Learning Artistic Signatures: Symmetry Discovery and Style Transfer

Despite nearly a decade of literature on style transfer, there is no undisputed definition of artistic style. State-of-the-art models produce impressive results but are difficult to interpret since, without a coherent definition of style, the problem of style transfer is inherently ill-posed. Early work framed style-transfer as an optimization problem but treated style as a measure only of texture. This led to artifacts in the outputs of early models where content features from the style image sometimes bled into the output image. Conversely, more recent work with diffusion models offers compelling empirical results but provides little theoretical grounding. To address these issues, we propose an alternative definition of artistic style. We suggest that style should be thought of as a set of global symmetries that dictate the arrangement of local textures. We validate this perspective empirically by learning the symmetries of a large dataset of paintings and showing that symmetries are predictive of the artistic movement to which each painting belongs. Finally, we show that by considering both local and global features, using both Lie generators and traditional measures of texture, we can quantitatively capture the stylistic similarity between artists better than with either set of features alone. This approach not only aligns well with art historians' consensus but also offers a robust framework for distinguishing nuanced stylistic differences, allowing for a more interpretable, theoretically grounded approach to style transfer.

Deep Generative Models of Music Expectation

A prominent theory of affective response to music revolves around the concepts of surprisal and expectation. In prior work, this idea has been operationalized in the form of probabilistic models of music which allow for precise computation of song (or note-by-note) probabilities, conditioned on a 'training set' of prior musical or cultural experiences. To date, however, these models have been limited to compute exact probabilities through hand-crafted features or restricted to linear models which are likely not sufficient to represent the complex conditional distributions present in music. In this work, we propose to use modern deep probabilistic generative models in the form of a Diffusion Model to compute an approximate likelihood of a musical input sequence. Unlike prior work, such a generative model parameterized by deep neural networks is able to learn complex non-linear features directly from a training set itself. In doing so, we expect to find that such models are able to more accurately represent the 'surprisal' of music for human listeners. From the literature, it is known that there is an inverted U-shaped relationship between surprisal and the amount human subjects 'like' a given song. In this work we show that pre-trained diffusion models indeed yield musical surprisal values which exhibit a negative quadratic relationship with measured subject 'liking' ratings, and that the quality of this relationship is competitive with state of the art methods such as IDyOM. We therefore present this model a preliminary step in developing modern deep generative models of music expectation and subjective likability.

Flow Factorized Representation Learning

A prominent goal of representation learning research is to achieve representations which are factorized in a useful manner with respect to the ground truth factors of variation. The fields of disentangled and equivariant representation learning have approached this ideal from a range of complimentary perspectives; however, to date, most approaches have proven to either be ill-specified or insufficiently flexible to effectively separate all realistic factors of interest in a learned latent space. In this work, we propose an alternative viewpoint on such structured representation learning which we call Flow Factorized Representation Learning, and demonstrate it to learn both more efficient and more usefully structured representations than existing frameworks. Specifically, we introduce a generative model which specifies a distinct set of latent probability paths that define different input transformations. Each latent flow is generated by the gradient field of a learned potential following dynamic optimal transport. Our novel setup brings new understandings to both \textit{disentanglement} and \textit{equivariance}. We show that our model achieves higher likelihoods on standard representation learning benchmarks while simultaneously being closer to approximately equivariant models. Furthermore, we demonstrate that the transformations learned by our model are flexibly composable and can also extrapolate to new data, implying a degree of robustness and generalizability approaching the ultimate goal of usefully factorized representation learning.

Traveling Waves Encode the Recent Past and Enhance Sequence Learning

Traveling waves of neural activity have been observed throughout the brain at a diversity of regions and scales; however, their precise computational role is still debated. One physically grounded hypothesis suggests that the cortical sheet may act like a wave-field capable of storing a short-term memory of sequential stimuli through induced waves traveling across the cortical surface. To date, however, the computational implications of this idea have remained hypothetical due to the lack of a simple recurrent neural network architecture capable of exhibiting such waves. In this work, we introduce a model to fill this gap, which we denote the Wave-RNN (wRNN), and demonstrate how both connectivity constraints and initialization play a crucial role in the emergence of wave-like dynamics. We then empirically show how such an architecture indeed efficiently encodes the recent past through a suite of synthetic memory tasks where wRNNs learn faster and perform significantly better than wave-free counterparts. Finally, we explore the implications of this memory storage system on more complex sequence modeling tasks such as sequential image classification and find that wave-based models not only again outperform comparable wave-free RNNs while using significantly fewer parameters, but additionally perform comparably to more complex gated architectures such as LSTMs and GRUs. We conclude with a discussion of the implications of these results for both neuroscience and machine learning.

