Double machine learning is a theoretically grounded and practically efficient procedure for a variety of causal estimands and functional estimation problems when adopting black-box machine learning models for estimating nuisance parameters. It is known that double machine learning may have sub-optimal performance in the structure-aware settings, e.g., the nuisances are H{ö}lder smooth functions, and recent articles (Balakrishnan et al., 2023) are delivering the message that double machine learning is optimal in structure-agnostic settings. This note claims that whether double machine learning is optimal for black-box machine learning models remains open, even for the simplest linear coefficient estimation in the partial linear model. We argue that the key gap that differentiates structure-agnostic and structure-aware settings, and also the previous lower bound results do not address, is the role of variance – the awareness of well-conditioned structures offers the possibility to mitigate the effects of variance, while that is not clear for structure-agnostic settings. The answer to this question has significant implications both in theory and practice.

Models are expected to engage in invariance learning, which involves distinguishing the core relations that remain consistent across varying environments to ensure the predictions are safe, robust and fair. While existing works consider specific algorithms to realize invariance learning, we show that model has the potential to learn invariance through standard training procedures. In other words, this paper studies the implicit bias of Stochastic Gradient Descent (SGD) over heterogeneous data and shows that the implicit bias drives the model learning towards an invariant solution. We call the phenomenon the implicit invariance learning. Specifically, we theoretically investigate the multi-environment low-rank matrix sensing problem where in each environment, the signal comprises (i) a lower-rank invariant part shared across all environments; and (ii) a significantly varying environment-dependent spurious component. The key insight is, through simply employing the large step size large-batch SGD sequentially in each environment without any explicit regularization, the oscillation caused by heterogeneity can provably prevent model learning spurious signals. The model reaches the invariant solution after certain iterations. In contrast, model learned using pooled SGD over all data would simultaneously learn both the invariant and spurious signals. Overall, we unveil another implicit bias that is a result of the symbiosis between the heterogeneity of data and modern algorithms, which is, to the best of our knowledge, first in the literature.

The analysis of over-parameterized neural networks has drawn significant attention in recent years. It was shown that such systems behave like convex systems under various restricted settings, such as for two-layer neural networks, and when learning is only restricted locally in the so-called neural tangent kernel space around specialized initializations. However, there is a lack of powerful theoretical techniques that can analyze fully trained deep neural networks under general conditions. This paper considers this fundamental problem by investigating such overparameterized deep neural networks when fully trained. Specifically, we characterize a deep neural network by its features’ distributions and propose a metric to intuitively measure the usefulness of feature representations. Under certain regularizers that bounds the metric, we show deep neural networks can be reformulated as aconvexoptimization and the system can guarantee effective feature representations in terms of the metric. Our new analysis is more consistent with empirical observations that deep neural networks are capable of learning efficient feature representations. Empirical studies confirm that predictions of our theory are consistent with results observed in practice.

We study the question of how to imitate tasks across domains with discrepancies such as embodiment, viewpoint, and dynamics mismatch. Many prior works require paired, aligned demonstrations and an additional RL step that requires environment interactions. However, paired, aligned demonstrations are seldom obtainable and RL procedures are expensive. In this work, we formalize the Domain Adaptive Imitation Learning (DAIL) problem - a unified framework for imitation learning in the presence of viewpoint, embodiment, and/or dynamics mismatch. Informally, DAIL is the process of learning how to perform a task optimally, given demonstrations of the task in a distinct domain. We propose a two step approach to DAIL: alignment followed by adaptation. In the alignment step we execute a novel unsupervised MDP alignment algorithm, Generative Adversarial MDP Alignment (GAMA), to learn state and action correspondences from \emph{unpaired, unaligned} demonstrations. In the adaptation step we leverage the correspondences to zero-shot imitate tasks across domains. To describe when DAIL is feasible via alignment and adaptation, we introduce a theory of MDP alignability. We experimentally evaluate GAMA against baselines in embodiment, viewpoint, and dynamics mismatch scenarios where aligned demonstrations don’t exist and show the effectiveness of our approach

For many initialization schemes, parameters of two randomly initialized deep neural networks (DNNs) can be quite different, but feature distributions of the hidden nodes are similar at each layer. With the help of a new technique called {\it neural network grafting}, we demonstrate that even during the entire training process, feature distributions of differently initialized networks remain similar at each layer. In this paper, we present an explanation of this phenomenon. Specifically, we consider the loss landscape of an overparameterized convolutional neural network (CNN) in the continuous limit, where the numbers of channels/hidden nodes in the hidden layers go to infinity. Although the landscape of the overparameterized CNN is still non-convex with respect to the trainable parameters, we show that very surprisingly, it can be reformulated as a convex function with respect to the feature distributions in the hidden layers. Therefore by reparameterizing neural networks in terms of feature distributions, we obtain a much simpler characterization of the landscape of overparameterized CNNs. We further argue that training with respect to network parameters leads to a fixed trajectory in the feature distributions.

Most language modeling methods rely on large-scale data to statistically learn the sequential patterns of words.In this paper, we argue that words are atomic language units but not necessarily atomic semantic units.Inspired by HowNet, we use sememes, the minimum semantic units in human languages, to represent the implicit semantics behind words for language modeling, named Sememe-Driven Language Model (SDLM).More specifically, to predict the next word, SDLM first estimates the sememe distribution given textual context.Afterwards, it regards each sememe as a distinct semantic expert, and these experts jointly identify the most probable senses and the corresponding word.In this way, SDLM enables language models to work beyond word-level manipulation to fine-grained sememe-level semantics, and offers us more powerful tools to fine-tune language models and improve the interpretability as well as the robustness of language models.Experiments on language modeling and the downstream application of headline generation demonstrate the significant effectiveness of SDLM.