Reversing the process is not immediately obvious and thus several schedulers were proposed [23, 26, 31, 58]. In this paper, we employ DDIM [58] scheduler, a popular deterministic scheduler. Other deterministic scheduler would be suitable, and we show in section I below that our method performs well with other schedulers.

They map random samples (seeds) from a high-dimensional space, conditioned on a user-provided text prompt, to a corresponding image.

Text-to-image diffusion models show great potential in synthesizing a large variety of concepts in new compositions and scenarios. However, the latent space of initial seeds is still not well understood and its structure was shown to impact the generation of various concepts. Specifically, simple operations like interpolation and finding the centroid of a set of seeds perform poorly when using standard Euclidean or spherical metrics in the latent space. This paper makes the observation that, in current training procedures, diffusion models observed inputs with a narrow range of norm values. This has strong implications for methods that rely on seed manipulation for image generation, with applications to few-shot and long-tail learning tasks. To address this issue, we propose a novel method for interpolating between two seeds and demonstrate that it defines a new non-Euclidean metric that takes into account a norm-based prior on seeds. We describe a simple yet efficient algorithm for approximating this interpolation procedure and use it to further define centroids in the latent seed space. We show that our new interpolation and centroid techniques significantly enhance the generation of rare concept images. This further leads to state-of-the-art performance on few-shot and long-tail benchmarks, improving prior approaches in terms of generation speed, image quality, and semantic content.

We revisit the recently developed framework of proportionally fair clustering, where the goal is to provide group fairness guarantees that become stronger for groups of data points that are large and cohesive. Prior work applies this framework to centroid-based clustering, where points are partitioned into clusters, and the cost to each data point is measured by its distance to a centroid assigned to its cluster. However, real-life applications often do not require such centroids. We extend the theory of proportionally fair clustering to non-centroid clustering by considering a variety of cost functions, both metric and non-metric, for a data point to be placed in a cluster with other data points. Our results indicate that Greedy Capture, a clustering algorithm developed for centroid clustering, continues to provide strong proportional fairness guarantees for non-centroid clustering, although the guarantees are significantly different and establishing them requires novel proof ideas. We also design algorithms for auditing proportional fairness of a given clustering solution. We conduct experiments on real data which suggest that traditional clustering algorithms are highly unfair, while our algorithms achieve strong fairness guarantees with a moderate loss in common clustering objectives.

The challenge of finding compromises between agent proposals is fundamental to AI sub-fields such as argumentation, mediation, and negotiation. Building on this tradition, Elkind et al. (2021) introduced a process for coalition formation that seeks majority-supported proposals preferable to the status quo, using a metric space where each agent has an ideal point. The crucial step in this iterative process involves identifying compromise proposals around which agent coalitions can unite. How to effectively find such compromise proposals, however, remains an open question. We address this gap by formalizing a holistic model that encompasses agent bounded rationality and uncertainty and developing AI models to generate such compromise proposals. We focus on the domain of collaboratively writing text documents -- e.g., to enable the democratic creation of a community constitution. We apply NLP (Natural Language Processing) techniques and utilize LLMs (Large Language Models) to create a semantic metric space for text and develop algorithms to suggest suitable compromise points. To evaluate the effectiveness of our algorithms, we simulate various coalition formation processes and demonstrate the potential of AI to facilitate large-scale democratic text editing, such as collaboratively drafting a constitution, an area where traditional tools are limited.

We build upon vec2vec, a procedure designed to align text embedding spaces without parallel data. vec2vec finds a near-perfect alignment, but it is expensive and unstable. We present mini-vec2vec, a simple and efficient alternative that requires substantially lower computational cost and is highly robust. Moreover, the learned mapping is a linear transformation. Our method consists of three main stages: a tentative matching of pseudo-parallel embedding vectors, transformation fitting, and iterative refinement. Our linear alternative exceeds the original instantiation of vec2vec by orders of magnitude in efficiency, while matching or exceeding their results. The method's stability and interpretable algorithmic steps facilitate scaling and unlock new opportunities for adoption in new domains and fields.