arXiv subjects

Sébastien Lachapelle

Publications and source records attributed to Sébastien Lachapelle.

At least 19 recordsLinked to original sources

arXiv2026

Nonparametric Partial Disentanglement via Mechanism Sparsity: Sparse Actions, Interventions and Sparse Temporal Dependencies

This work introduces a novel principle for disentanglement we call mechanism sparsity regularization, which applies when the latent factors of interest depend sparsely on observed auxiliary variables and/or past latent factors. We propose a representation learning method that induces disentanglement by simultaneously learning the latent factors and the sparse causal graphical model that explains them. We develop a nonparametric identifiability theory that formalizes this principle and shows that the latent factors can be recovered by regularizing the learned causal graph to be sparse, under some assumptions such as the absence of instantaneous causal effects between latent factors. More precisely, we show identifiability up to a novel equivalence relation we call consistency, which allows some latent factors to remain entangled (hence the term partial disentanglement). To describe the structure of this entanglement, we introduce the notions of entanglement graphs and graph preserving functions. We further provide a graphical criterion which guarantees complete disentanglement, that is identifiability up to permutations and element-wise transformations. We demonstrate the scope of the mechanism sparsity principle as well as the assumptions it relies on with several worked out examples. For instance, the framework shows how one can leverage multi-node interventions with unknown targets on the latent factors to disentangle them. We further draw connections between our nonparametric results and the now popular exponential family assumption. Lastly, we propose an estimation procedure based on variational autoencoders and a sparsity constraint and demonstrate it on various synthetic datasets. This work is meant to be a significantly extended version of a work published at CLeaR 2022.

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arXiv2026

On the Sample Efficiency of Inverse Dynamics Models for Semi-Supervised Imitation Learning

Semi-supervised imitation learning (SSIL) consists in learning a policy from a small dataset of action-labeled trajectories and a much larger dataset of action-free trajectories. Some SSIL methods learn an inverse dynamics model (IDM) to predict the action from the current state and the next state. An IDM can act as a policy when paired with a video model (VM-IDM) or as a label generator to perform behavior cloning on action-free data (IDM labeling). In this work, we first show that VM-IDM and IDM labeling learn the same policy in a limit case, which we call the IDM-based policy. We then argue that the previously observed advantage of IDM-based policies over behavior cloning is due to the superior sample efficiency of IDM learning, which we attribute to two causes: (i) the ground-truth IDM tends to be contained in a lower complexity hypothesis class relative to the expert policy, and (ii) the ground-truth IDM is often less stochastic than the expert policy. We argue these claims based on insights from statistical learning theory and novel experiments, including a study of IDM-based policies using recent architectures for unified video-action prediction (UVA). Motivated by these insights, we finally propose an improved version of the existing LAPO algorithm for latent action policy learning. We experiment on the Procgen, Push-T and LIBERO benchmarks.

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arXiv2026

Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixing

Causal representation learning (CRL) aims to identify the underlying latent variables from high-dimensional observations, even when variables are dependent with each other. We study this problem for latent variables that follow a potentially degenerate Gaussian mixture distribution and that are only observed through the transformation via a piecewise affine mixing function. We provide a series of progressively stronger identifiability results for this challenging setting in which the probability density functions are ill-defined because of the potential degeneracy. For identifiability up to permutation and scaling, we leverage a sparsity regularization on the learned representation. Based on our theoretical results, we propose a two-stage method to estimate the latent variables by enforcing sparsity and Gaussianity in the learned representations. Experiments on synthetic and image data highlight our method's effectiveness in recovering the ground-truth latent variables.

