Disentangled Representation Learning

Self-supervised learning (SSL) and diffusion models have respectively advanced representation learning and generative modeling for high-dimensional 3D visual data, yet they are often developed as separate paradigms. Their unification remains challenging under multi-source heterogeneity, as anatomical content must be preserved for analysis while acquisition-related style varies across centers and affects synthesis. In this paper, we propose MeDUET, a 3D Medical image Disentangled UnifiEd PreTraining framework in the variational autoencoder latent space. MeDUET formulates unified pretraining as an empirical factor identifiability problem, aiming to learn domain-invariant content factors for anatomy and domain-specific style factors for appearance. To improve factor separation, MeDUET first uses token demixing with a standard adversarial domain regularizer to establish basic content-style specialization, and further introduces Mixed Factor Token Distillation and Swap-invariance Quadruplet Contrast to reduce mixed-region factor leakage and organize factor spaces with factor-wise invariance and discriminability. With these learned factors, MeDUET transfers effectively to both synthesis and analysis, yielding higher fidelity, faster convergence, and better controllability for synthesis, while achieving competitive or superior domain generalization and label efficiency on diverse datasets, tasks, and modalities. Overall, MeDUET shows that multi-source heterogeneity can serve as useful supervision, with disentanglement providing an effective interface for unifying 3D medical image synthesis and analysis. Our code is available at https://github.com/JK-Liu7/MeDUET.

Humans can infer material characteristics of objects from their visual appearance, and this ability extends to artistic depictions, where similar perceptual strategies guide the interpretation of paintings or drawings. Among the factors that define material appearance, gloss, along with color, is widely regarded as one of the most important, and recent studies indicate that humans can perceive gloss independently of the artistic style used to depict an object. To investigate how gloss and artistic style are represented in learned models, we train an unsupervised generative model on a newly curated dataset of painterly objects designed to systematically vary such factors. Our analysis reveals a hierarchical latent space in which gloss is disentangled from other appearance factors, allowing for a detailed study of how gloss is represented and varies across artistic styles. Building on this representation, we introduce a lightweight adapter that connects our style- and gloss-aware latent space to a latent-diffusion model, enabling the synthesis of non-photorealistic images with fine-grained control of these factors. We compare our approach with previous models and observe improved disentanglement and controllability of the learned factors.

Although deep learning models in medical imaging often achieve excellent classification performance, they can rely on shortcut learning, exploiting spurious correlations or confounding factors that are not causally related to the target task. This poses risks in clinical settings, where models must generalize across institutions, populations, and acquisition conditions. Feature disentanglement is a promising approach to mitigate shortcut learning by separating task-relevant information from confounder-related features in latent representations. In this study, we systematically evaluated feature disentanglement methods for mitigating shortcuts in medical imaging, including adversarial learning and latent space splitting based on dependence minimization. We assessed classification performance and disentanglement quality using latent space analyses across one artificial and two medical datasets with natural and synthetic confounders. We also examined robustness under varying levels of confounding and compared computational efficiency across methods. We found that shortcut mitigation methods improved classification performance under strong spurious correlations during training. Latent space analyses revealed differences in representation quality not captured by classification metrics, highlighting the strengths and limitations of each method. Model reliance on shortcuts depended on the degree of confounding in the training data. The best-performing models combine data-centric rebalancing with model-centric disentanglement, achieving stronger and more robust shortcut mitigation than rebalancing alone while maintaining similar computational efficiency. The project code is publicly available at https://github.com/berenslab/medical-shortcut-mitigation.