DUET: 2D Structured and Approximately Equivariant Representations

Multiview Self-Supervised Learning (MSSL) is based on learning invariances with respect to a set of input transformations. However, invariance partially or totally removes transformation-related information from the representations, which might harm performance for specific downstream tasks that require such information. We propose 2D strUctured and EquivarianT representations (coined DUET), which are 2d representations organized in a matrix structure, and equivariant with respect to transformations acting on the input data. DUET representations maintain information about an input transformation, while remaining semantically expressive. Compared to SimCLR (Chen et al., 2020) (unstructured and invariant) and ESSL (Dangovski et al., 2022) (unstructured and equivariant), the structured and equivariant nature of DUET representations enables controlled generation with lower reconstruction error, while controllability is not possible with SimCLR or ESSL. DUET also achieves higher accuracy for several discriminative tasks, and improves transfer learning.

Homomorphic Self-Supervised Learning

In this work, we observe that many existing self-supervised learning algorithms can be both unified and generalized when seen through the lens of equivariant representations. Specifically, we introduce a general framework we call Homomorphic Self-Supervised Learning, and theoretically show how it may subsume the use of input-augmentations provided an augmentation-homomorphic feature extractor. We validate this theory experimentally for simple augmentations, demonstrate how the framework fails when representational structure is removed, and further empirically explore how the parameters of this framework relate to those of traditional augmentation-based self-supervised learning. We conclude with a discussion of the potential benefits afforded by this new perspective on self-supervised learning.

Modeling Category-Selective Cortical Regions with Topographic Variational Autoencoders

Category-selectivity in the brain describes the observation that certain spatially localized areas of the cerebral cortex tend to respond robustly and selectively to stimuli from specific limited categories. One of the most well known examples of category-selectivity is the Fusiform Face Area (FFA), an area of the inferior temporal cortex in primates which responds preferentially to images of faces when compared with objects or other generic stimuli. In this work, we leverage the newly introduced Topographic Variational Autoencoder to model of the emergence of such localized category-selectivity in an unsupervised manner. Experimentally, we demonstrate our model yields spatially dense neural clusters selective to faces, bodies, and places through visualized maps of Cohen's d metric. We compare our model with related supervised approaches, namely the TDANN, and discuss both theoretical and empirical similarities. Finally, we show preliminary results suggesting that our model yields a nested spatial hierarchy of increasingly abstract categories, analogous to observations from the human ventral temporal cortex.

Topographic VAEs learn Equivariant Capsules

In this work we seek to bridge the concepts of topographic organization and equivariance in neural networks. To accomplish this, we introduce the Topographic VAE: a novel method for efficiently training deep generative models with topographically organized latent variables. We show that such a model indeed learns to organize its activations according to salient characteristics such as digit class, width, and style on MNIST. Furthermore, through topographic organization over time (i.e. temporal coherence), we demonstrate how predefined latent space transformation operators can be encouraged for observed transformed input sequences -- a primitive form of unsupervised learned equivariance. We demonstrate that this model successfully learns sets of approximately equivariant features (i.e. "capsules") directly from sequences and achieves higher likelihood on correspondingly transforming test sequences. Equivariance is verified quantitatively by measuring the approximate commutativity of the inference network and the sequence transformations. Finally, we demonstrate approximate equivariance to complex transformations, expanding upon the capabilities of existing group equivariant neural networks.

As easy as APC: Leveraging self-supervised learning in the context of time series classification with varying levels of sparsity and severe class imbalance

High levels of sparsity and strong class imbalance are ubiquitous challenges that are often presented simultaneously in real-world time series data. While most methods tackle each problem separately, our proposed approach handles both in conjunction, while imposing fewer assumptions on the data. In this work, we propose leveraging a self-supervised learning method, specifically Autoregressive Predictive Coding (APC), to learn relevant hidden representations of time series data in the context of both missing data and class imbalance. We apply APC using either a GRU or GRU-D encoder on two real-world datasets, and show that applying one-step-ahead prediction with APC improves the classification results in all settings. In fact, by applying GRU-D - APC, we achieve state-of-the-art AUPRC results on the Physionet benchmark.

Self Normalizing Flows

Efficient gradient computation of the Jacobian determinant term is a core problem of the normalizing flow framework. Thus, most proposed flow models either restrict to a function class with easy evaluation of the Jacobian determinant, or an efficient estimator thereof. However, these restrictions limit the performance of such density models, frequently requiring significant depth to reach desired performance levels. In this work, we propose Self Normalizing Flows, a flexible framework for training normalizing flows by replacing expensive terms in the gradient by learned approximate inverses at each layer. This reduces the computational complexity of each layer's exact update from $\mathcal{O}(D^3)$ to $\mathcal{O}(D^2)$, allowing for the training of flow architectures which were otherwise computationally infeasible, while also providing efficient sampling. We show experimentally that such models are remarkably stable and optimize to similar data likelihood values as their exact gradient counterparts, while surpassing the performance of their functionally constrained counterparts.