Multilayer perceptrons (MLPs) are an integral part of large language models, yet their dense representations render them difficult to understand, edit, and steer. Recent methods learn interpretable approximations via neuron-level sparsity, yet fail to faithfully reconstruct the original mapping--significantly increasing model's next-token cross-entropy loss. In this paper, we advocate for moving to layer-level sparsity to overcome the accuracy trade-off in sparse layer approximation. Under this paradigm, we introduce Mixture of Decoders (MxDs). MxDs generalize MLPs and Gated Linear Units, expanding pre-trained dense layers into tens of thousands of specialized sublayers. Through a flexible form of tensor factorization, each sparsely activating MxD sublayer implements a linear transformation with full-rank weights--preserving the original decoders' expressive capacity even under heavy sparsity. Experimentally, we show that MxDs significantly outperform state-of-the-art methods (e.g., Transcoders) on the sparsity-accuracy frontier in language models with up to 3B parameters. Further evaluations on sparse probing and feature steering demonstrate that MxDs learn similarly specialized features of natural language--opening up a promising new avenue for designing interpretable yet faithful decompositions. Our code is included at: https://github.com/james-oldfield/MxD.

The Mixture of Experts (MoE) paradigm provides a powerful way to decompose dense layers into smaller, modular computations often more amenable to human interpretation, debugging, and editability. However, a major challenge lies in the computational cost of scaling the number of experts high enough to achieve fine-grained specialization. In this paper, we propose the Multilinear Mixture of Experts (μMoE) layer to address this, focusing on vision models. μMoE layers enable scalable expert specialization by performing an implicit computation on prohibitively large weight tensors entirely in factorized form. Consequently, μMoEs (1) avoid the restrictively high inference-time costs of dense MoEs, yet (2) do not inherit the training issues of the popular sparse MoEs' discrete (non-differentiable) expert routing. We present both qualitative and quantitative evidence that scaling μMoE layers when fine-tuning foundation models for vision tasks leads to more specialized experts at the class-level, further enabling manual bias correction in CelebA attribute classification. Finally, we show qualitative results demonstrating the expert specialism achieved when pre-training large GPT2 and MLP-Mixer models with parameter-matched μMoE blocks at every layer, maintaining comparable accuracy. Our code is available at: https://github.com/james-oldfield/muMoE.

Recent advances in the understanding of Generative Adversarial Networks (GANs) have led to remarkable progress in visual editing and synthesis tasks, capitalizing on the rich semantics that are embedded in the latent spaces of pre-trained GANs. However, existing methods are often tailored to specific GAN architectures and are limited to either discovering global semantic directions that do not facilitate localized control, or require some form of supervision through manually provided regions or segmentation masks. In this light, we present an architecture-agnostic approach that jointly discovers factors representing spatial parts and their appearances in an entirely unsupervised fashion. These factors are obtained by applying a semi-nonnegative tensor factorization on the feature maps, which in turn enables context-aware local image editing with pixel-level control. In addition, we show that the discovered appearance factors correspond to saliency maps that localize concepts of interest, without using any labels. Experiments on a wide range of GAN architectures and datasets show that, in comparison to the state of the art, our method is far more efficient in terms of training time and, most importantly, provides much more accurate localized control.

Latent image representations arising from vision-language models have proved immensely useful for a variety of downstream tasks. However, their utility is limited by their entanglement with respect to different visual attributes. For instance, recent work has shown that CLIP image representations are often biased toward specific visual properties (such as objects or actions) in an unpredictable manner. In this paper, we propose to separate representations of the different visual modalities in CLIP’s joint vision-language space by leveraging the association between parts of speech and specific visual modes of variation (e.g. nouns relate to objects, adjectives describe appearance). This is achieved by formulating an appropriate component analysis model that learns subspaces capturing variability corresponding to a specific part of speech, while jointly minimising variability to the rest. Such a subspace yields disentangled representations of the different visual properties of an image or text in closed form while respecting the underlying geometry of the manifold on which the representations lie. What’s more, we show the proposed model additionally facilitates learning subspaces corresponding to specific visual appearances (e.g. artists’ painting styles), which enables the selective removal of entire visual themes from CLIP-based text-to-image synthesis. We validate the model both qualitatively, by visualising the subspace projections with a text-to-image model and by preventing the imitation of artists’ styles, and quantitatively, through class invariance metrics and improvements to baseline zero-shot classification.

