Towards the Reusability and Compositionality of Causal Representations

Causal Representation Learning (CRL) aims at identifying high-level causal factors and their relationships from high-dimensional observations, e.g., images. While most CRL works focus on learning causal representations in a single environment, in this work we instead propose a first step towards learning causal representations from temporal sequences of images that can be adapted in a new environment, or composed across multiple related environments. In particular, we introduce DECAF, a framework that detects which causal factors can be reused and which need to be adapted from previously learned causal representations. Our approach is based on the availability of intervention targets, that indicate which variables are perturbed at each time step. Experiments on three benchmark datasets show that integrating our framework with four state-of-the-art CRL approaches leads to accurate representations in a new environment with only a few samples.

A Sparsity Principle for Partially Observable Causal Representation Learning

Causal representation learning aims at identifying high-level causal variables from perceptual data. Most methods assume that all latent causal variables are captured in the high-dimensional observations. We instead consider a partially observed setting, in which each measurement only provides information about a subset of the underlying causal state. Prior work has studied this setting with multiple domains or views, each depending on a fixed subset of latents. Here, we focus on learning from unpaired observations from a dataset with an instance-dependent partial observability pattern. Our main contribution is to establish two identifiability results for this setting: one for linear mixing functions without parametric assumptions on the underlying causal model, and one for piecewise linear mixing functions with Gaussian latent causal variables. Based on these insights, we propose two methods for estimating the underlying causal variables by enforcing sparsity in the inferred representation. Experiments on different simulated datasets and established benchmarks highlight the effectiveness of our approach in recovering the ground-truth latents.

Multi-View Causal Representation Learning with Partial Observability

We present a unified framework for studying the identifiability of representations learned from simultaneously observed views, such as different data modalities. We allow a partially observed setting in which each view constitutes a nonlinear mixture of a subset of underlying latent variables, which can be causally related. We prove that the information shared across all subsets of any number of views can be learned up to a smooth bijection using contrastive learning and a single encoder per view. We also provide graphical criteria indicating which latent variables can be identified through a simple set of rules, which we refer to as identifiability algebra. Our general framework and theoretical results unify and extend several previous works on multi-view nonlinear ICA, disentanglement, and causal representation learning. We experimentally validate our claims on numerical, image, and multi-modal data sets. Further, we demonstrate that the performance of prior methods is recovered in different special cases of our setup. Overall, we find that access to multiple partial views enables us to identify a more fine-grained representation, under the generally milder assumption of partial observability.

Learning Dynamic Attribute-factored World Models for Efficient Multi-object Reinforcement Learning

In many reinforcement learning tasks, the agent has to learn to interact with many objects of different types and generalize to unseen combinations and numbers of objects. Often a task is a composition of previously learned tasks (e.g. block stacking). These are examples of compositional generalization, in which we compose object-centric representations to solve complex tasks. Recent works have shown the benefits of object-factored representations and hierarchical abstractions for improving sample efficiency in these settings. On the other hand, these methods do not fully exploit the benefits of factorization in terms of object attributes. In this paper, we address this opportunity and introduce the Dynamic Attribute FacTored RL (DAFT-RL) framework. In DAFT-RL, we leverage object-centric representation learning to extract objects from visual inputs. We learn to classify them in classes and infer their latent parameters. For each class of object, we learn a class template graph that describes how the dynamics and reward of an object of this class factorize according to its attributes. We also learn an interaction pattern graph that describes how objects of different classes interact with each other at the attribute level. Through these graphs and a dynamic interaction graph that models the interactions between objects, we can learn a policy that can then be directly applied in a new environment by just estimating the interactions and latent parameters. We evaluate DAFT-RL in three benchmark datasets and show our framework outperforms the state-of-the-art in generalizing across unseen objects with varying attributes and latent parameters, as well as in the composition of previously learned tasks.

BISCUIT: Causal Representation Learning from Binary Interactions

Identifying the causal variables of an environment and how to intervene on them is of core value in applications such as robotics and embodied AI. While an agent can commonly interact with the environment and may implicitly perturb the behavior of some of these causal variables, often the targets it affects remain unknown. In this paper, we show that causal variables can still be identified for many common setups, e.g., additive Gaussian noise models, if the agent's interactions with a causal variable can be described by an unknown binary variable. This happens when each causal variable has two different mechanisms, e.g., an observational and an interventional one. Using this identifiability result, we propose BISCUIT, a method for simultaneously learning causal variables and their corresponding binary interaction variables. On three robotic-inspired datasets, BISCUIT accurately identifies causal variables and can even be scaled to complex, realistic environments for embodied AI.

