Sparse autoencoders (SAEs) are a recent technique for decomposing neural network activations into human-interpretable features. However, in order for SAEs to identify all features represented in frontier models, it will be necessary to scale them up to very high width, posing a computational challenge. In this work, we introduce Switch Sparse Autoencoders, a novel SAE architecture aimed at reducing the compute cost of training SAEs. Inspired by sparse mixture of experts models, Switch SAEs route activation vectors between smaller "expert" SAEs, enabling SAEs to efficiently scale to many more features. We present experiments comparing Switch SAEs with other SAE architectures, and find that Switch SAEs deliver a substantial Pareto improvement in the reconstruction vs. sparsity frontier for a given fixed training compute budget. We also study the geometry of features across experts, analyze features duplicated across experts, and verify that Switch SAE features are as interpretable as features found by other SAE architectures.
Extremely large reconfigurable intelligent surface (XL-RIS) is emerging as a promising key technology for 6G systems. To exploit XL-RIS's full potential, accurate channel estimation is essential. This paper investigates channel estimation in XL-RIS-aided massive MIMO systems under hybrid-field scenarios where far-field and near-field channels coexist. We formulate this problem using dictionary learning, which allows for joint optimization of the dictionary and estimated channel. To handle the high-dimensional nature of XL-RIS channels, we specifically adopt a convolutional dictionary learning (CDL) formulation. The CDL formulation is cast as a bilevel optimization problem, which we solve using a gradient-based approach. To address the challenge of computing the gradient of the upper-level objective, we introduce an unrolled optimization method based on proximal gradient descent (PGD) and its special case, the iterative soft-thresholding algorithm (ISTA). We propose two neural network architectures, Convolutional ISTA-Net and its enhanced version Convolutional ISTA-Net+, for end-to-end optimization of the CDL. To overcome the limitations of linear convolutional filters in capturing complex hybrid-field channel structures, we propose the CNN-CDL approach, which enhances PGD by replacing linear convolution filters with CNN blocks in its gradient descent step, employing a learnable proximal mapping module in its proximal mapping step, and incorporating cross-layer feature integration. Simulation results demonstrate the effectiveness of the proposed methods for channel estimation in hybrid-field XL-RIS systems.
The Universality Hypothesis in large language models (LLMs) claims that different models converge towards similar concept representations in their latent spaces. Providing evidence for this hypothesis would enable researchers to exploit universal properties, facilitating the generalization of mechanistic interpretability techniques across models. Previous works studied if LLMs learned the same features, which are internal representations that activate on specific concepts. Since comparing features across LLMs is challenging due to polysemanticity, in which LLM neurons often correspond to multiple unrelated features rather than to distinct concepts, sparse autoencoders (SAEs) have been employed to disentangle LLM neurons into SAE features corresponding to distinct concepts. In this paper, we introduce a new variation of the universality hypothesis called Analogous Feature Universality: we hypothesize that even if SAEs across different models learn different feature representations, the spaces spanned by SAE features are similar, such that one SAE space is similar to another SAE space under rotation-invariant transformations. Evidence for this hypothesis would imply that interpretability techniques related to latent spaces, such as steering vectors, may be transferred across models via certain transformations. To investigate this hypothesis, we first pair SAE features across different models via activation correlation, and then measure spatial relation similarities between paired features via representational similarity measures, which transform spaces into representations that reveal hidden relational similarities. Our experiments demonstrate high similarities for SAE feature spaces across various LLMs, providing evidence for feature space universality.
Learning compact and meaningful latent space representations has been shown to be very useful in generative modeling tasks for visual data. One particular example is applying Vector Quantization (VQ) in variational autoencoders (VQ-VAEs, VQ-GANs, etc.), which has demonstrated state-of-the-art performance in many modern generative modeling applications. Quantizing the latent space has been justified by the assumption that the data themselves are inherently discrete in the latent space (like pixel values). In this paper, we propose an alternative representation of the latent space by relaxing the structural assumption than the VQ formulation. Specifically, we assume that the latent space can be approximated by a union of subspaces model corresponding to a dictionary-based representation under a sparsity constraint. The dictionary is learned/updated during the training process. We apply this approach to look at two models: Dictionary Learning Variational Autoencoders (DL-VAEs) and DL-VAEs with Generative Adversarial Networks (DL-GANs). We show empirically that our more latent space is more expressive and has leads to better representations than the VQ approach in terms of reconstruction quality at the expense of a small computational overhead for the latent space computation. Our results thus suggest that the true benefit of the VQ approach might not be from discretization of the latent space, but rather the lossy compression of the latent space. We confirm this hypothesis by showing that our sparse representations also address the codebook collapse issue as found common in VQ-family models.