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arXiv2026

Sparse Shift Autoencoders for Identifying Concepts from Large Language Model Activations

Unsupervised approaches to large language model (LLM) interpretability, such as sparse autoencoders (SAEs), offer a way to decode LLM activations into interpretable and, ideally, controllable concepts. On the one hand, these approaches alleviate the need for supervision from concept labels, paired prompts, or explicit causal models. On the other hand, without additional assumptions, SAEs are not guaranteed to be identifiable. In practice, they may learn latent dimensions that entangle multiple underlying concepts. If we use these dimensions to extract vectors for steering specific LLM behaviours, this non-identifiability might result in interventions that inadvertently affect unrelated properties. In this paper, we bring the question of identifiability to the forefront of LLM interpretability research. Specifically, we introduce Sparse Shift Autoencoders (SSAEs) which learn sparse representations of differences between embeddings rather than the embeddings themselves. Crucially, we show that SSAEs are identifiable from paired observations which differ in multiple unknown concepts, but not all. With this key identifiability result, we show that we can steer single concepts with only this weak form of supervision. Finally, we empirically demonstrate identifiable concept recovery across multiple real-world language datasets by disentangling activations from different LLMs.

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arXiv2025

On the Identifiability of Latent Action Policies

We study the identifiability of latent action policy learning (LAPO), a framework introduced recently to discover representations of actions from video data. We formally describe desiderata for such representations, their statistical benefits and potential sources of unidentifiability. Finally, we prove that an entropy-regularized LAPO objective identifies action representations satisfying our desiderata, under suitable conditions. Our analysis provides an explanation for why discrete action representations perform well in practice.

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arXiv2025

All or None: Identifiable Linear Properties of Next-token Predictors in Language Modeling

We analyze identifiability as a possible explanation for the ubiquity of linear properties across language models, such as the vector difference between the representations of "easy" and "easiest" being parallel to that between "lucky" and "luckiest". For this, we ask whether finding a linear property in one model implies that any model that induces the same distribution has that property, too. To answer that, we first prove an identifiability result to characterize distribution-equivalent next-token predictors, lifting a diversity requirement of previous results. Second, based on a refinement of relational linearity [Paccanaro and Hinton, 2001; Hernandez et al., 2024], we show how many notions of linearity are amenable to our analysis. Finally, we show that under suitable conditions, these linear properties either hold in all or none distribution-equivalent next-token predictors.

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arXiv2024

Interaction Asymmetry: A General Principle for Learning Composable Abstractions

Learning disentangled representations of concepts and re-composing them in unseen ways is crucial for generalizing to out-of-domain situations. However, the underlying properties of concepts that enable such disentanglement and compositional generalization remain poorly understood. In this work, we propose the principle of interaction asymmetry which states: "Parts of the same concept have more complex interactions than parts of different concepts". We formalize this via block diagonality conditions on the $(n+1)$th order derivatives of the generator mapping concepts to observed data, where different orders of "complexity" correspond to different $n$. Using this formalism, we prove that interaction asymmetry enables both disentanglement and compositional generalization. Our results unify recent theoretical results for learning concepts of objects, which we show are recovered as special cases with $n\!=\!0$ or $1$. We provide results for up to $n\!=\!2$, thus extending these prior works to more flexible generator functions, and conjecture that the same proof strategies generalize to larger $n$. Practically, our theory suggests that, to disentangle concepts, an autoencoder should penalize its latent capacity and the interactions between concepts during decoding. We propose an implementation of these criteria using a flexible Transformer-based VAE, with a novel regularizer on the attention weights of the decoder. On synthetic image datasets consisting of objects, we provide evidence that this model can achieve comparable object disentanglement to existing models that use more explicit object-centric priors.

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arXiv2024

Causal Representation Learning in Temporal Data via Single-Parent Decoding

Scientific research often seeks to understand the causal structure underlying high-level variables in a system. For example, climate scientists study how phenomena, such as El Niño, affect other climate processes at remote locations across the globe. However, scientists typically collect low-level measurements, such as geographically distributed temperature readings. From these, one needs to learn both a mapping to causally-relevant latent variables, such as a high-level representation of the El Niño phenomenon and other processes, as well as the causal model over them. The challenge is that this task, called causal representation learning, is highly underdetermined from observational data alone, requiring other constraints during learning to resolve the indeterminacies. In this work, we consider a temporal model with a sparsity assumption, namely single-parent decoding: each observed low-level variable is only affected by a single latent variable. Such an assumption is reasonable in many scientific applications that require finding groups of low-level variables, such as extracting regions from geographically gridded measurement data in climate research or capturing brain regions from neural activity data. We demonstrate the identifiability of the resulting model and propose a differentiable method, Causal Discovery with Single-parent Decoding (CDSD), that simultaneously learns the underlying latents and a causal graph over them. We assess the validity of our theoretical results using simulated data and showcase the practical validity of our method in an application to real-world data from the climate science field.