The unsupervised discovery of features that are both semantically meaningful and stable across runs remains a central challenge in representation learning. We introduce entropy-ordered flows (EOFlows), a normalizing flow (NF) framework that augments standard maximum likelihood training with an orthogonality regularizer on the decoder Jacobian. The regularizer is rooted in Independent Mechanism Analysis and encourages geometric disentanglement, and a stochastic estimator makes it tractable at image scale (CelebA at $D=2352$ and $12288$). Learned features form near-orthogonal curvilinear coordinates and can be ordered by their $\textit{explained (manifold) entropy}$ after training, analogous to the ranking by explained variance in PCA, which turns EOFlows into a non-linear generalization of PCA. EOFlows identify an order of magnitude more stable features than existing methods, and these features emerge in distinguishable categories (global, local, and generic) and support tentative semantic interpretations. The local features have strikingly sparse support in pixel space, although our method never enforces this. Retaining only the most important, i.e. highest entropy, features turns the bijective flow into an autoencoder with adjustable bottleneck, rivaling the rate-distortion performance of dedicated autoencoders.

Conditional representation learning aims to extract criterion-specific features for customized tasks. Recent methods construct conditional subspaces spanned by criterion-specific text bases in the embedding space of vision-language models (VLMs). Image embeddings are then projected onto these subspaces to obtain conditional representations. However, since VLMs are not explicitly trained to disentangle semantics associated with different criteria, the corresponding conditional subspaces remain coupled. This coupling induces semantic leakage during projection, thereby degrading the semantic purity of conditional representations. To suppress semantic leakage, we propose Semantic Purification for Conditional Representation Learning (SP-CRL). Specifically, SP-CRL first decomposes the original text basis and performs curvature-based adaptive truncation on the resulting basis vectors to construct a purer conditional subspace. It then identifies an appropriate noise subspace and projects image embeddings onto its null space to remove irrelevant semantic components. Extensive experiments across customized clustering, customized few-shot classification, and customized retrieval tasks demonstrate that SP-CRL achieves state-of-the-art performance with superior generalization.

A central premise in mechanistic interpretability is that meaningful concepts in language models are represented by linear features in activation space. For such features to support reliable interventions, manipulating one feature should not substantially alter the effects of others. In practice, however, feature entanglement leads to interference such that localized interventions can have unintended downstream effects. Motivated by the Independent Causal Mechanisms principle, we propose to constrain internal features to be almost orthogonal. We argue that this promotes modular representations amenable to causal intervention. We formalize this problem by characterizing the gap between an idealized isolated intervention and its realized effect on model outputs in terms of feature interference. We upper-bound the propagation of feature interference in terms of the self-coherence of the feature dictionary, and relate this discrepancy to an explicit orthogonality regularization on the dictionary itself. Empirically, we show that this regularization enables more isolated interventions on mathematical reasoning concepts while preserving model performance. Our code is available under https://github.com/mrtzmllr/sae-icm.

Most LLM unlearning methods aim to approximate retrain-from-scratch behaviors with minimal distribution shift, often via alignment-style objectives defined in the prediction space. While effective at reducing forgotten content generation, such approaches may act as suppression: forgotten concepts can persist in representations and remain entangled with retained knowledge. We introduce CLReg, a contrastive representation regularizer that identifies forget features while pushing them away from retain features, reducing forget--retain interference while empirically preserving the scale and shape of retain features. As light motivation for the mechanism, we provide a one-step analysis showing that CLReg decreases a simple entanglement proxy in the embedding space. Across unlearning benchmarks and LLMs of different sizes, CLReg decreases forget-retain representation entanglement to enhance mainstream unlearning methods without extra privacy risks, inspiring future unlearning work to remove forget concepts via representation shaping. Code is available at https://github.com/HaoranTang/CLReg.

