In modern machine learning, models can often fit training data in numerous ways, some of which perform well on unseen (test) data, while others do not. Remarkably, in such cases gradient descent frequently exhibits an implicit bias that leads to excellent performance on unseen data. This implicit bias was extensively studied in supervised learning, but is far less understood in optimal control (reinforcement learning). There, learning a controller applied to a system via gradient descent is known as policy gradient, and a question of prime importance is the extent to which a learned controller extrapolates to unseen initial states. This paper theoretically studies the implicit bias of policy gradient in terms of extrapolation to unseen initial states. Focusing on the fundamental Linear Quadratic Regulator (LQR) problem, we establish that the extent of extrapolation depends on the degree of exploration induced by the system when commencing from initial states included in training. Experiments corroborate our theory, and demonstrate its conclusions on problems beyond LQR, where systems are non-linear and controllers are neural networks. We hypothesize that real-world optimal control may be greatly improved by developing methods for informed selection of initial states to train on.

Structured state space models (SSMs), the core engine behind prominent neural networks such as S4 and Mamba, are linear dynamical systems adhering to a specified structure, most notably diagonal. In contrast to typical neural network modules, whose parameterizations are real, SSMs often use complex parameterizations. Theoretically explaining the benefits of complex parameterizations for SSMs is an open problem. The current paper takes a step towards its resolution, by establishing formal gaps between real and complex diagonal SSMs. Firstly, we prove that while a moderate dimension suffices in order for a complex SSM to express all mappings of a real SSM, a much higher dimension is needed for a real SSM to express mappings of a complex SSM. Secondly, we prove that even if the dimension of a real SSM is high enough to express a given mapping, typically, doing so requires the parameters of the real SSM to hold exponentially large values, which cannot be learned in practice. In contrast, a complex SSM can express any given mapping with moderate parameter values. Experiments corroborate our theory, and suggest a potential extension of the theory that accounts for selectivity, a new architectural feature yielding state of the art performance.

When using recurrent neural networks (RNNs) it is common practice to apply trained models to sequences longer than those seen in training. This “extrapolating” usage deviates from the traditional statistical learning setup where guarantees are provided under the assumption that train and test distributions are identical. Here we set out to understand when RNNs can extrapolate, focusing on a simple case where the data generating distribution is memoryless. We first show that even with infinite training data, there exist RNN models that interpolate perfectly (i.e., they fit the training data) yet extrapolate poorly to longer sequences. We then show that if gradient descent is used for training, learning will converge to perfect extrapolation under certain assumptions on initialization. Our results complement recent studies on the implicit bias of gradient descent, showing that it plays a key role in extrapolation when learning temporal prediction models.

Identifying the quality of free-text arguments has become an important task in the rapidly expanding field of computational argumentation. In this work, we explore the challenging task of argument quality ranking. To this end, we created a corpus of 30,497 arguments carefully annotated for point-wise quality, released as part of this work. To the best of our knowledge, this is the largest dataset annotated for point-wise argument quality, larger by a factor of five than previously released datasets. Moreover, we address the core issue of inducing a labeled score from crowd annotations by performing a comprehensive evaluation of different approaches to this problem. In addition, we analyze the quality dimensions that characterize this dataset. Finally, we present a neural method for argument quality ranking, which outperforms several baselines on our own dataset, as well as previous methods published for another dataset.

In many machine learning problems the output should not depend on the order of the inputs. Such ``permutation invariant'' functions have been studied extensively recently. Here we argue that temporal architectures such as RNNs are highly relevant for such problems, despite the inherent dependence of RNNs on order. We show that RNNs can be regularized towards permutation invariance, and that this can result in compact models, as compared to non-recursive architectures. Existing solutions (e.g., DeepSets) mostly suggest restricting the learning problem to hypothesis classes which are permutation invariant by design. Our approach of enforcing permutation invariance via regularization gives rise to learning functions which are "semi permutation invariant", e.g. invariant to some permutations and not to others. Our approach relies on a novel form of stochastic regularization. We demonstrate that our method is beneficial compared to existing permutation invariant methods on synthetic and real world datasets.

Assaf Toledo, Shai Gretz, Edo Cohen-Karlik, Roni Friedman, Elad Venezian, Dan Lahav, Michal Jacovi, Ranit Aharonov, Noam Slonim. Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP). 2019.