ICML 2022 Papers

Recently, certifiable robust training methods via bound propagation have been proposed for training neural networks with certifiable robustness guarantees. However, no neural architectures with regular convolution and linear layers perform better in the certifiable training than the plain CNNs, since the output bounds for the deep explicit models increase quickly as their depth increases. And such a phenomenon significantly hinders certifiable training. Meanwhile, the Deep Equilibrium Model (DEQ) is more representative and robust due to their equivalent infinite depth and controllable global Lipschitz. But no work has been proposed to explore whether DEQ can show advantages in certified training. In this work, we aim to tackle the problem of DEQ’s certified training. To obtain the output bound based on the bound propagation scheme in the implicit model, we first involve the adjoint DEQ for bound approximation. Furthermore, we also use the weight orthogonalization method and other tricks specified for DEQ to stabilize the certifiable training. With our approach, we can obtain the certifiable DEQ called CerDEQ. Our CerDEQ can achieve state-of-the-art performance compared with models using regular convolution and linear layers on $\ell_\infty$ tasks with $\epsilon=8/255$: $64.72%$ certified error for CIFAR-$10$ and $94.45%$ certified error for Tiny ImageNet.

Bootstrap is a principled and powerful frequentist statistical tool for uncertainty quantification. Unfortunately, standard bootstrap methods are computationally intensive due to the need of drawing a large i.i.d. bootstrap sample to approximate the ideal bootstrap distribution; this largely hinders their application in large-scale machine learning, especially deep learning problems. In this work, we propose an efficient method to explicitly

Current techniques for explaining outliers cannot tell what caused the outliers. We present a formal method to identify "root causes" of outliers, amongst variables. The method requires a causal graph of the variables along with the functional causal model. It quantifies the contribution of each variable to the target outlier score, which explains to what extent each variable is a "root cause" of the target outlier. We study the empirical performance of the method through simulations and present a real-world case study identifying "root causes" of extreme river flows.

Estimating counterfactual outcomes over time from observational data is relevant for many applications (e.g., personalized medicine). Yet, state-of-the-art methods build upon simple long short-term memory (LSTM) networks, thus rendering inferences for complex, long-range dependencies challenging. In this paper, we develop a novel Causal Transformer for estimating counterfactual outcomes over time. Our model is specifically designed to capture complex, long-range dependencies among time-varying confounders. For this, we combine three transformer subnetworks with separate inputs for time-varying covariates, previous treatments, and previous outcomes into a joint network with in-between cross-attentions. We further develop a custom, end-to-end training procedure for our Causal Transformer. Specifically, we propose a novel counterfactual domain confusion loss to address confounding bias: it aims to learn adversarial balanced representations, so that they are predictive of the next outcome but non-predictive of the current treatment assignment. We evaluate our Causal Transformer based on synthetic and real-world datasets, where it achieves superior performance over current baselines. To the best of our knowledge, this is the first work proposing transformer-based architecture for estimating counterfactual outcomes from longitudinal data.

We introduce an approach to counterfactual inference based on merging information from multiple datasets. We consider a causal reformulation of the statistical marginal problem: given a collection of marginal structural causal models (SCMs) over distinct but overlapping sets of variables, determine the set of joint SCMs that are counterfactually consistent with the marginal ones. We formalise this approach for categorical SCMs using the response function formulation and show that it reduces the space of allowed marginal and joint SCMs. Our work thus highlights a new mode of falsifiability through additional variables, in contrast to the statistical one via additional data.

We develop algorithms for imitation learning from policy data that was corrupted by temporally correlated noise in expert actions. When noise affects multiple timesteps of recorded data, it can manifest as spurious correlations between states and actions that a learner might latch on to, leading to poor policy performance. To break up these spurious correlations, we apply modern variants of the instrumental variable regression (IVR) technique of econometrics, enabling us to recover the underlying policy without requiring access to an interactive expert. In particular, we present two techniques, one of a generative-modeling flavor (DoubIL) that can utilize access to a simulator, and one of a game-theoretic flavor (ResiduIL) that can be run entirely offline. We find both of our algorithms compare favorably to behavioral cloning on simulated control tasks.

Learning dynamics models accurately is an important goal for Model-Based Reinforcement Learning (MBRL), but most MBRL methods learn a dense dynamics model which is vulnerable to spurious correlations and therefore generalizes poorly to unseen states. In this paper, we introduce Causal Dynamics Learning for Task-Independent State Abstraction (CDL), which first learns a theoretically proved causal dynamics model that removes unnecessary dependencies between state variables and the action, thus generalizing well to unseen states. A state abstraction can then be derived from the learned dynamics, which not only improves sample efficiency but also applies to a wider range of tasks than existing state abstraction methods. Evaluated on two simulated environments and downstream tasks, both the dynamics model and policies learned by the proposed method generalize well to unseen states and the derived state abstraction improves sample efficiency compared to learning without it.