Disentangled representation learning aims to map independent factors of variation to independent representation components. On one hand, purely unsupervised approaches have proven successful on fully disentangled synthetic data, but fail to recover semantic factors from real data without strong inductive biases. On the other hand, supervised approaches are unstable and hard to scale to large attribute sets because they rely on adversarial objectives or auxiliary classifiers. We introduce XFactors, a weakly-supervised VAE framework that disentangles and provides explicit control over a chosen set of factors. Building on the Disentangled Information Bottleneck perspective, we decompose the representation into a residual subspace $\mathcal{S}$ and factor-specific subspaces $\mathcal{T}_1,\ldots,\mathcal{T}_K$ and a residual subspace $\mathcal{S}$. Each target factor is encoded in its assigned $\mathcal{T}_i$ through contrastive supervision: an InfoNCE loss pulls together latents sharing the same factor value and pushes apart mismatched pairs. In parallel, KL regularization imposes a Gaussian structure on both $\mathcal{S}$ and the aggregated factor subspaces, organizing the geometry without additional supervision for non-targeted factors and avoiding adversarial training and classifiers. Across multiple datasets, with constant hyperparameters, XFactors achieves state-of-the-art disentanglement scores and yields consistent qualitative factor alignment in the corresponding subspaces, enabling controlled factor swapping via latent replacement. We further demonstrate that our method scales correctly with increasing latent capacity and evaluate it on the real-world dataset CelebA. Our code is available at github.com/ICML26-anon/XFactors.

Time series forecasting has witnessed significant progress with deep learning. While prevailing approaches enhance forecasting performance by modifying architectures or introducing novel enhancement strategies, they often fail to dynamically disentangle and leverage the complex, intertwined temporal patterns inherent in time series, thus resulting in the learning of static, averaged representations that lack context-aware capabilities. To address this, we propose the Dual-Prototype Adaptive Disentanglement framework (DPAD), a model-agnostic auxiliary method that equips forecasting models with the ability of pattern disentanglement and context-aware adaptation. Specifically, we construct a Dynamic Dual-Prototype bank (DDP), comprising a common pattern bank with strong temporal priors to capture prevailing trend or seasonal patterns, and a rare pattern bank dynamically memorizing critical yet infrequent events, and then an Dual-Path Context-aware routing (DPC) mechanism is proposed to enhance outputs with selectively retrieved context-specific pattern representations from the DDP. Additionally, we introduce a Disentanglement-Guided Loss (DGLoss) to ensure that each prototype bank specializes in its designated role while maintaining comprehensive coverage. Comprehensive experiments demonstrate that DPAD consistently improves forecasting performance and reliability of state-of-the-art models across diverse real-world benchmarks.

Reference-guided instance editing is fundamentally limited by semantic entanglement, where a reference's intrinsic appearance is intertwined with its extrinsic attributes. The key challenge lies in disentangling what information should be borrowed from the reference, and determining how to apply it appropriately to the target. To tackle this challenge, we propose GENIE, a Generalizable Instance Editing framework capable of achieving explicit disentanglement. GENIE first corrects spatial misalignments with a Spatial Alignment Module (SAM). Then, an Adaptive Residual Scaling Module (ARSM) learns what to borrow by amplifying salient intrinsic cues while suppressing extrinsic attributes, while a Progressive Attention Fusion (PAF) mechanism learns how to render this appearance onto the target, preserving its structure. Extensive experiments on the challenging AnyInsertion dataset demonstrate that GENIE achieves state-of-the-art fidelity and robustness, setting a new standard for disentanglement-based instance editing.

Large Language Models (LLMs) encode factual knowledge within hidden parametric spaces that are difficult to inspect or control. While Sparse Autoencoders (SAEs) can decompose hidden activations into more fine-grained, interpretable features, they often struggle to reliably align these features with human-defined concepts, resulting in entangled and distributed feature representations. To address this, we introduce AlignSAE, a method that aligns SAE features with a predefined ontology through a "pre-train, then post-train" curriculum. After an initial unsupervised training phase, we apply supervised post-training to bind specific concepts to dedicated latent slots while preserving the remaining capacity for general reconstruction. This separation creates an interpretable interface where specific concepts can be inspected and controlled without interference from unrelated features. Empirical results on GPT-2 across synthetic biographical QA (1-hop, 6 concepts) and compositional relational reasoning (2-hop, 20 concepts) demonstrate that AlignSAE enables precise causal interventions, such as reliable concept swaps (94.8% success in 1-hop), by targeting single, semantically aligned slots. AlignSAE achieves disentanglement improvements of $9$--$\infty\times$ over standard SAEs (measured via Mutual Information Gap), and further supports multi-hop reasoning and a mechanistic probe of grokking-like generalization dynamics. Although our evaluation focuses on GPT-2, AlignSAE itself is model-agnostic.