Generative Adversarial Networks (GANs) are the driving force behind the state-of-the-art in image generation. Despite their ability to synthesize high-resolution photo-realistic images, generating content with on-demand conditioning of different granularity remains a challenge. This challenge is usually tackled by annotating massive datasets with the attributes of interest, a laborious task that is not always a viable option. Therefore, it is vital to introduce control into the generation process of unsupervised generative models. In this work, we focus on controllable image generation by leveraging GANs that are well-trained in an unsupervised fashion. To this end, we discover that the representation space of intermediate layers of the generator forms a number of clusters that separate the data according to semantically meaningful attributes (e.g., hair color and pose). By conditioning on the cluster assignments, the proposed method is able to control the semantic class of the generated image. Our approach enables sampling from each cluster by Implicit Maximum Likelihood Estimation (IMLE). We showcase the efficacy of our approach on faces (CelebA-HQ and FFHQ), animals (Imagenet) and objects (LSUN) using different pre-trained generative models. The results highlight the ability of our approach to condition image generation on attributes like gender, pose and hair style on faces, as well as a variety of features on different object classes.

Recently, a multitude of methods for image-to-image translation have demonstrated impressive results on problems, such as multidomain or multiattribute transfer. The vast majority of such works leverages the strengths of adversarial learning and deep convolutional autoencoders to achieve realistic results by well-capturing the target data distribution. Nevertheless, the most prominent representatives of this class of methods do not facilitate semantic structure in the latent space and usually rely on binary domain labels for test-time transfer. This leads to rigid models, unable to capture the variance of each domain label. In this light, we propose a novel adversarial learning method that: 1) facilitates the emergence of latent structure by semantically disentangling sources of variation and 2) encourages learning generalizable, continuous, and transferable latent codes that enable flexible attribute mixing. This is achieved by introducing a novel loss function that encourages representations to result in uniformly distributed class posteriors for disentangled attributes. In tandem with an algorithm for inducing generalizable properties, the resulting representations can be utilized for a variety of tasks such as intensity-preserving multiattribute image translation and synthesis, without requiring labeled test data. We demonstrate the merits of the proposed method by a set of qualitative and quantitative experiments on popular databases such as MultiPIE, RaFD, and BU-3DFE, where our method outperforms other state-of-the-art methods in tasks such as intensity-preserving multiattribute transfer and synthesis.

Abstract Deep learning has catalysed progress in tasks such as face recognition and analysis, leading to a quick integration of technological solutions in multiple layers of our society. While such systems have proven to be accurate by standard evaluation metrics and benchmarks, a surge of work has recently exposed the demographic bias that such algorithms exhibit–highlighting that accuracy does not entail fairness. Clearly, deploying biased systems under real-world settings can have grave consequences for affected populations. Indeed, learning methods are prone to inheriting, or even amplifying the bias present in a training set, manifested by uneven representation across demographic groups. In facial datasets, this particularly relates to attributes such as skin tone, gender, and age. In this work, we address the problem of mitigating bias in facial datasets by data augmentation. We propose a multi-attribute framework that can successfully transfer complex, multi-scale facial patterns even if these belong to underrepresented groups in the training set. This is achieved by relaxing the rigid dependence on a single attribute label, and further introducing a tensor-based mixing structure that captures multiplicative interactions between attributes in a multilinear fashion. We evaluate our method with an extensive set of qualitative and quantitative experiments on several datasets, with rigorous comparisons to state-of-the-art methods. We find that the proposed framework can successfully mitigate dataset bias, as evinced by extensive evaluations on established diversity metrics, while significantly improving fairness metrics such as equality of opportunity.

Tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions. Inherently able to efficiently capture structured, latent semantic spaces and high-order interactions, tensors have a long history of applications in a wide span of computer vision problems. With the advent of the deep learning paradigm shift in computer vision, tensors have become even more fundamental. Indeed, essential ingredients in modern deep learning architectures, such as convolutions and attention mechanisms, can readily be considered as tensor mappings. In effect, tensor methods are increasingly finding significant applications in deep learning, including the design of memory and compute efficient network architectures, improving robustness to random noise and adversarial attacks, and aiding the theoretical understanding of deep networks. This article provides an in-depth and practical review of tensors and tensor methods in the context of representation learning and deep learning, with a particular focus on visual data analysis and computer vision applications. Concretely, besides fundamental work in tensor-based visual data analysis methods, we focus on recent developments that have brought on a gradual increase in tensor methods, especially in deep learning architectures and their implications in computer vision applications. To further enable the newcomer to grasp such concepts quickly, we provide companion Python notebooks, covering key aspects of this article and implementing them, step-by-step with TensorLy.