In this paper, we propose and investigate algorithms for the structured orthogonal dictionary learning problem. First, we investigate the case when the dictionary is a Householder matrix. We give sample complexity results and show theoretically guaranteed approximate recovery (in the $l_{\infty}$ sense) with optimal computational complexity. We then attempt to generalize these techniques when the dictionary is a product of a few Householder matrices. We numerically validate these techniques in the sample-limited setting to show performance similar to or better than existing techniques while having much improved computational complexity.
Recent work on dictionary learning with set-atoms has shown benefits in anomaly detection. Instead of viewing an atom as a single vector, these methods allow building sparse representations with atoms taken from a set around a central vector; the set can be a cone or may have a probability distribution associated to it. We propose a method for adaptively adjusting the size of set-atoms in Gaussian and cone dictionary learning. The purpose of the algorithm is to match the atom sizes with their contribution in representing the signals. The proposed algorithm not only decreases the representation error, but also improves anomaly detection, for a class of anomalies called `dependency'. We obtain better detection performance than state-of-the-art methods.
Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however, has a complex structure that cannot be adequately described using conventional statistical tools. We introduce a measure-theoretic formalism for modeling generalized network structures such as graphs, hypergraphs, or graphs whose nodes come with a partition into categorical classes. We then propose a metric that extends the Gromov-Wasserstein distance between graphs and the co-optimal transport distance between hypergraphs. We characterize the geometry of this space, thereby providing a unified theoretical treatment of generalized networks that encompasses the cases of pairwise, as well as higher-order, relations. In particular, we show that our metric is an Alexandrov space of non-negative curvature, and leverage this structure to define gradients for certain functionals commonly arising in geometric data analysis tasks. We extend our analysis to the setting where vertices have additional label information, and derive efficient computational schemes to use in practice. Equipped with these theoretical and computational tools, we demonstrate the utility of our framework in a suite of applications, including hypergraph alignment, clustering and dictionary learning from ensemble data, multi-omics alignment, as well as multiscale network alignment.
This document contains an educational introduction to the problem of sparsifying parametric models with L0 regularization. We utilize this approach together with dictionary learning to learn sparse polynomial policies for deep reinforcement learning to control parametric partial differential equations. The code and a tutorial are provided here: https://github.com/nicob15/Sparsifying-Parametric-Models-with-L0.
Model parsimony is an important \emph{cognitive bias} in data-driven modelling that aids interpretability and helps to prevent over-fitting. Sparse identification of nonlinear dynamics (SINDy) methods are able to learn sparse representations of complex dynamics directly from data, given a basis of library functions. In this work, a novel Bayesian treatment of dictionary learning system identification, as an alternative to SINDy, is envisaged. The proposed method -- Bayesian identification of nonlinear dynamics (BINDy) -- is distinct from previous approaches in that it targets the full joint posterior distribution over both the terms in the library and their parameterisation in the model. This formulation confers the advantage that an arbitrary prior may be placed over the model structure to produce models that are sparse in the model space rather than in parameter space. Because this posterior is defined over parameter vectors that can change in dimension, the inference cannot be performed by standard techniques. Instead, a Gibbs sampler based on reversible-jump Markov-chain Monte-Carlo is proposed. BINDy is shown to compare favourably to ensemble SINDy in three benchmark case-studies. In particular, it is seen that the proposed method is better able to assign high probability to correct model terms.
Nonlocal self-similarity within images has become an increasingly popular prior in deep-learning models. Despite their successful image restoration performance, such models remain largely uninterpretable due to their black-box construction. Our previous studies have shown that interpretable construction of a fully convolutional denoiser (CDLNet), with performance on par with state-of-the-art black-box counterparts, is achievable by unrolling a convolutional dictionary learning algorithm. In this manuscript, we seek an interpretable construction of a convolutional network with a nonlocal self-similarity prior that performs on par with black-box nonlocal models. We show that such an architecture can be effectively achieved by upgrading the L1 sparsity prior (soft-thresholding) of CDLNet to an image-adaptive group-sparsity prior (group-thresholding). The proposed learned group-thresholding makes use of nonlocal attention to perform spatially varying soft-thresholding on the latent representation. To enable effective training and inference on large images with global artifacts, we propose a novel circulant-sparse attention. We achieve competitive natural-image denoising performance compared to black-box nonlocal DNNs and transformers. The interpretable construction of our network allows for a straightforward extension to Compressed Sensing MRI (CS-MRI), yielding state-of-the-art performance. Lastly, we show robustness to noise-level mismatches between training and inference for denoising and CS-MRI reconstruction.