Recent work highlights the role of causality in designing equitable decision-making algorithms. It is not immediately clear, however, how existing causal conceptions of fairness relate to one another, or what the consequences are of using these definitions as design principles. Here, we first assemble and categorize popular causal definitions of algorithmic fairness into two broad families: (1) those that constrain the effects of decisions on counterfactual disparities; and (2) those that constrain the effects of legally protected characteristics, like race and gender, on decisions. We then show, analytically and empirically, that both families of definitions

In this paper, we study gap-dependent regret guarantees for risk-sensitive reinforcement learning based on the entropic risk measure. We propose a novel definition of sub-optimality gaps, which we call cascaded gaps, and we discuss their key components that adapt to underlying structures of the problem. Based on the cascaded gaps, we derive non-asymptotic and logarithmic regret bounds for two model-free algorithms under episodic Markov decision processes. We show that, in appropriate settings, these bounds feature exponential improvement over existing ones that are independent of gaps. We also prove gap-dependent lower bounds, which certify the near optimality of the upper bounds.

Accurate probabilistic predictions can be characterized by two properties{—}calibration and sharpness. However, standard maximum likelihood training yields models that are poorly calibrated and thus inaccurate{—}a 90% confidence interval typically does not contain the true outcome 90% of the time. This paper argues that calibration is important in practice and is easy to maintain by performing low-dimensional density estimation. We introduce a simple training procedure based on recalibration that yields calibrated models without sacrificing overall performance; unlike previous approaches, ours ensures the most general property of distribution calibration and applies to any model, including neural networks. We formally prove the correctness of our procedure assuming that we can estimate densities in low dimensions and we establish uniform convergence bounds. Our results yield empirical performance improvements on linear and deep Bayesian models and suggest that calibration should be increasingly leveraged across machine learning.

The learning to defer (L2D) framework has the potential to make AI systems safer. For a given input, the system can defer the decision to a human if the human is more likely than the model to take the correct action. We study the calibration of L2D systems, investigating if the probabilities they output are sound. We find that Mozannar & Sontag’s (2020) multiclass framework is not calibrated with respect to expert correctness. Moreover, it is not even guaranteed to produce valid probabilities due to its parameterization being degenerate for this purpose. We propose an L2D system based on one-vs-all classifiers that is able to produce calibrated probabilities of expert correctness. Furthermore, our loss function is also a consistent surrogate for multiclass L2D, like Mozannar & Sontag’s (2020). Our experiments verify that not only is our system calibrated, but this benefit comes at no cost to accuracy. Our model’s accuracy is always comparable (and often superior) to Mozannar & Sontag’s (2020) model’s in tasks ranging from hate speech detection to galaxy classification to diagnosis of skin lesions.

Learning in general-sum games is unstable and frequently leads to socially undesirable (Pareto-dominated) outcomes. To mitigate this, Learning with Opponent-Learning Awareness (LOLA) introduced opponent shaping to this setting, by accounting for each agent’s influence on their opponents’ anticipated learning steps. However, the original LOLA formulation (and follow-up work) is inconsistent because LOLA models other agents as naive learners rather than LOLA agents. In previous work, this inconsistency was suggested as a cause of LOLA’s failure to preserve stable fixed points (SFPs). First, we formalize consistency and show that higher-order LOLA (HOLA) solves LOLA’s inconsistency problem if it converges. Second, we correct a claim made in the literature by Sch{ä}fer and Anandkumar (2019), proving that Competitive Gradient Descent (CGD) does not recover HOLA as a series expansion (and fails to solve the consistency problem). Third, we propose a new method called Consistent LOLA (COLA), which learns update functions that are consistent under mutual opponent shaping. It requires no more than second-order derivatives and learns consistent update functions even when HOLA fails to converge. However, we also prove that even consistent update functions do not preserve SFPs, contradicting the hypothesis that this shortcoming is caused by LOLA’s inconsistency. Finally, in an empirical evaluation on a set of general-sum games, we find that COLA finds prosocial solutions and that it converges under a wider range of learning rates than HOLA and LOLA. We support the latter finding with a theoretical result for a simple game.

