily hidden within vast amounts of data. Such errors often run counter to rules based on human intuition. However, rules based on human knowledge are challenging to scale or to even formalize. We thereby seek to infer statistical rules from the data and quantify the extent to which a model has learned them. We propose a framework SQRL that integrates logic-based methods with statistical inference to derive these rules from a model’s training data without supervision. We further show how to adapt models at test time to reduce rule violations and produce more coherent predictions. SQRL generates up to 300K rules over datasets from vision, tabular, and language settings. We uncover up to 158K violations of those rules by state-of-the-art models for classification, object detection, and data imputation. Test-time adaptation reduces these violations by up to 68.7% with relative performance improvement up to 32%. SQRL is available at https://github.com/DebugML/sqrl.

Qing Lyu, Shreya Havaldar, Adam Stein, Li Zhang, Delip Rao, Eric Wong, Marianna Apidianaki, Chris Callison-Burch. Proceedings of the 13th International Joint Conference on Natural Language Processing and the 3rd Conference of the Asia-Pacific Chapter of the Association for Computational Linguistics (Volume 1: Long Papers). 2023.

Explanation methods for machine learning models tend not to provide any formal guarantees and may not reflect the underlying decision-making process. In this work, we analyze stability as a property for reliable feature attribution methods. We prove that relaxed variants of stability are guaranteed if the model is sufficiently Lipschitz with respect to the masking of features. We develop a smoothing method called Multiplicative Smoothing (MuS) to achieve such a model. We show that MuS overcomes the theoretical limitations of standard smoothing techniques and can be integrated with any classifier and feature attribution method. We evaluate MuS on vision and language models with various feature attribution methods, such as LIME and SHAP, and demonstrate that MuS endows feature attributions with non-trivial stability guarantees.

Several works have shown that deep learning models are vulnerable to adversarial attacks where seemingly simple label-preserving changes to the input image lead to incorrect predictions. To combat this, gradient based adversarial training is generally employed as a standard defense mechanism. However, in cases where the loss landscape is discontinuous with respect to a given perturbation set, first order methods get stuck in local optima, and fail to defend against threat. This is often a problem for many physically realizable perturbation sets such as 2D affine transformations and 3D scene parameters. To work in such settings, we introduce a new optimization framework that alternates between global zeroth order sampling and local gradient updates to compute strong adversaries that can be used to harden the model against attack. Further, we design a powerful optimization algorithm using this framework, called Alternating Evolutionary Sampling and Descent (ASD), which combines an evolutionary search strategy (viz. covariance matrix adaptation) with gradient descent. We consider two settings with discontinuous/discrete and non-convex loss landscapes to evaluate ASD: a) 3D scene parameters and b) 2D patch attacks, and find that it achieves state-of-the-art results on adversarial robustness.

Certified patch defenses can guarantee robustness of an image classifier to arbitrary changes within a bounded contiguous region. But, currently, this robustness comes at a cost of degraded standard accuracies and slower inference times. We demonstrate how using vision transformers enables significantly better certified patch robustness that is also more computationally efficient and does not incur a substantial drop in standard accuracy. These improvements stem from the inherent ability of the vision transformer to gracefully handle largely masked images.11Our code is available at https://github.com/MadryLab/smoothed-vit..

We show how fitting sparse linear models over learned deep feature representations can lead to more debuggable neural networks. These networks remain highly accurate while also being more amenable to human interpretation, as we demonstrate quantitatively and via human experiments. We further illustrate how the resulting sparse explanations can help to identify spurious correlations, explain misclassifications, and diagnose model biases in vision and language tasks.

Owing to the susceptibility of deep learning systems to adversarial attacks, there has been a great deal of work in developing (both empirically and certifiably) robust classifiers. While most work has defended against a single type of attack, recent work has looked at defending against multiple perturbation models using simple aggregations of multiple attacks. However, these methods can be difficult to tune, and can easily result in imbalanced degrees of robustness to individual perturbation models, resulting in a sub-optimal worst-case loss over the union. In this work, we develop a natural generalization of the standard PGD-based procedure to incorporate multiple perturbation models into a single attack, by taking the worst-case over all steepest descent directions. This approach has the advantage of directly converging upon a trade-off between different perturbation models which minimizes the worst-case performance over the union. With this approach, we are able to train standard architectures which are simultaneously robust against $\ell_\infty$, $\ell_2$, and $\ell_1$ attacks, outperforming past approaches on the MNIST and CIFAR10 datasets and achieving adversarial accuracy of 47.0% against the union of ($\ell_\infty$, $\ell_2$, $\ell_1$) perturbations with radius = (0.03, 0.5, 12) on the latter, improving upon previous approaches which achieve 40.6% accuracy.

It is common practice in deep learning to use overparameterized networks and train for as long as possible; there are numerous studies that show, both theoretically and empirically, that such practices surprisingly do not unduly harm the generalization performance of the classifier. In this paper, we empirically study this phenomenon in the setting of adversarially trained deep networks, which are trained to minimize the loss under worst-case adversarial perturbations. We find that overfitting to the training set does in fact harm robust performance to a very large degree in adversarially robust training across multiple datasets (SVHN, CIFAR-10, CIFAR-100, and ImageNet) and perturbation models (L-infinity and L-2). Based upon this observed effect, we show that the performance gains of virtually all recent algorithmic improvements upon adversarial training can be matched by simply using early stopping. We also show that effects such as the double descent curve do still occur in adversarially trained models, yet fail to explain the observed overfitting. Finally, we study several classical and modern deep learning remedies for overfitting, including regularization and data augmentation, and find that no approach in isolation improves significantly upon the gains achieved by early stopping. All code for reproducing the experiments as well as pretrained model weights and training logs can be found at https://github.com/ locuslab/robust_overfitting.