Graph Switching Dynamical Systems

Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour into different regimes, or modes, each with simpler dynamics, and then learning the switching behaviour from one mode to another. Switching Dynamical Systems (SDS) are a powerful tool that automatically discovers these modes and mode-switching behaviour from time series data. While effective, these methods focus on independent objects, where the modes of one object are independent of the modes of the other objects. In this paper, we focus on the more general interacting object setting for switching dynamical systems, where the per-object dynamics also depends on an unknown and dynamically changing subset of other objects and their modes. To this end, we propose a novel graph-based approach for switching dynamical systems, GRAph Switching dynamical Systems (GRASS), in which we use a dynamic graph to characterize interactions between objects and learn both intra-object and inter-object mode-switching behaviour. We introduce two new datasets for this setting, a synthesized ODE-driven particles dataset and a real-world Salsa Couple Dancing dataset. Experiments show that GRASS can consistently outperforms previous state-of-the-art methods.

Invariant Neural Ordinary Differential Equations

Latent neural ordinary differential equations have been proven useful for learning non-linear dynamics of arbitrary sequences. In contrast with their mechanistic counterparts, the predictive accuracy of neural ODEs decreases over longer prediction horizons (Rubanova et al., 2019). To mitigate this issue, we propose disentangling dynamic states from time-invariant variables in a completely data-driven way, enabling robust neural ODE models that can generalize across different settings. We show that such variables can control the latent differential function and/or parameterize the mapping from latent variables to observations. By explicitly modeling the time-invariant variables, our framework enables the use of recent advances in representation learning. We demonstrate this by introducing a straightforward self-supervised objective that enhances the learning of these variables. The experiments on low-dimensional oscillating systems and video sequences reveal that our disentangled model achieves improved long-term predictions, when the training data involve sequence-specific factors of variation such as different rotational speeds, calligraphic styles, and friction constants.

iCITRIS: Causal Representation Learning for Instantaneous Temporal Effects

Causal representation learning is the task of identifying the underlying causal variables and their relations from high-dimensional observations, such as images. Recent work has shown that one can reconstruct the causal variables from temporal sequences of observations under the assumption that there are no instantaneous causal relations between them. In practical applications, however, our measurement or frame rate might be slower than many of the causal effects. This effectively creates "instantaneous" effects and invalidates previous identifiability results. To address this issue, we propose iCITRIS, a causal representation learning method that can handle instantaneous effects in temporal sequences when given perfect interventions with known intervention targets. iCITRIS identifies the causal factors from temporal observations, while simultaneously using a differentiable causal discovery method to learn their causal graph. In experiments on three video datasets, iCITRIS accurately identifies the causal factors and their causal graph.

Factored Adaptation for Non-Stationary Reinforcement Learning

Dealing with non-stationarity in environments (i.e., transition dynamics) and objectives (i.e., reward functions) is a challenging problem that is crucial in real-world applications of reinforcement learning (RL). Most existing approaches only focus on families of stationary MDPs, in which the non-stationarity is episodic, i.e., the change is only possible across episodes. The few works that do consider non-stationarity without a specific boundary, i.e., also allow for changes within an episode, model the changes monolithically in a single shared embedding vector. In this paper, we propose Factored Adaptation for Non-Stationary RL (FANS-RL), a factored adaption approach that explicitly learns the individual latent change factors affecting the transition dynamics and reward functions. FANS-RL learns jointly the structure of a factored MDP and a factored representation of the time-varying change factors, as well as the specific state components that they affect, via a factored non-stationary variational autoencoder. Through this general framework, we can consider general non-stationary scenarios with different changing function types and changing frequency. Experimental results demonstrate that FANS-RL outperforms existing approaches in terms of rewards, compactness of the latent state representation and robustness to varying degrees of non-stationarity.

CITRIS: Causal Identifiability from Temporal Intervened Sequences

Understanding the latent causal factors of a dynamical system from visual observations is a crucial step towards agents reasoning in complex environments. In this paper, we propose CITRIS, a variational autoencoder framework that learns causal representations from temporal sequences of images in which underlying causal factors have possibly been intervened upon. In contrast to the recent literature, CITRIS exploits temporality and observing intervention targets to identify scalar and multidimensional causal factors, such as 3D rotation angles. Furthermore, by introducing a normalizing flow, CITRIS can be easily extended to leverage and disentangle representations obtained by already pretrained autoencoders. Extending previous results on scalar causal factors, we prove identifiability in a more general setting, in which only some components of a causal factor are affected by interventions. In experiments on 3D rendered image sequences, CITRIS outperforms previous methods on recovering the underlying causal variables. Moreover, using pretrained autoencoders, CITRIS can even generalize to unseen instantiations of causal factors, opening future research areas in sim-to-real generalization for causal representation learning.