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arXiv2024

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.

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arXiv2024

Sparsity regularization via tree-structured environments for disentangled representations

Many causal systems such as biological processes in cells can only be observed indirectly via measurements, such as gene expression. Causal representation learning -- the task of correctly mapping low-level observations to latent causal variables -- could advance scientific understanding by enabling inference of latent variables such as pathway activation. In this paper, we develop methods for inferring latent variables from multiple related datasets (environments) and tasks. As a running example, we consider the task of predicting a phenotype from gene expression, where we often collect data from multiple cell types or organisms that are related in known ways. The key insight is that the mapping from latent variables driven by gene expression to the phenotype of interest changes sparsely across closely related environments. To model sparse changes, we introduce Tree-Based Regularization (TBR), an objective that minimizes both prediction error and regularizes closely related environments to learn similar predictors. We prove that under assumptions about the degree of sparse changes, TBR identifies the true latent variables up to some simple transformations. We evaluate the theory empirically with both simulations and ground-truth gene expression data. We find that TBR recovers the latent causal variables better than related methods across these settings, even under settings that violate some assumptions of the theory.

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arXiv2024

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.

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arXiv2023

Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolation

We tackle the problems of latent variables identification and ``out-of-support'' image generation in representation learning. We show that both are possible for a class of decoders that we call additive, which are reminiscent of decoders used for object-centric representation learning (OCRL) and well suited for images that can be decomposed as a sum of object-specific images. We provide conditions under which exactly solving the reconstruction problem using an additive decoder is guaranteed to identify the blocks of latent variables up to permutation and block-wise invertible transformations. This guarantee relies only on very weak assumptions about the distribution of the latent factors, which might present statistical dependencies and have an almost arbitrarily shaped support. Our result provides a new setting where nonlinear independent component analysis (ICA) is possible and adds to our theoretical understanding of OCRL methods. We also show theoretically that additive decoders can generate novel images by recombining observed factors of variations in novel ways, an ability we refer to as Cartesian-product extrapolation. We show empirically that additivity is crucial for both identifiability and extrapolation on simulated data.

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arXiv2023

Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learning

Although disentangled representations are often said to be beneficial for downstream tasks, current empirical and theoretical understanding is limited. In this work, we provide evidence that disentangled representations coupled with sparse base-predictors improve generalization. In the context of multi-task learning, we prove a new identifiability result that provides conditions under which maximally sparse base-predictors yield disentangled representations. Motivated by this theoretical result, we propose a practical approach to learn disentangled representations based on a sparsity-promoting bi-level optimization problem. Finally, we explore a meta-learning version of this algorithm based on group Lasso multiclass SVM base-predictors, for which we derive a tractable dual formulation. It obtains competitive results on standard few-shot classification benchmarks, while each task is using only a fraction of the learned representations.

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arXiv2022

Partial Disentanglement via Mechanism Sparsity

Disentanglement via mechanism sparsity was introduced recently as a principled approach to extract latent factors without supervision when the causal graph relating them in time is sparse, and/or when actions are observed and affect them sparsely. However, this theory applies only to ground-truth graphs satisfying a specific criterion. In this work, we introduce a generalization of this theory which applies to any ground-truth graph and specifies qualitatively how disentangled the learned representation is expected to be, via a new equivalence relation over models we call consistency. This equivalence captures which factors are expected to remain entangled and which are not based on the specific form of the ground-truth graph. We call this weaker form of identifiability partial disentanglement. The graphical criterion that allows complete disentanglement, proposed in an earlier work, can be derived as a special case of our theory. Finally, we enforce graph sparsity with constrained optimization and illustrate our theory and algorithm in simulations.

