ICLR 2023 Papers

Grokking, the unusual phenomenon for algorithmic datasets where generalization happens long after overfitting the training data, has remained elusive. We aim to understand grokking by analyzing the loss landscapes of neural networks, identifying the mismatch between training and test losses as the cause for grokking. We refer to this as the "LU mechanism" because training and test losses (against model weight norm) typically resemble "L" and "U", respectively. This simple mechanism can nicely explain many aspects of grokking: data size dependence, weight decay dependence, the emergence of representations, etc. Guided by the intuitive picture, we are able to induce grokking on tasks involving images, language and molecules, although the grokking signals are sometimes less dramatic. We attribute the dramatic nature of grokking for algorithmic datasets to representation learning.

This paper presents a method to build explicit tensor-train (TT) representations. We show that a wide class of tensors can be explicitly represented with sparse TT-cores, obtaining, in many cases, optimal TT-ranks. Numerical experiments show that our method outperforms the existing ones in several practical applications, including game theory problems. Theoretical estimations of the number of operations show that in some problems, such as permanent calculation, our methods are close to the known optimal asymptotics, which are obtained by a completely different type of methods.

We present a neural network architecture, Bispectral Neural Networks (BNNs) for learning representations that are invariant to the actions of compact commutative groups on the space over which a signal is defined. The model incorporates the ansatz of the bispectrum, an analytically defined group invariant that is complete -- that is, it preserves all signal structure while removing only the variation due to group actions. Here, we demonstrate that BNNs are able to simultaneously learn groups, their irreducible representations, and corresponding equivariant and complete-invariant maps purely from the symmetries implicit in data. Further, we demonstrate that the completeness property endows these networks with strong invariance-based adversarial robustness. This work establishes Bispectral Neural Networks as a powerful computational primitive for robust invariant representation learning.

We create a reusable Transformer, BrainBERT, for intracranial recordings bringing modern representation learning approaches to neuroscience. Much like in NLP and speech recognition, this Transformer enables classifying complex concepts, i.e., decoding neural data, with higher accuracy and with much less data by being pretrained in an unsupervised manner on a large corpus of unannotated neural recordings. Our approach generalizes to new subjects with electrodes in new positions and to unrelated tasks showing that the representations robustly disentangle the neural signal. Just like in NLP where one can study language by investigating what a language model learns, this approach opens the door to investigating the brain by what a model of the brain learns. As a first step along this path, we demonstrate a new analysis of the intrinsic dimensionality of the computations in different areas of the brain. To construct these representations, we combine a technique for producing super-resolution spectrograms of neural data with an approach designed for generating contextual representations of audio by masking. In the future, far more concepts will be decodable from neural recordings by using representation learning, potentially unlocking the brain like language models unlocked language.

To afford flexible behaviour, the brain must build internal representations that mirror the structure of variables in the external world. For example, 2D space obeys rules: the same set of actions combine in the same way everywhere (step north, then south, and you won't have moved, wherever you start). We suggest the brain must represent this consistent meaning of actions across space, as it allows you to find new short-cuts and navigate in unfamiliar settings. We term this representation an `actionable representation'. We formulate actionable representations using group and representation theory, and show that, when combined with biological and functional constraints - non-negative firing, bounded neural activity, and precise coding - multiple modules of hexagonal grid cells are the optimal representation of 2D space. We support this claim with intuition, analytic justification, and simulations. Our analytic results normatively explain a set of surprising grid cell phenomena, and make testable predictions for future experiments. Lastly, we highlight the generality of our approach beyond just understanding 2D space. Our work characterises a new principle for understanding and designing flexible internal representations: they should be actionable, allowing animals and machines to predict the consequences of their actions, rather than just encode.

Beyond the success story of adversarial training (AT) in the recent text domain on top of pre-trained language models (PLMs), our empirical study showcases the inconsistent gains from AT on some tasks, e.g. commonsense reasoning, named entity recognition. This paper investigates AT from the perspective of the contextualized language representation outputted by PLM encoders. We find the current AT attacks lean to generate sub-optimal adversarial examples that can fool the decoder part but have a minor effect on the encoder. However, we find it necessary to effectively deviate the latter one to allow AT to gain. Based on the observation, we propose simple yet effective \textit{Contextualized representation-Adversarial Training} (CreAT), in which the attack is explicitly optimized to deviate the contextualized representation of the encoder. It allows a global optimization of adversarial examples that can fool the entire model. We also find CreAT gives rise to a better direction to optimize the adversarial examples, to let them less sensitive to hyperparameters. Compared to AT, CreAT produces consistent performance gains on a wider range of tasks and is proven to be more effective for language pre-training where only the encoder part is kept for downstream tasks. We achieve the new state-of-the-art performances on a series of challenging benchmarks, e.g. AdvGLUE (59.1 $ \rightarrow $ 61.1), HellaSWAG (93.0 $ \rightarrow $ 94.9), ANLI (68.1 $ \rightarrow $ 69.3).

Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying dynamical system where new observations at arbitrary time points can be used to update the latent representation of the dynamical system. Existing parameterizations for the dynamics functions of Neural ODEs limit the ability of the model to retain global information about the time series; specifically, a piece-wise integration of the latent process between observations can result in a loss of memory on the dynamic patterns of previously observed data points. We propose PolyODE, a Neural ODE that models the latent continuous-time process as a projection onto a basis of orthogonal polynomials. This formulation enforces long-range memory and preserves a global representation of the underlying dynamical system. Our construction is backed by favourable theoretical guarantees and in a series of experiments, we demonstrate that it outperforms previous works in the reconstruction of past and future data, and in downstream prediction tasks.

Modern studies in radiograph representation learning (R$^2$L) rely on either self-supervision to encode invariant semantics or associated radiology reports to incorporate medical expertise, while the complementarity between them is barely noticed. To explore this, we formulate the self- and report-completion as two complementary objectives and present a unified framework based on masked record modeling (MRM). In practice, MRM reconstructs masked image patches and masked report tokens following a multi-task scheme to learn knowledge-enhanced semantic representations. With MRM pre-training, we obtain pre-trained models that can be well transferred to various radiography tasks. Specifically, we find that MRM offers superior performance in label-efficient fine-tuning. For instance, MRM achieves 88.5% mean AUC on CheXpert using 1% labeled data, outperforming previous R$^2$L methods with 100% labels. On NIH ChestX-ray, MRM outperforms the best performing counterpart by about 3% under small labeling ratios. Besides, MRM surpasses self- and report-supervised pre-training in identifying the pneumonia type and the pneumothorax area, sometimes by large margins.

Despite that going deep has proven successful in many neural architectures, the existing graph transformers are relatively shallow. In this work, we explore whether more layers are beneficial to graph transformers, and find that current graph transformers suffer from the bottleneck of improving performance by increasing depth. Our further analysis reveals the reason is that deep graph transformers are limited by the vanishing capacity of global attention, restricting the graph transformer from focusing on the critical substructure and obtaining expressive features. To this end, we propose a novel graph transformer model named DeepGraph that explicitly employs substructure tokens in the encoded representation, and applies local attention on related nodes to obtain substructure based attention encoding. Our model enhances the ability of the global attention to focus on substructures and promotes the expressiveness of the representations, addressing the limitation of self-attention as the graph transformer deepens. Experiments show that our method unblocks the depth limitation of graph transformers and results in state-of-the-art performance across various graph benchmarks with deeper models.

Learning effective protein representations is critical in a variety of tasks in biology such as predicting protein function or structure. Existing approaches usually pretrain protein language models on a large number of unlabeled amino acid sequences and then finetune the models with some labeled data in downstream tasks. Despite the effectiveness of sequence-based approaches, the power of pretraining on known protein structures, which are available in smaller numbers only, has not been explored for protein property prediction, though protein structures are known to be determinants of protein function. In this paper, we propose to pretrain protein representations according to their 3D structures. We first present a simple yet effective encoder to learn the geometric features of a protein. We pretrain the protein graph encoder by leveraging multiview contrastive learning and different self-prediction tasks. Experimental results on both function prediction and fold classification tasks show that our proposed pretraining methods outperform or are on par with the state-of-the-art sequence-based methods, while using much less pretraining data. Our implementation is available at https://github.com/DeepGraphLearning/GearNet.

Variational Autoencoder (VAE)-based generative models offer flexible representation learning by incorporating meta-priors, general premises considered beneficial for downstream tasks. However, the incorporated meta-priors often involve ad-hoc model deviations from the original likelihood architecture, causing undesirable changes in their training. In this paper, we propose a novel representation learning method, Gromov-Wasserstein Autoencoders (GWAE), which directly matches the latent and data distributions using the variational autoencoding scheme. Instead of likelihood-based objectives, GWAE models minimize the Gromov-Wasserstein (GW) metric between the trainable prior and given data distributions. The GW metric measures the distance structure-oriented discrepancy between distributions even with different dimensionalities, which provides a direct measure between the latent and data spaces. By restricting the prior family, we can introduce meta-priors into the latent space without changing their objective. The empirical comparisons with VAE-based models show that GWAE models work in two prominent meta-priors, disentanglement and clustering, with their GW objective unchanged.

