As autonomous systems rapidly become ubiquitous, there is a growing need for a legal and regulatory framework that addresses when and how such a system harms someone. There have been several attempts within the philosophy literature to define harm, but none of them has proven capable of dealing with the many examples that have been presented, leading some to suggest that the notion of harm should be abandoned and "replaced by more well-behaved notions". As harm is generally something that is caused, most of these definitions have involved causality at some level. Yet surprisingly, none of them makes use of causal models and the definitions of actual causality that they can express. In this paper we formally define a qualitative notion of harm that uses causal models and is based on a well-known definition of actual causality [13]. The key features of our definition are that it is based on contrastive causation and uses a default utility to which the utility of actual outcomes is compared. We show that our definition is able to handle the examples from the literature, and illustrate its importance for reasoning about situations involving autonomous systems.

A.1 Data Configuration The inputs to a hydraulic simulation include an elevation map, initial conditions, and the boundary conditions. For a given elevation map, there is an infinite possible combinations of initial and boundary conditions that could potentially realize in future events. It is an interesting question how to automatically configure the most relevant initial and boundary conditions to train on, to get a representation that will be useful in potential future real-world scenarios. We suggest a basic configuration that adequate for the purpose of this paper. These include the water height h Rm m at each pixel and a staggered grid flux q R2 (m 1) (m 1) in each direction x,y.

Federated learning (FL) has emerged as an enabling framework for communicationefficient decentralized training. We study three broadly applicable problem classes in FL: (i) Nondifferentiable nonconvex federated optimization; (ii) Federated bilevel optimization; (iii) Federated minimax problems. Notably, in an implicit sense, both (ii) and (iii) are instances of (i). However, the hierarchical problems in (ii) and (iii) are often complicated by the absence of a closed-form expression for the implicit objective function. Unfortunately, research on these problems has been limited and afflicted by reliance on strong assumptions, including the need for differentiability and L-smoothness of the implicit function. We address this shortcoming by making the following contributions. In (i), by leveraging convolution-based smoothing and Clarke's subdifferential calculus, we devise a randomized smoothing-enabled zeroth-order FL method and derive communication and iteration complexity guarantees for computing an approximate Clarke stationary point. To contend with (ii) and (iii), we devise a unified randomized implicit zeroth-order FL framework, equipped with explicit communication and iteration complexities. Importantly, our method utilizes delays during local steps to skip making calls to the inexact lower-level FL oracle.

In many contexts, simpler models are preferable to more complex models and the control of this model complexity is the goal for many methods in machine learning such as regularization, hyperparameter tuning and architecture design. In deep learning, it has been difficult to understand the underlying mechanisms of complexity control, since many traditional measures are not naturally suitable for deep neural networks. Here we develop the notion of geometric complexity, which is a measure of the variability of the model function, computed using a discrete Dirichlet energy. Using a combination of theoretical arguments and empirical results, we show that many common training heuristics such as parameter norm regularization, spectral norm regularization, flatness regularization, implicit gradient regularization, noise regularization and the choice of parameter initialization all act to control geometric complexity, providing a unifying framework in which to characterize the behavior of deep learning models.

Language models employ a very large number of trainable parameters. Despite being highly overparameterized, these networks often achieve good out-of-sample test performance on the original task and easily fine-tune to related tasks. Recent observations involving, for example, intrinsic dimension of the objective landscape and the lottery ticket hypothesis, indicate that often training actively involves only a small fraction of the parameter space. Thus, a question remains how large a parameter space needs to be in the first place -- the evidence from recent work on model compression, parameter sharing, factorized representations, and knowledge distillation increasingly shows that models can be made much smaller and still perform well. Here, we focus on factorized representations of matrices that underpin dense, embedding, and self-attention layers. We use low-rank factorized representation of a reshaped and rearranged original matrix to achieve space efficient and expressive linear layers. We prove that stacking such low-rank layers increases their expressiveness, providing theoretical understanding for their effectiveness in deep networks. In Transformer models, our approach leads to more than tenfold reduction in the number of total trainable parameters, including embedding, attention, and feed-forward layers, with little degradation in on-task performance. The approach operates out-of-the-box, replacing each parameter matrix with its compact equivalent while maintaining the architecture of the network.