# DCI-ES: An Extended Disentanglement Framework with Connections to Identifiability

arXiv: https://arxiv.org/abs/2210.00364 · HTML: https://mlsanity.com/paper/2210.00364/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 43 references that are in the map.
- First posted on arXiv 1 Oct 2022.

## Builds on (most cited first, 28 of 28)

- [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)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [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)
- [Isolating Sources of Disentanglement in Variational Autoencoders](https://mlsanity.com/paper/1802.04942/) (2018)
- [Deep ReLU Networks Have Surprisingly Few Activation Patterns](https://mlsanity.com/paper/1906.00904/) (2019)
- [Deep Convolutional Inverse Graphics Network](https://mlsanity.com/paper/1503.03167/) (2015)
- [Robustly Disentangled Causal Mechanisms: Validating Deep Representations for Interventional Robustness](https://mlsanity.com/paper/1811.00007/) (2018)
- [Learning Deep Disentangled Embeddings with the F-Statistic Loss](https://mlsanity.com/paper/1802.05312/) (2018)
- [On the Transfer of Inductive Bias from Simulation to the Real World: a New Disentanglement Dataset](https://mlsanity.com/paper/1906.03292/) (2019)
- [Weakly Supervised Disentanglement with Guarantees](https://mlsanity.com/paper/1910.09772/) (2019)
- [In Search of Robust Measures of Generalization](https://mlsanity.com/paper/2010.11924/) (2020)
- [The Shape of Learning Curves: a Review](https://mlsanity.com/paper/2103.10948/) (2021)
- [A Sober Look at the Unsupervised Learning of Disentangled Representations and their Evaluation](https://mlsanity.com/paper/2010.14766/) (2020)
- [Rethinking Parameter Counting in Deep Models: Effective Dimensionality Revisited](https://mlsanity.com/paper/2003.02139/) (2020)
- [Are wider nets better given the same number of parameters?](https://mlsanity.com/paper/2010.14495/) (2020)
- [Evaluating representations by the complexity of learning low-loss predictors](https://mlsanity.com/paper/2009.07368/) (2020)
- [The Role of Pretrained Representations for the OOD Generalization of Reinforcement Learning Agents](https://mlsanity.com/paper/2107.05686/) (2021)

## Built on by (most cited first, 23 of 23)

- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Concept Algebra for (Score-Based) Text-Controlled Generative Models](https://mlsanity.com/paper/2302.03693/) (2023)
- [Disentanglement via Latent Quantization](https://mlsanity.com/paper/2305.18378/) (2023)
- [Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learning](https://mlsanity.com/paper/2309.07742/) (2023)
- [From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modeling](https://mlsanity.com/paper/2310.11011/) (2023)
- [Causal Diffusion Autoencoders: Toward Counterfactual Generation via Diffusion Probabilistic Models](https://mlsanity.com/paper/2404.17735/) (2024)
- [Self-Supervised Disentanglement by Leveraging Structure in Data Augmentations](https://mlsanity.com/paper/2311.08815/) (2023)
- [Learning Causally Disentangled Representations via the Principle of Independent Causal Mechanisms](https://mlsanity.com/paper/2306.01213/) (2023)
- [Exploring the Effectiveness of Object-Centric Representations in Visual Question Answering: Comparative Insights with Foundation Models](https://mlsanity.com/paper/2407.15589/) (2024)
- [Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment](https://mlsanity.com/paper/2406.13371/) (2024)
- [From Isolation to Entanglement: When Do Interpretability Methods Identify and Disentangle Known Concepts?](https://mlsanity.com/paper/2512.15134/) (2025)
- [Representational Similarity via Interpretable Visual Concepts](https://mlsanity.com/paper/2503.15699/) (2025)
- [Disentangling Representations through Multi-task Learning](https://mlsanity.com/paper/2407.11249/) (2024)
- [From Pixels to Factors: Learning Independently Controllable State Variables for Reinforcement Learning](https://mlsanity.com/paper/2510.02484/) (2025)
- [Enriching Disentanglement: From Logical Definitions to Quantitative Metrics](https://mlsanity.com/paper/2305.11512/) (2023)
- [A framework for analyzing concept representations in neural models](https://mlsanity.com/paper/2605.01381/) (2026)
- [Concepts Worth Having: Refining VLM-Guided Concept Bottleneck Models with Minimal Annotations](https://mlsanity.com/paper/2605.16405/) (2026)
- [Measuring Orthogonality in Representations of Generative Models](https://mlsanity.com/paper/2407.03728/) (2024)
- [Disentanglement Analysis in Deep Latent Variable Models Matching Aggregate Posterior Distributions](https://mlsanity.com/paper/2501.15705/) (2025)
- [Selecting Interpretability Techniques for Healthcare Machine Learning models](https://mlsanity.com/paper/2406.10213/) (2024)
- [Operationalizing Quantized Disentanglement](https://mlsanity.com/paper/2511.20927/) (2025)
- [Temporal Fusion Nexus: A task-agnostic multi-modal embedding model for clinical narratives and irregular time series in post-kidney transplant care](https://mlsanity.com/paper/2601.08503/) (2026)
- [Who Guards the Guardians? The Challenges of Evaluating Identifiability of Learned Representations](https://mlsanity.com/paper/2602.24278/) (2026)

## Abstract (arXiv)

In representation learning, a common approach is to seek representations which disentangle the underlying factors of variation. Eastwood & Williams (2018) proposed three metrics for quantifying the quality of such disentangled representations: disentanglement (D), completeness (C) and informativeness (I). In this work, we first connect this DCI framework to two common notions of linear and nonlinear identifiability, thereby establishing a formal link between disentanglement and the closely-related field of independent component analysis. We then propose an extended DCI-ES framework with two new measures of representation quality - explicitness (E) and size (S) - and point out how D and C can be computed for black-box predictors. Our main idea is that the functional capacity required to use a representation is an important but thus-far neglected aspect of representation quality, which we quantify using explicitness or ease-of-use (E). We illustrate the relevance of our extensions on the MPI3D and Cars3D datasets.