We propose a continuous optimization framework for discovering a latent directed acyclic graph (DAG) from observational data. Our approach optimizes over the polytope of permutation vectors, the so-called Permutahedron, to learn a topological ordering. Edges can be optimized jointly, or learned conditional on the ordering via a non-differentiable subroutine. Compared to existing continuous optimization approaches our formulation has a number of advantages including: 1. validity: optimizes over exact DAGs as opposed to other relaxations optimizing approximate DAGs; 2. modularity: accommodates any edge-optimization procedure, edge structural parameterization, and optimization loss; 3. end-to-end: either alternately iterates between node-ordering and edge-optimization, or optimizes them jointly. We demonstrate, on real-world data problems in protein-signaling and transcriptional network discovery, that our approach lies on the Pareto frontier of two key metrics, the SID and SHD. In many domains, including cell biology (Sachs et al., 2005), finance (Sanford & Moosa, 2012), and genetics (Zhang et al., 2013), the data generating process is thought to be represented by an underlying directed acylic graph (DAG). Many models rely on DAG assumptions, e.g., causal modeling uses DAGs to model distribution shifts, ensure predictor fairness among subpopulations, or learn agents more sample-efficiently (Kaddour et al., 2022). A key question, with implications ranging from better modeling to causal discovery, is how to recover this unknown DAG from observed data alone. Learning DAGs from observational data alone is fundamentally difficult for two reasons. This riddles the search space with local minima; (ii) Computation: DAG discovery is a costly combinatorial optimization problem over an exponentially large solution space and subject to global acyclicity constraints. To address issue (ii), recent work has proposed continuous relaxations of the DAG learning problem.

Artificial intelligence is all over the news. When ChatGPT, OpenAI's new chatbot, was released last month it seemed, finally, to match the hype that generative A.I. has been promising for years--an easy-to-use machine intelligence for the general public. Wild predictions soon followed: The death of search engines, the end of homework, the hollowing-out of creative professions. And, for the first time, such predictions didn't seem abstract. When an A.I. bot like ChatGPT can write a coherent story or essay in seconds, and visual applications like Midjourney, Stable Diffusion and DALL-E 2, produce similarly comprehensible images you have to wonder if human creativity--slow and often uncertain--might be superfluous.

There's a hilarious illustration from Paris in late 1839, mere months after an early type of photograph called a daguerreotype was announced to the world, that warned what this tiny picture portended. In Théodore Maurisset's imagination, the daguerreotype would bring about a collective hysteria, La Daguerréotypomanie, in which crazed masses arrive from the ends of the earth and overrun a small photo studio. Some in the crowd want pictures of themselves, but, mon Dieu, others demand cameras to take their own pictures--Maurisset shows them loading the machines like contraband onto steamships bound for foreign ports--and still others throng simply to ogle at this newfangled thing and all the lunatic proceedings surrounding it. The clamor is so feverish that it brings about a mass hallucination, in which nearly everything else in the landscape around the studio, including railroad cars, a clock tower, a basket for a hot air balloon, indeed anything remotely boxy in shape, morphs into cameras. As they march to the studio, the crowds pass by half a dozen gallows, where in response to the daguerreotype's appearance artists have hung themselves.

This essay discusses whether computers, using Artificial Intelligence (AI), could create art. First, the history of technologies that automated aspects of art is surveyed, including photography and animation. In each case, there were initial fears and denial of the technology, followed by a blossoming of new creative and professional opportunities for artists. The current hype and reality of Artificial Intelligence (AI) tools for art making is then discussed, together with predictions about how AI tools will be used. It is then speculated about whether it could ever happen that AI systems could be credited with authorship of artwork. It is theorized that art is something created by social agents, and so computers cannot be credited with authorship of art in our current understanding. A few ways that this could change are also hypothesized.