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arXiv2022

On the Convergence of Continuous Constrained Optimization for Structure Learning

Recently, structure learning of directed acyclic graphs (DAGs) has been formulated as a continuous optimization problem by leveraging an algebraic characterization of acyclicity. The constrained problem is solved using the augmented Lagrangian method (ALM) which is often preferred to the quadratic penalty method (QPM) by virtue of its standard convergence result that does not require the penalty coefficient to go to infinity, hence avoiding ill-conditioning. However, the convergence properties of these methods for structure learning, including whether they are guaranteed to return a DAG solution, remain unclear, which might limit their practical applications. In this work, we examine the convergence of ALM and QPM for structure learning in the linear, nonlinear, and confounded cases. We show that the standard convergence result of ALM does not hold in these settings, and demonstrate empirically that its behavior is akin to that of the QPM which is prone to ill-conditioning. We further establish the convergence guarantee of QPM to a DAG solution, under mild conditions. Lastly, we connect our theoretical results with existing approaches to help resolve the convergence issue, and verify our findings in light of an empirical comparison of them.

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arXiv2022

Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA

This work introduces a novel principle we call disentanglement via mechanism sparsity regularization, which can be applied when the latent factors of interest depend sparsely on past latent factors and/or observed auxiliary variables. We propose a representation learning method that induces disentanglement by simultaneously learning the latent factors and the sparse causal graphical model that relates them. We develop a rigorous identifiability theory, building on recent nonlinear independent component analysis (ICA) results, that formalizes this principle and shows how the latent variables can be recovered up to permutation if one regularizes the latent mechanisms to be sparse and if some graph connectivity criterion is satisfied by the data generating process. As a special case of our framework, we show how one can leverage unknown-target interventions on the latent factors to disentangle them, thereby drawing further connections between ICA and causality. We propose a VAE-based method in which the latent mechanisms are learned and regularized via binary masks, and validate our theory by showing it learns disentangled representations in simulations.

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arXiv2021

Predicting Tactical Solutions to Operational Planning Problems under Imperfect Information

This paper offers a methodological contribution at the intersection of machine learning and operations research. Namely, we propose a methodology to quickly predict expected tactical descriptions of operational solutions (TDOSs). The problem we address occurs in the context of two-stage stochastic programming where the second stage is demanding computationally. We aim to predict at a high speed the expected TDOS associated with the second stage problem, conditionally on the first stage variables. This may be used in support of the solution to the overall two-stage problem by avoiding the online generation of multiple second stage scenarios and solutions. We formulate the tactical prediction problem as a stochastic optimal prediction program, whose solution we approximate with supervised machine learning. The training dataset consists of a large number of deterministic operational problems generated by controlled probabilistic sampling. The labels are computed based on solutions to these problems (solved independently and offline), employing appropriate aggregation and subselection methods to address uncertainty. Results on our motivating application on load planning for rail transportation show that deep learning models produce accurate predictions in very short computing time (milliseconds or less). The predictive accuracy is close to the lower bounds calculated based on sample average approximation of the stochastic prediction programs.

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arXiv2020

Differentiable Causal Discovery from Interventional Data

Learning a causal directed acyclic graph from data is a challenging task that involves solving a combinatorial problem for which the solution is not always identifiable. A new line of work reformulates this problem as a continuous constrained optimization one, which is solved via the augmented Lagrangian method. However, most methods based on this idea do not make use of interventional data, which can significantly alleviate identifiability issues. This work constitutes a new step in this direction by proposing a theoretically-grounded method based on neural networks that can leverage interventional data. We illustrate the flexibility of the continuous-constrained framework by taking advantage of expressive neural architectures such as normalizing flows. We show that our approach compares favorably to the state of the art in a variety of settings, including perfect and imperfect interventions for which the targeted nodes may even be unknown.

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