This paper reveals that the common downstream practice of taking a dot product is only a zeroth-order approximation of the optimization goal, resulting in a loss of information during test-time.

Advances in the field of visual-language contrastive learning have made it possible for many downstream applications to be carried out efficiently and accurately by simply taking the dot product between image and text representations. One of the most representative approaches proposed recently known as CLIP has quickly garnered widespread adoption due to its effectiveness. CLIP is trained with an InfoNCE loss that takes into account both positive and negative samples to help learn a much more robust representation space. This paper however reveals that the common downstream practice of taking a dot product is only a zeroth-order approximation of the optimization goal, resulting in a loss of information during test-time. Intuitively, since the model has been optimized based on the InfoNCE loss, test-time procedures should ideally also be in alignment.

We introduce the Lennard-Jones layer (LJL) for the equalization of the density of 2D and 3D point clouds through systematically rearranging points without destroying their overall structure (distribution normalization). LJL simulates a dissipative process of repulsive and weakly attractive interactions between individual points by considering the nearest neighbor of each point at a given moment in time. This pushes the particles into a potential valley, reaching a well-defined stable configuration that approximates an equidistant sampling after the stabilization process. We apply LJLs to redistribute randomly generated point clouds into a randomized uniform distribution. Moreover, LJLs are embedded in the generation process of point cloud networks by adding them at later stages of the inference process. The improvements in 3D point cloud generation utilizing LJLs are evaluated qualitatively and quantitatively. Finally, we apply LJLs to improve the point distribution of a score-based 3D point cloud denoising network. In general, we demonstrate that LJLs are effective for distribution normalization which can be applied at negligible cost without retraining the given neural network.

Most literature in fairness has focused on improving fairness with respect to one single model or one single objective. However, real-world machine learning systems are usually composed of many different components. Unfortunately, recent research has shown that even if each component is "fair", the overall system can still be "unfair". In this paper, we focus on how well fairness composes over multiple components in real systems. We consider two recently proposed fairness metrics for rankings: exposure and pairwise ranking accuracy gap. We provide theory that demonstrates a set of conditions under which fairness of individual models does compose. We then present an analytical framework for both understanding whether a system's signals can achieve compositional fairness, and diagnosing which of these signals lowers the overall system's end-to-end fairness the most. Despite previously bleak theoretical results, on multiple data-sets -- including a large-scale real-world recommender system -- we find that the overall system's end-to-end fairness is largely achievable by improving fairness in individual components.