Learning representations that can decompose a multi-object scene into its constituent objects and recompose them flexibly is desirable for object-oriented reasoning and planning. Built upon object masks in the pixel space, existing metrics for objectness can only evaluate generative models with an object-specific “slot” structure. We propose to directly measure compositionality in the representation space as a form of objections, making such evaluations tractable for a wider class of models. Our metric, COAT (Compositional Object Algebra Test), evaluates if a generic representation exhibits certain geometric properties that underpin object compositionality beyond what is already captured by the raw pixel space. Our experiments on the popular CLEVR (Johnson et.al., 2018) domain reveal that existing disentanglement-based generative models are not as compositional as one might expect, suggesting room for further modeling improvements. We hope our work allows for a unified evaluation of object-centric representations, spanning generative as well as discriminative, self-supervised models.

Understanding the latent causal factors of a dynamical system from visual observations is considered a crucial step towards agents reasoning in complex environments. In this paper, we propose CITRIS, a variational autoencoder framework that learns causal representations from temporal sequences of images in which underlying causal factors have possibly been intervened upon. In contrast to the recent literature, CITRIS exploits temporality and observing intervention targets to identify scalar and multidimensional causal factors, such as 3D rotation angles. Furthermore, by introducing a normalizing flow, CITRIS can be easily extended to leverage and disentangle representations obtained by already pretrained autoencoders. Extending previous results on scalar causal factors, we prove identifiability in a more general setting, in which only some components of a causal factor are affected by interventions. In experiments on 3D rendered image sequences, CITRIS outperforms previous methods on recovering the underlying causal variables. Moreover, using pretrained autoencoders, CITRIS can even generalize to unseen instantiations of causal factors, opening future research areas in sim-to-real generalization for causal representation learning.

Minwise hashing (MinHash) is an important and practical algorithm for generating random hashes to approximate the Jaccard (resemblance) similarity in massive binary (0/1) data. The basic theory of MinHash requires applying hundreds or even thousands of independent random permutations to each data vector in the dataset, in order to obtain reliable results for (e.g.,) building large-scale learning models or approximate near neighbor search. In this paper, we propose Circulant MinHash (C-MinHash) and provide the surprising theoretical results that using only two independent random permutations in a circulant manner leads to uniformly smaller Jaccard estimation variance than that of the classical MinHash with K independent permutations. Experiments are conducted to show the effectiveness of the proposed method. We also propose a more convenient C-MinHash variant which reduces two permutations to just one, with extensive numerical results to validate that it achieves essentially the same estimation accuracy as using two permutations.

We propose a new framework that generalizes the parameters of neural network models to $C^*$-algebra-valued ones. $C^*$-algebra is a generalization of the space of complex numbers. A typical example is the space of continuous functions on a compact space. This generalization enables us to combine multiple models continuously and use tools for functions such as regression and integration. Consequently, we can learn features of data efficiently and adapt the models to problems continuously. We apply our framework to practical problems such as density estimation and few-shot learning and show that our framework enables us to learn features of data even with a limited number of samples. Our new framework highlights the potential possibility of applying the theory of $C^*$-algebra to general neural network models.

Byzantine resilience emerged as a prominent topic within the distributed machine learning community. Essentially, the goal is to enhance distributed optimization algorithms, such as distributed SGD, in a way that guarantees convergence despite the presence of some misbehaving (a.k.a.,

Normalizing flows model complex probability distributions using maps obtained by composing invertible layers. Special linear layers such as masked and 1{\texttimes}1 convolutions play a key role in existing architectures because they increase expressive power while having tractable Jacobians and inverses. We propose a new family of invertible linear layers based on butterfly layers, which are known to theoretically capture complex linear structures including permutations and periodicity, yet can be inverted efficiently. This representational power is a key advantage of our approach, as such structures are common in many real-world datasets. Based on our invertible butterfly layers, we construct a new class of normalizing flow mod- els called ButterflyFlow. Empirically, we demonstrate that ButterflyFlows not only achieve strong density estimation results on natural images such as MNIST, CIFAR-10, and ImageNet-32{\texttimes}32, but also obtain significantly better log-likelihoods on structured datasets such as galaxy images and MIMIC-III patient cohorts{—}all while being more efficient in terms of memory and computation than relevant baselines.

The brain can learn to solve a wide range of tasks with high temporal and energetic efficiency. However, most biological models are composed of simple single-compartment neurons and cannot achieve the state-of-the-art performances of artificial intelligence. We propose a multi-compartment model of pyramidal neuron, in which bursts and dendritic input segregation give the possibility to plausibly support a biological target-based learning. In target-based learning, the internal solution of a problem (a spatio-temporal pattern of bursts in our case) is suggested to the network, bypassing the problems of error backpropagation and credit assignment. Finally, we show that this neuronal architecture naturally supports the orchestration of “hierarchical imitation learning”, enabling the decomposition of challenging long-horizon decision-making tasks into simpler subtasks.