Text-to-image diffusion models have demonstrated an unparalleled ability to generate high-quality, diverse images from a textual prompt. However, the internal representations learned by these models remain an enigma. In this work, we present Conceptor, a novel method to interpret the internal representation of a textual concept by a diffusion model. This interpretation is obtained by decomposing the concept into a small set of human-interpretable textual elements. Applied over the state-of-the-art Stable Diffusion model, Conceptor reveals non-trivial structures in the representations of concepts. For example, we find surprising visual connections between concepts, that transcend their textual semantics. We additionally discover concepts that rely on mixtures of exemplars, biases, renowned artistic styles, or a simultaneous fusion of multiple meanings of the concept. Through a large battery of experiments, we demonstrate Conceptor's ability to provide meaningful, robust, and faithful decompositions for a wide variety of abstract, concrete, and complex textual concepts, while allowing to naturally connect each decomposition element to its corresponding visual impact on the generated images.

We extract a core principle that underlies seemingly different fundamental distributed settings, which is that sparsity awareness may induce faster algorithms for core problems in these settings. To leverage this, we establish a new framework by developing an intermediate auxiliary model which is weak enough to be successfully simulated in the classic congest model given low mixing time, as well as in the recently introduced hybrid model. We prove that despite imposing harsh restrictions, this artificial model allows balancing massive data transfers with a maximal utilization of bandwidth. We then exemplify the power we gain from our methods, by deriving fast shortest-paths algorithms which greatly improve upon the state-of-the-art.

The Hybrid network model was introduced in [Augustine et al., SODA '20] for laying down a theoretical foundation for networks which combine two possible modes of communication: One mode allows high-bandwidth communication with neighboring nodes, and the other allows low-bandwidth communication over few long-range connections at a time. This fundamentally abstracts networks such as hybrid data centers, and class-based software-defined networks. Our technical contribution is a density-aware approach that allows us to simulate a set of oracles for an overlay skeleton graph over a Hybrid network. As applications of our oracle simulations, with additional machinery that we provide, we derive fast algorithms for fundamental distance-related tasks. One of our core contributions is an algorithm in the Hybrid model for computing exact weighted shortest paths from Õ(n^{1/3}) sources which completes in Õ(n^{1/3}) rounds w.h.p. This improves, in both the runtime and the number of sources, upon the algorithm of [Kuhn and Schneider, PODC ’20], which computes shortest paths from a single source in Õ(n^{2/5}) rounds w.h.p. We additionally show a 2-approximation for weighted diameter and a (1+ε)-approximation for unweighted diameter, both in Õ(n^{1/3}) rounds w.h.p., which is comparable to the ̃ Ω(n^{1/3}) lower bound of [Kuhn and Schneider, PODC ’20] for a (2-ε)-approximation for weighted diameter and an exact unweighted diameter. We also provide fast distance approximations from multiple sources and fast approximations for eccentricities.