On Linear Identifiability of Learned Representations

By Geoffrey Roeder, Luke Metz, Diederik P. Kingma. 2020

115 citations recorded by the source corpus.

Identifiability is a desirable property of a statistical model: it implies that the true model parameters may be estimated to any desired precision, given sufficient computational resources and data. We study identifiability in the context of representation learning: discovering nonlinear data representations that are optimal with respect to some downstream task. When parameterized as deep neural networks, such representation functions typically lack identifiability in parameter space, because they are overparameterized by design. In this paper, building on recent advances in nonlinear ICA, we aim to rehabilitate identifiability by showing that a large family of discriminative models are in fact identifiable in function space, up to a linear indeterminacy. Many models for representation learning in a wide variety of domains have been identifiable in this sense, including text, images and audio, state-of-the-art at time of publication. We derive sufficient conditions for linear identifiability and provide empirical support for the result on both simulated and real-world data.

Subfields: Artificial Intelligence, Representation & Self-Supervised Learning, Signal Processing

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Citations in the corpus

Score-Based Generative Modeling through Stochastic Differential Equations (2020, positive): “Uniquely identifiable encoding Unlike most current invertible models, our encoding is uniquely identifiable, meaning that with sufficient training data, model capacity, and optimization accuracy, the encoding for an input is uniquely determined by the data distribution (Roeder et al., 2020).”
Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA (2021, methodology): “, 2020), in which identifiability has been used as an analysis tool (Roeder et al., 2021; Zimmermann et al., 2021; Von Kügelgen et al., 2021).”
Learning to Learn with Generative Models of Neural Network Checkpoints (2022, methodology): “If we apply some permutation to the outgoing weights (and biases) of the input layer and to the incoming weights of the next layer, the output of the neural network will be preserved (Roeder et al., 2021; Sch¨urholt et al., 2021).”
Contrastive Learning Inverts the Data Generating Process (2021, unknown): “In a similar vein, Roeder et al. (2020) build on the work of Hyvärinen et al. (2019) to show that for a model family which includes InfoNCE, distribution matching implies parameter matching.”
Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style (2021, background): “This development has sparked a renewed interest in identifiability in the context of deep representation learning [63, 64, 69, 83, 102, 108, 109, 129].”
The Platonic Representation Hypothesis (2024, unknown): “Alignment increases with scale and performance Kornblith et al. (2019) and Roeder et al. (2021) observed model alignment not only exists but also increases with model scale and dataset size.”