We study the problem of learning disentangled signals from data using non-linear Independent Component Analysis (ICA). Motivated by advances in self-supervised learning, we propose to learn self-sufficient signals: Given the remaining values of a recovered signal, observing other signals should not change the conditional distribution of its missing value. We formulate this problem as the minimization of a conditional KL divergence. Our algorithm is prior-free and likelihood-free in the sense that it prescribes neither parametric source densities nor an observation likelihood. To tackle the KL divergence minimization problem, we propose a sequential algorithm that learns a de-mixing flow model at each iteration, and prove local descent of the total correlation for its idealized Wasserstein-gradient-flow variant with exact velocities and a population projection condition. This approach completely avoids the unstable adversarial training, a common issue in minimizing the KL divergence. Experiments on toy and real-world datasets show the effectiveness of our method.

Natural Language Explanations (NLEs) describe how Large Language Models (LLMs) make decisions by drawing on external Context Knowledge (CK) and Parametric Knowledge (PK). Understanding the interaction between these sources is key to assessing NLE grounding, yet these dynamics remain underexplored. Prior work has largely focused on i) single-step generation and ii) modeled PK--CK interaction as a binary choice within a rank-1 subspace. This approach overlooks richer interactions and how they unfold over longer generations, such as complementary or supportive knowledge. We propose a novel rank-2 projection subspace that disentangles PK and CK contributions more accurately and use it for the first multi-step analysis of knowledge interactions across longer NLE sequences. Experiments across four QA datasets and three open-weight LLMs demonstrate that rank-1 subspaces struggle to represent diverse interactions, whereas our rank-2 formulation captures them effectively, highlighting PK alignment for supportive interactions and CK alignment for conflicting ones. Our multi-step analysis reveals that hallucinated generations exhibit strong alignment with the PK direction, though context-faithful generations maintain a more balanced alignment between PK and CK.

Learning disentangled representations, where semantic features are independently captured in a latent space, is dominated by Variational Auto Encoders (VAE) and Adversarial Training. In this paper, we provide direct quantitative and visual evidence that these methods consistently fail to enforce the target factorized representation on the aggregate posterior, leading to entangled representations. We quantify this failure using the Latent Predictability Score (LPS), an unsupervised metric of mutual predictability that empirically lower bounds the level of entanglement in a latent space. To address these limitations, we leverage the non-parametric Maximum Mean Discrepancy (MMD) to directly sculpt the aggregate posterior enabling programmable priors. We demonstrate (1) state-of-the-art unsupervised statistical independence, with a 70% reduction in detected entanglement compared to leading baselines; (2) the flexibility to optionally inject semi-supervised information for explicit semantic alignment; and (3) precise shaping of the aggregate posterior distribution (validated through quantization-aware training) without sacrificing reconstruction quality.

Vision-language models (VLMs) have advanced multimodal perception, demonstrated by open-vocabulary object detection with simple language queries. State-of-the-art VLMs still struggle to handle complex queries involving descriptive attributes and relational clauses. To address this problem, we propose restructuring linguistic representations according to the hierarchical relations within sentences for language-based object detection. A key insight is that textual tokens should be disentangled into core components-objects, attributes, and relations-and aggregated into hierarchically structured sentence-level representations. Building on this principle, we introduce the TaSe (Talk in Pieces, See in Whole) framework with three main contributions: (1) a hierarchical synthetic captioning dataset spanning three tiers from category names to descriptive sentences; (2) the three-component disentanglement module guided by a novel disentanglement loss function, transforms text embeddings into subspace compositions; and (3) aggregating disentangled components into hierarchically structured embeddings guided by the proposed hierarchical objectives. Experimental results under the OmniLabel benchmark show a 24% performance improvement, demonstrating the importance of linguistic compositionality.