Recent work has shown that it is possible to learn neural networks with provable guarantees on the output of the model when subject to input perturbations, however these works have focused primarily on defending against adversarial examples for image classifiers. In this paper, we study how these provable guarantees can be naturally applied to other real world settings, namely getting performance specifications for robust virtual sensors measuring fuel injection quantities within an engine. We first demonstrate that, in this setting, even simple neural network models are highly susceptible to reasonable levels of adversarial sensor noise, which are capable of increasing the mean relative error of a standard neural network from 6.6% to 43.8%. We then leverage methods for learning provably robust networks and verifying robustness properties, resulting in a robust model which we can provably guarantee has at most 16.5% mean relative error under any sensor noise. Additionally, we show how specific intervals of fuel injection quantities can be targeted to maximize robustness for certain ranges, allowing us to train a virtual sensor for fuel injection which is provably guaranteed to have at most 10.69% relative error under noise while maintaining 3% relative error on non-adversarial data within normalized fuel injection ranges of 0.6 to 1.0.

A rapidly growing area of work has studied the existence of adversarial examples, datapoints which have been perturbed to fool a classifier, but the vast majority of these works have focused primarily on threat models defined by $\ell_p$ norm-bounded perturbations. In this paper, we propose a new threat model for adversarial attacks based on the Wasserstein distance. In the image classification setting, such distances measure the cost of moving pixel mass, which can naturally represent “standard” image manipulations such as scaling, rotation, translation, and distortion (and can potentially be applied to other settings as well). To generate Wasserstein adversarial examples, we develop a procedure for approximate projection onto the Wasserstein ball, based upon a modified version of the Sinkhorn iteration. The resulting algorithm can successfully attack image classification models, bringing traditional CIFAR10 models down to 3% accuracy within a Wasserstein ball with radius 0.1 (i.e., moving 10% of the image mass 1 pixel), and we demonstrate that PGD-based adversarial training can improve this adversarial accuracy to 76%. In total, this work opens up a new direction of study in adversarial robustness, more formally considering convex metrics that accurately capture the invariances that we typically believe should exist in classifiers, and code for all experiments in the paper is available at https://github.com/locuslab/projected_sinkhorn.

We propose a method to learn deep ReLU-based classifiers that are provably robust against norm-bounded adversarial perturbations on the training data. For previously unseen examples, the approach is guaranteed to detect all adversarial examples, though it may flag some non-adversarial examples as well. The basic idea is to consider a convex outer approximation of the set of activations reachable through a norm-bounded perturbation, and we develop a robust optimization procedure that minimizes the worst case loss over this outer region (via a linear program). Crucially, we show that the dual problem to this linear program can be represented itself as a deep network similar to the backpropagation network, leading to very efficient optimization approaches that produce guaranteed bounds on the robust loss. The end result is that by executing a few more forward and backward passes through a slightly modified version of the original network (though possibly with much larger batch sizes), we can learn a classifier that is provably robust to any norm-bounded adversarial attack. We illustrate the approach on a number of tasks to train classifiers with robust adversarial guarantees (e.g. for MNIST, we produce a convolutional classifier that provably has less than 5.8% test error for any adversarial attack with bounded $\ell_\infty$ norm less than $\epsilon = 0.1$).

Recent work has developed methods for learning deep network classifiers that are \emph{provably} robust to norm-bounded adversarial perturbation; however, these methods are currently only possible for relatively small feedforward networks. In this paper, in an effort to scale these approaches to substantially larger models, we extend previous work in three main directly. First, we present a technique for extending these training procedures to much more general networks, with skip connections (such as ResNets) and general nonlinearities; the approach is fully modular, and can be implemented automatically analogously to automatic differentiation. Second, in the specific case of $\ell_\infty$ adversarial perturbations and networks with ReLU nonlinearities, we adopt a nonlinear random projection for training, which scales \emph{linearly} in the number of hidden units (previous approached scaled quadratically). Third, we show how to further improve robust error through cascade models. On both MNIST and CIFAR data sets, we train classifiers that improve substantially on the state of the art in provable robust adversarial error bounds: from 5.8% to 3.1% on MNIST (with $\ell_\infty$ perturbations of $\epsilon=0.1$), and from 80% to 36.4% on CIFAR (with $\ell_\infty$ perturbations of $\epsilon=2/255$).

We introduce Newton-ADMM, a method for fast conic optimization. The basic idea is to view the residuals of consecutive iterates generated by the alternating direction method of multipliers (ADMM) as a set of fixed point equations, and then use a nonsmooth Newton method to find a solution; we apply the basic idea to the Splitting Cone Solver (SCS), a state-of-the-art method for solving generic conic optimization problems. We demonstrate theoretically, by extending the theory of semismooth operators, that Newton-ADMM converges rapidly (i.e., quadratically) to a solution; empirically, Newton-ADMM is significantly faster than SCS on a number of problems. The method also has essentially no tuning parameters, generates certificates of primal or dual infeasibility, when appropriate, and can be specialized to solve specific convex problems.

Motivated by problems such as molecular energy prediction, we derive an (improper) kernel between geometric inputs, that is able to capture the relevant rotational and translation invariances in geometric data. Since many physical simulations based upon geometric data produce derivatives of the output quantity with respect to the input positions, we derive an approach that incorporates derivative information into our kernel learning. We further show how to exploit the low rank structure of the resulting kernel matrices to speed up learning. Finally, we evaluated the method in the context of molecular energy prediction, showing good performance for modeling previously unseen molecular configurations. Integrating the approach into a Bayesian optimization, we show substantial improvement over the state of the art in molecular energy optimization.