What latent features are encoded in language model (LM) representations? Recent work on training sparse autoencoders (SAEs) to disentangle interpretable features in LM representations has shown significant promise. However, evaluating the quality of these SAEs is difficult because we lack a ground-truth collection of interpretable features that we expect good SAEs to recover. We thus propose to measure progress in interpretable dictionary learning by working in the setting of LMs trained on chess and Othello transcripts. These settings carry natural collections of interpretable features -- for example, "there is a knight on F3" -- which we leverage into $\textit{supervised}$ metrics for SAE quality. To guide progress in interpretable dictionary learning, we introduce a new SAE training technique, $\textit{p-annealing}$, which improves performance on prior unsupervised metrics as well as our new metrics.
This paper addresses the challenge of online multi-source domain adaptation (MSDA) in transfer learning, a scenario where one needs to adapt multiple, heterogeneous source domains towards a target domain that comes in a stream. We introduce a novel approach for the online fit of a Gaussian Mixture Model (GMM), based on the Wasserstein geometry of Gaussian measures. We build upon this method and recent developments in dataset dictionary learning for proposing a novel strategy in online MSDA. Experiments on the challenging Tennessee Eastman Process benchmark demonstrate that our approach is able to adapt \emph{on the fly} to the stream of target domain data. Furthermore, our online GMM serves as a memory, representing the whole stream of data.
We are often interested in decomposing complex, structured data into simple components that explain the data. The linear version of this problem is well-studied as dictionary learning and factor analysis. In this work, we propose a combinatorial model in which to study this question, motivated by the way objects occlude each other in a scene to form an image. First, we identify a property we call "well-structuredness" of a set of low-dimensional components which ensures that no two components in the set are too similar. We show how well-structuredness is sufficient for learning the set of latent components comprising a set of sample instances. We then consider the problem: given a set of components and an instance generated from some unknown subset of them, identify which parts of the instance arise from which components. We consider two variants: (1) determine the minimal number of components required to explain the instance; (2) determine the correct explanation for as many locations as possible. For the latter goal, we also devise a version that is robust to adversarial corruptions, with just a slightly stronger assumption on the components. Finally, we show that the learning problem is computationally infeasible in the absence of any assumptions.
In this study, we present the Graph Sub-Graph Network (GSN), a novel hybrid image classification model merging the strengths of Convolutional Neural Networks (CNNs) for feature extraction and Graph Neural Networks (GNNs) for structural modeling. GSN employs k-means clustering to group graph nodes into clusters, facilitating the creation of subgraphs. These subgraphs are then utilized to learn representative `atoms` for dictionary learning, enabling the identification of sparse, class-distinguishable features. This integrated approach is particularly relevant in domains like medical imaging, where discerning subtle feature differences is crucial for accurate classification. To evaluate the performance of our proposed GSN, we conducted experiments on benchmark datasets, including PascalVOC and HAM10000. Our results demonstrate the efficacy of our model in optimizing dictionary configurations across varied classes, which contributes to its effectiveness in medical classification tasks. This performance enhancement is primarily attributed to the integration of CNNs, GNNs, and graph learning techniques, which collectively improve the handling of datasets with limited labeled examples. Specifically, our experiments show that the model achieves a higher accuracy on benchmark datasets such as Pascal VOC and HAM10000 compared to conventional CNN approaches.
The ability of deep convolutional neural networks (CNNs) to learn discriminative spectro-temporal patterns makes them well suited to environmental sound classification. However, the relative scarcity of labeled data has impeded the exploitation of this family of high-capacity models. This study has two primary contributions: first, we propose a deep CNN architecture for environmental sound classification. Second, we propose the use of audio data augmentation for overcoming the problem of data scarcity and explore the influence of different augmentations on the performance of the proposed CNN architecture. Combined with data augmentation, the proposed model produces state-of-the-art results for environmental sound classification. We show that the improved performance stems from the combination of a deep, high-capacity model and an augmented training set: this combination outperforms both the proposed CNN without augmentation and a “shallow” dictionary learning model with augmentation. Finally, we examine the influence of each augmentation on the model's classification accuracy for each class, and observe that the accuracy for each class is influenced differently by each augmentation, suggesting that the performance of the model could be improved further by applying class-conditional data augmentation.
Electron backscatter diffraction (EBSD) has developed over the last few decades into a valuable crystallographic characterisation method for a wide range of sample types. Despite these advances, issues such as the complexity of sample preparation, relatively slow acquisition, and damage in beam-sensitive samples, still limit the quantity and quality of interpretable data that can be obtained. To mitigate these issues, here we propose a method based on the subsampling of probe positions and subsequent reconstruction of an incomplete dataset. The missing probe locations (or pixels in the image) are recovered via an inpainting process using a dictionary-learning based method called beta-process factor analysis (BPFA). To investigate the robustness of both our inpainting method and Hough-based indexing, we simulate subsampled and noisy EBSD datasets from a real fully sampled Ni-superalloy dataset for different subsampling ratios of probe positions using both Gaussian and Poisson noise models. We find that zero solution pixel detection (inpainting un-indexed pixels) enables higher quality reconstructions to be obtained. Numerical tests confirm high quality reconstruction of band contrast and inverse pole figure maps from only 10% of the probe positions, with the potential to reduce this to 5% if only inverse pole figure maps are needed. These results show the potential application of this method in EBSD, allowing for faster analysis and extending the use of this technique to beam sensitive materials.