Pretrained vision models encode semantic information in latent embedding spaces that are useful for downstream tasks. We hypothesize that this information can be disentangled to separate the content of complex scenes by decomposing each embedding into multiple concept-specific components. We propose Sparse Linear Concept Cones (SLiCC), a supervised dictionary learning approach that estimates a linear synthesis model consisting of sparse, non-negative combinations of groups of dictionary atoms, whose group-wise activity is guided by multi-label information. Each concept-specific component is a non-negative combination of atoms associated with a label and lies in a corresponding concept cone. We introduce an alternating optimization algorithm and an autoencoder formulation of SLiCC. We apply SLiCC to three types of CLIP and DINOv2 embeddings across five datasets. For CLIP, we additionally exploit image-text alignment to enable a self-supervised SLiCC. We also introduce a fully unsupervised autoencoder that enforces group sparsity based on the norm of neuron activations. Quantitative results show that supervised SLiCC improves concept-filtered image retrieval over unfiltered embeddings, including retrieval of finer-grained information not provided during training. Beyond retrieval of individual concepts, the disentangled components enable concept deletion and recombination across images. We further explore conditional image generation using Image-to-Prompt, with qualitative results illustrating retrieval and generation from manipulated concept representations.

Disentangled representations separate factors that are shared across conditions from those that are condition-specific. Such separation is needed for generalization to new domains, treatments, patients, or species. A dominant line of work pursues this goal through variational formulations. While these approaches achieve partial disentanglement, they often exhibit three common limitations: they either do not remove all condition-specific information from the condition-specific representation, allow the condition-specific representation to become uninformative, or impose independence assumptions that do not reflect the underlying generative process. In this work, we introduce DisCoVR, a variational framework that addresses these limitations. Its objective is aligned with the probabilistic structure of the data-generating process, and includes an adversarial term that prevents condition-specific information from being encoded in the condition-specific representation.DisCoVR reconstructs the data from both shared and condition-specific representations, ensuring that each remains informative, and uses a structured prior that further reinforces the informativeness of both representations. We show that across synthetic, image, and single-cell RNA-sequencing datasets, DisCoVR achieves stronger disentanglement compared to previous approaches.

In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency. While geometric deep learning has made empirical advances by incorporating symmetry and geometry priors, less attention has been given to statistical learning guarantees. In this paper, we introduce an equivariant representation learning framework that simultaneously addresses regression, conditional probability estimation, and uncertainty quantification while providing first-of-its-kind non-asymptotic statistical learning guarantees. Grounded in operator and group representation theory, our framework approximates the spectral decomposition of the conditional expectation operator, building representations that are both equivariant and disentangled along independent symmetry quotient groups. Empirical evaluations on synthetic datasets and real-world robotics applications confirm the potential of our approach, matching or outperforming existing equivariant baselines in regression while providing well-calibrated uncertainty estimates.

We introduce Color Disentangled Style Transfer (CDST), a novel and efficient two-stream style transfer training paradigm which completely isolates color from style and forces the style stream to be color-blinded. With one same model, CDST unlocks universal style transfer capabilities in a tuning-free manner during inference. Especially, the characteristics-preserved style transfer with style and content references is solved in the tuning-free way for the first time. CDST significantly improves the style similarity by multi-feature image embeddings compression and preserves strong editing capability via our new CDST style definition inspired by Diffusion UNet disentanglement law. By conducting thorough qualitative and quantitative experiments and human evaluations, we demonstrate that CDST achieves state-of-the-art results on various style transfer tasks.

Meta-learning represents a strong class of approaches for solving few-shot learning tasks. Nonetheless, recent research suggests that simply pre-training a generic encoder can potentially surpass meta-learning algorithms. In this paper, we first discuss the reasons why meta-learning fails to stand out in these few-shot learning experiments, and hypothesize that it is due to the few-shot learning tasks lacking diversity. We propose DRESS, a task-agnostic Disentangled REpresentation-based Self-Supervised meta-learning approach that enables fast model adaptation on highly diversified few-shot learning tasks. Specifically, DRESS utilizes disentangled representation learning to create self-supervised tasks that can fuel the meta-training process. Furthermore, we also propose a class-partition based metric for quantifying the task diversity directly on the input space. We validate the effectiveness of DRESS through experiments on datasets with multiple factors of variation and varying complexity. The results suggest that DRESS is able to outperform competing methods on the majority of the datasets and task setups. Through this paper, we advocate for a re-examination of proper setups for task adaptation studies, and aim to reignite interest in the potential of meta-learning for solving few-shot learning tasks via disentangled representations.

