# BISCUIT: Causal Representation Learning from Binary Interactions

arXiv: https://arxiv.org/abs/2306.09643 · HTML: https://mlsanity.com/paper/2306.09643/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 58 references that are in the map.
- First posted on arXiv 16 Jun 2023.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [AI2-THOR: An Interactive 3D Environment for Visual AI](https://mlsanity.com/paper/1712.05474/) (2017)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [Weakly supervised causal representation learning](https://mlsanity.com/paper/2203.16437/) (2022)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [State Representation Learning for Control: An Overview](https://mlsanity.com/paper/1802.04181/) (2018)
- [Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Coding](https://mlsanity.com/paper/2007.10930/) (2020)
- [CausalWorld: A Robotic Manipulation Benchmark for Causal Structure and Transfer Learning](https://mlsanity.com/paper/2010.04296/) (2020)
- [ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA](https://mlsanity.com/paper/2002.11537/) (2020)
- [Learning Temporally Causal Latent Processes from General Temporal Data](https://mlsanity.com/paper/2110.05428/) (2021)
- [Independent mechanism analysis, a new concept?](https://mlsanity.com/paper/2106.05200/) (2021)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [Permutation-Based Causal Structure Learning with Unknown Intervention Targets](https://mlsanity.com/paper/1910.09007/) (2019)
- [Weakly Supervised Representation Learning with Sparse Perturbations](https://mlsanity.com/paper/2206.01101/) (2022)
- [Temporally Disentangled Representation Learning](https://mlsanity.com/paper/2210.13647/) (2022)

## Built on by (most cited first, 30 of 38)

- [BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcuts](https://mlsanity.com/paper/2402.12240/) (2024)
- [A Sparsity Principle for Partially Observable Causal Representation Learning](https://mlsanity.com/paper/2403.08335/) (2024)
- [Unifying Causal Representation Learning with the Invariance Principle](https://mlsanity.com/paper/2409.02772/) (2024)
- [Learning Interpretable Concepts: Unifying Causal Representation Learning and Foundation Models](https://mlsanity.com/paper/2402.09236/) (2024)
- [From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modeling](https://mlsanity.com/paper/2310.11011/) (2023)
- [Object-centric architectures enable efficient causal representation learning](https://mlsanity.com/paper/2310.19054/) (2023)
- [Identifying Linearly-Mixed Causal Representations from Multi-Node Interventions](https://mlsanity.com/paper/2311.02695/) (2023)
- [Learning Dynamic Attribute-factored World Models for Efficient Multi-object Reinforcement Learning](https://mlsanity.com/paper/2307.09205/) (2023)
- [Learning Causal Representations from General Environments: Identifiability and Intrinsic Ambiguity](https://mlsanity.com/paper/2311.12267/) (2023)
- [Linear Causal Representation Learning from Unknown Multi-node Interventions](https://mlsanity.com/paper/2406.05937/) (2024)
- [Incorporating Hierarchical Semantics in Sparse Autoencoder Architectures](https://mlsanity.com/paper/2506.01197/) (2025)
- [Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lens](https://mlsanity.com/paper/2502.11245/) (2025)
- [Towards Interpretable Deep Generative Models via Causal Representation Learning](https://mlsanity.com/paper/2504.11609/) (2025)
- [Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment](https://mlsanity.com/paper/2406.13371/) (2024)
- [Deep Backtracking Counterfactuals for Causally Compliant Explanations](https://mlsanity.com/paper/2310.07665/) (2023)
- [Language Agents Meet Causality -- Bridging LLMs and Causal World Models](https://mlsanity.com/paper/2410.19923/) (2024)
- [Position: An Empirically Grounded Identifiability Theory Will Accelerate Self-Supervised Learning Research](https://mlsanity.com/paper/2504.13101/) (2025)
- [From Isolation to Entanglement: When Do Interpretability Methods Identify and Disentangle Known Concepts?](https://mlsanity.com/paper/2512.15134/) (2025)
- [Null Counterfactual Factor Interactions for Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2505.03172/) (2025)
- [Invariance & Causal Representation Learning: Prospects and Limitations](https://mlsanity.com/paper/2312.03580/) (2023)
- [Towards the Reusability and Compositionality of Causal Representations](https://mlsanity.com/paper/2403.09830/) (2024)
- [Sanity Checking Causal Representation Learning on a Simple Real-World System](https://mlsanity.com/paper/2502.20099/) (2025)
- [CausalPlayground: Addressing Data-Generation Requirements in Cutting-Edge Causality Research](https://mlsanity.com/paper/2405.13092/) (2024)
- [The Causal Information Bottleneck and Optimal Causal Variable Abstractions](https://mlsanity.com/paper/2410.00535/) (2024)
- [Curious Causality-Seeking Agents Learn Meta Causal World](https://mlsanity.com/paper/2506.23068/) (2025)
- [Structural Causal Bottleneck Models](https://mlsanity.com/paper/2603.08682/) (2026)
- [CAnDOIT: Causal Discovery with Observational and Interventional Data from Time-Series](https://mlsanity.com/paper/2410.02844/) (2024)
- [From Pixels to Factors: Learning Independently Controllable State Variables for Reinforcement Learning](https://mlsanity.com/paper/2510.02484/) (2025)
- [Self-Supervised Learning from Structural Invariance](https://mlsanity.com/paper/2602.02381/) (2026)
- [Beyond identifiability: Learning causal representations with few environments and finite samples](https://mlsanity.com/paper/2603.25796/) (2026)

## Abstract (arXiv)

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.