Dynamics of Concept Learning and Compositional Generalization

Prior work has shown that text-conditioned diffusion models can learn to identify and manipulate primitive concepts underlying a compositional data-generating process, enabling generalization to entirely novel, out-of-distribution compositions. Beyond performance evaluations, these studies develop a rich empirical phenomenology of learning dynamics, showing that models generalize sequentially, respecting the compositional hierarchy of the data-generating process. Moreover, concept-centric structures within the data significantly influence a model's speed of learning the ability to manipulate a concept. In this paper, we aim to better characterize these empirical results from a theoretical standpoint. Specifically, we propose an abstraction of prior work's compositional generalization problem by introducing a structured identity mapping (SIM) task, where a model is trained to learn the identity mapping on a Gaussian mixture with structurally organized centroids. We mathematically analyze the learning dynamics of neural networks trained on this SIM task and show that, despite its simplicity, SIM's learning dynamics capture and help explain key empirical observations on compositional generalization with diffusion models identified in prior work. Our theory also offers several new insights -- e.g., we find a novel mechanism for non-monotonic learning dynamics of test loss in early phases of training. We validate our new predictions by training a text-conditioned diffusion model, bridging our simplified framework and complex generative models. Overall, this work establishes the SIM task as a meaningful theoretical abstraction of concept learning dynamics in modern generative models.

Emergence of Hidden Capabilities: Exploring Learning Dynamics in Concept Space

Modern generative models demonstrate impressive capabilities, likely stemming from an ability to identify and manipulate abstract concepts underlying their training data. However, fundamental questions remain: what determines the concepts a model learns, the order in which it learns them, and its ability to manipulate those concepts? To address these questions, we propose analyzing a model's learning dynamics via a framework we call the concept space, where each axis represents an independent concept underlying the data generating process. By characterizing learning dynamics in this space, we identify how the speed at which a concept is learned, and hence the order of concept learning, is controlled by properties of the data we term concept signal. Further, we observe moments of sudden turns in the direction of a model's learning dynamics in concept space. Surprisingly, these points precisely correspond to the emergence of hidden capabilities, i.e., where latent interventions show the model possesses the capability to manipulate a concept, but these capabilities cannot yet be elicited via naive input prompting. While our results focus on synthetically defined toy datasets, we hypothesize a general claim on emergence of hidden capabilities may hold: generative models possess latent capabilities that emerge suddenly and consistently during training, though a model might not exhibit these capabilities under naive input prompting.

Hyperspectral shadow removal with Iterative Logistic Regression and latent Parametric Linear Combination of Gaussians

Shadow detection and removal is a challenging problem in the analysis of hyperspectral images. Yet, this step is crucial for analyzing data for remote sensing applications like methane detection. In this work, we develop a shadow detection and removal method only based on the spectrum of each pixel and the overall distribution of spectral values. We first introduce Iterative Logistic Regression (ILR) to learn a spectral basis in which shadows can be linearly classified. We then model the joint distribution of the mean radiance and the projection coefficients of the spectra onto the above basis as a parametric linear combination of Gaussians. We can then extract the maximum likelihood mixing parameter of the Gaussians to estimate the shadow coverage and to correct the shadowed spectra. Our correction scheme reduces correction artefacts at shadow borders. The shadow detection and removal method is applied to hyperspectral images from MethaneAIR, a precursor to the satellite MethaneSAT.

Probabilistic reconstruction of Dark Matter fields from biased tracers using diffusion models

Galaxies are biased tracers of the underlying cosmic web, which is dominated by dark matter components that cannot be directly observed. The relationship between dark matter density fields and galaxy distributions can be sensitive to assumptions in cosmology and astrophysical processes embedded in the galaxy formation models, that remain uncertain in many aspects. Based on state-of-the-art galaxy formation simulation suites with varied cosmological parameters and sub-grid astrophysics, we develop a diffusion generative model to predict the unbiased posterior distribution of the underlying dark matter fields from the given stellar mass fields, while being able to marginalize over the uncertainties in cosmology and galaxy formation.

Revisiting Latent-Space Interpolation via a Quantitative Evaluation Framework

Latent-space interpolation is commonly used to demonstrate the generalization ability of deep latent variable models. Various algorithms have been proposed to calculate the best trajectory between two encodings in the latent space. In this work, we show how data labeled with semantically continuous attributes can be utilized to conduct a quantitative evaluation of latent-space interpolation algorithms, for variational autoencoders. Our framework can be used to complement the standard qualitative comparison, and also enables evaluation for domains (such as graph) in which the visualization is difficult. Interestingly, our experiments reveal that the superiority of interpolation algorithms could be domain-dependent. While normalised interpolation works best for the image domain, spherical linear interpolation achieves the best performance in the graph domain. Next, we propose a simple-yet-effective method to restrict the latent space via a bottleneck structure in the encoder. We find that all interpolation algorithms evaluated in this work can benefit from this restriction. Finally, we conduct interpolation-aware training with the labeled attributes, and show that this explicit supervision can improve the interpolation performance.