The Deep Operator Network (DeepONet) is a powerful neural operator architecture that uses two neural networks to map between infinite-dimensional function spaces. This architecture allows for the evaluation of the solution field at any location within the domain but requires input functions to be discretized at identical locations, limiting practical applications. We introduce a general framework for operator learning from input-output data with arbitrary sensor locations and counts. This begins by introducing a resolution-independent DeepONet (RI-DeepONet), which handles input functions discretized arbitrarily but sufficiently finely. To achieve this, we propose two dictionary learning algorithms that adaptively learn continuous basis functions, parameterized as implicit neural representations (INRs), from correlated signals on arbitrary point clouds. These basis functions project input function data onto a finite-dimensional embedding space, making it compatible with DeepONet without architectural changes. We specifically use sinusoidal representation networks (SIRENs) as trainable INR basis functions. Similarly, the dictionary learning algorithms identify basis functions for output data, defining a new neural operator architecture: the Resolution Independent Neural Operator (RINO). In RINO, the operator learning task reduces to mapping coefficients of input basis functions to output basis functions. We demonstrate RINO's robustness and applicability in handling arbitrarily sampled input and output functions during both training and inference through several numerical examples.
Multi-Source Domain Adaptation (MSDA) is a challenging scenario where multiple related and heterogeneous source datasets must be adapted to an unlabeled target dataset. Conventional MSDA methods often overlook that data holders may have privacy concerns, hindering direct data sharing. In response, decentralized MSDA has emerged as a promising strategy to achieve adaptation without centralizing clients' data. Our work proposes a novel approach, Decentralized Dataset Dictionary Learning, to address this challenge. Our method leverages Wasserstein barycenters to model the distributional shift across multiple clients, enabling effective adaptation while preserving data privacy. Specifically, our algorithm expresses each client's underlying distribution as a Wasserstein barycenter of public atoms, weighted by private barycentric coordinates. Our approach ensures that the barycentric coordinates remain undisclosed throughout the adaptation process. Extensive experimentation across five visual domain adaptation benchmarks demonstrates the superiority of our strategy over existing decentralized MSDA techniques. Moreover, our method exhibits enhanced robustness to client parallelism while maintaining relative resilience compared to conventional decentralized MSDA methodologies.
Compressed sensing combines the power of convex optimization techniques with a sparsity-inducing prior on the signal space to solve an underdetermined system of equations. For many problems, the sparsifying dictionary is not directly given, nor its existence can be assumed. Besides, the sensing matrix can change across different scenarios. Addressing these issues requires solving a sparse representation learning problem, namely dictionary learning, taking into account the epistemic uncertainty of the learned dictionaries and, finally, jointly learning sparse representations and reconstructions under varying sensing matrix conditions. We address both concerns by proposing a variant of the LISTA architecture. First, we introduce Augmented Dictionary Learning ISTA (A-DLISTA), which incorporates an augmentation module to adapt parameters to the current measurement setup. Then, we propose to learn a distribution over dictionaries via a variational approach, dubbed Variational Learning ISTA (VLISTA). VLISTA exploits A-DLISTA as the likelihood model and approximates a posterior distribution over the dictionaries as part of an unfolded LISTA-based recovery algorithm. As a result, VLISTA provides a probabilistic way to jointly learn the dictionary distribution and the reconstruction algorithm with varying sensing matrices. We provide theoretical and experimental support for our architecture and show that our model learns calibrated uncertainties.
Physiological signal analysis often involves identifying events crucial to understanding biological dynamics. Traditional methods rely on handcrafted procedures or supervised learning, presenting challenges such as expert dependence, lack of robustness, and the need for extensive labeled data. Data-driven methods like Convolutional Dictionary Learning (CDL) offer an alternative but tend to produce spurious detections. This work introduces UNHaP (Unmix Noise from Hawkes Processes), a novel approach addressing the joint learning of temporal structures in events and the removal of spurious detections. Leveraging marked Hawkes processes, UNHaP distinguishes between events of interest and spurious ones. By treating the event detection output as a mixture of structured and unstructured events, UNHaP efficiently unmixes these processes and estimates their parameters. This approach significantly enhances the understanding of event distributions while minimizing false detection rates.