Pre-trained speech models build entangled internal representations, which capture a variety of features (e.g., pitch, loudness, syntax, or semantics of an utterance) in a distributed encoding. This entanglement makes it difficult to track how such representations rely on textual versus acoustic information when used in downstream applications, limiting their interpretability and transparency. In this paper, we explore an approach to post-hoc disentanglement that builds on the Information Bottleneck principle. We take representations from pre-trained speech encoders as input, and separate them into two distinct components in a cascaded fashion: first we learn a vector encoding content (i.e., what can be transcribed as text), and nothing else; second, we learn a vector encoding all complementary acoustic features relevant to a target task. We apply and evaluate our proposed setup to emotion recognition and speaker identification target tasks, quantifying the relative contribution of textual and acoustic features at each model layer. Finally, we use the approach for disentangled feature attribution as it allows us to identify the most salient speech frames from both the textual and acoustic perspectives.

Factor analysis, often regarded as a Bayesian variant of matrix factorization, offers superior capabilities in capturing uncertainty, modeling complex dependencies, and ensuring robustness. As the deep learning era arrives, factor analysis is receiving less and less attention due to their limited expressive ability. On the contrary, contrastive learning has emerged as a potent technique with demonstrated efficacy in unsupervised representational learning. While the two methods are different paradigms, recent theoretical analysis has revealed the mathematical equivalence between contrastive learning and matrix factorization, providing a potential possibility for factor analysis combined with contrastive learning. Motivated by the interconnectedness of contrastive learning, matrix factorization, and factor analysis, this paper introduces a novel Contrastive Factor Analysis framework, aiming to leverage factor analysis's advantageous properties within the realm of contrastive learning. To further leverage the interpretability properties of non-negative factor analysis, which can learn disentangled representations, contrastive factor analysis is extended to a non-negative version. Finally, extensive experimental validation showcases the efficacy of the proposed contrastive (non-negative) factor analysis methodology across multiple key properties, including expressiveness, robustness, interpretability, and accurate uncertainty estimation.

While diffusion models excel at generating high-quality samples, their latent variables typically lack semantic meaning and are not suitable for representation learning. Here, we propose InfoDiffusion, an algorithm that augments diffusion models with low-dimensional latent variables that capture high-level factors of variation in the data. InfoDiffusion relies on a learning objective regularized with the mutual information between observed and hidden variables, which is designed to improve latent space quality and to prevent the latents from being ignored by expressive diffusion-based decoders. Empirically, we find that InfoDiffusion learns disentangled and human-interpretable latent representations that are competitive with state-of-the-art generative and contrastive methods, while retaining the high sample quality of diffusion models. Our method enables manipulating the attributes of generated images and has the potential to assist tasks that require exploring a learned latent space to generate quality samples, e.g., generative design.

Neurons in the brain are often finely tuned for specific task variables. Moreover, such disentangled representations are highly sought after in machine learning. Here we mathematically prove that simple biological constraints on neurons, namely nonnegativity and energy efficiency in both activity and weights, promote such sought after disentangled representations by enforcing neurons to become selective for single factors of task variation. We demonstrate these constraints lead to disentanglement in a variety of tasks and architectures, including variational autoencoders. We also use this theory to explain why the brain partitions its cells into distinct cell types such as grid and object-vector cells, and also explain when the brain instead entangles representations in response to entangled task factors. Overall, this work provides a mathematical understanding of why single neurons in the brain often represent single human-interpretable factors, and steps towards an understanding task structure shapes the structure of brain representation.