Human object interaction (HOI) detection plays a crucial role in human-centric scene understanding and serves as a fundamental building block for many vision tasks. One generalizable and scalable strategy for HOI detection is to use weak supervision, learning from image-level annotations only. This is inherently challenging due to ambiguous human-object associations, large search space of detecting HOIs and highly noisy training signal. A promising strategy to address those challenges is to exploit knowledge from large-scale pretrained models (e.g., CLIP), but a direct knowledge distillation strategy does not perform well on the weakly-supervised setting. In contrast, we develop a CLIP-guided HOI representation capable of incorporating the prior knowledge at both image level and HOI instance level, and adopt a self-taught mechanism to prune incorrect human-object associations. Experimental results on HICO-DET and V-COCO show that our method outperforms the previous works by a sizable margin, showing the efficacy of our HOI representation.

Multivariate time series often faces the problem of missing value. Many time series imputation methods have been developed in the literature. However, these methods all rely on an entangled representation to model dynamics of time series, which may fail to fully exploit the multiple factors (e.g., periodic patterns) contained in the time series. Moreover, the entangled representation usually has no semantic meaning, and thus they often lack interpretability. In addition, many recent models are proposed to deal with the whole time series to capture cross-channel correlations and identify temporal dynamics, but they are not scalable to large-scale datasets. Different from existing approaches, we propose TIDER, a novel matrix factorization-based method with disentangled temporal representations that account for multiple factors, namely trend, seasonality, and local bias, to model complex dynamics. The learned disentanglement makes the imputation process more reliable and offers explainability for imputation results. Moreover, TIDER is scalable to large datasets. Empirical results show that our method not only outperforms existing approaches by notable margins on three real-world datasets, but also scales well to large datasets on which existing deep learning based methods struggle. Disentanglement validation experiments further demonstrate the robustness of our model in obtaining accurate and explainable disentangled components.

Transformer architectures have achieved great success in solving natural language tasks, which learn strong language representations from large-scale unlabeled texts. In this paper, we seek to go further beyond and explore a new logical inductive bias for better language representation learning. Logic reasoning is known as a formal methodology to reach answers from given knowledge and facts. Inspired by such a view, we develop a novel neural architecture named FOLNet (First-Order Logic Network), to encode this new inductive bias. We construct a set of neural logic operators as learnable Horn clauses, which are further forward-chained into a fully differentiable neural architecture (FOLNet). Interestingly, we find that the self-attention module in transformers can be composed by two of our neural logic operators, which probably explains their strong reasoning performance. Our proposed FOLNet has the same input and output interfaces as other pretrained models and thus could be pretrained/finetuned by using similar losses. It also allows FOLNet to be used in a plug-and-play manner when replacing other pretrained models. With our logical inductive bias, the same set of ``logic deduction skills'' learned through pretraining are expected to be equally capable of solving diverse downstream tasks. For this reason, FOLNet learns language representations that have much stronger transfer capabilities. Experimental results on several language understanding tasks show that our pretrained FOLNet model outperforms the existing strong transformer-based approaches.

Much of the data we encounter in the real world can be represented as directed graphs. In this work, we introduce a general family of representations for directed graphs through connected time-oriented Lorentz manifolds, called "spacetimes" in general relativity. Spacetimes intrinsically contain a causal structure that indicates whether or not there exists a causal or even chronological order between points of the manifold, called events. This chronological order allows us to naturally represent directed edges via imposing the correct ordering when the nodes are embedded as events in the spacetime. Previous work in machine learning only considers embeddings lying on the simplest Lorentz manifold or does not exploit the connection between Lorentzian pre-length spaces and directed graphs. We introduce a well-defined approach to map data onto a general family of spacetimes. We empirically evaluate our framework in the tasks of hierarchy extraction of undirected graphs, directed link prediction and representation of directed graphs.

Auxiliary tasks improve the representations learned by deep reinforcement learning agents. Analytically, their effect is reasonably well-understood; in practice, how-ever, their primary use remains in support of a main learning objective, rather than as a method for learning representations. This is perhaps surprising given that many auxiliary tasks are defined procedurally, and hence can be treated as an essentially infinite source of information about the environment. Based on this observation, we study the effectiveness of auxiliary tasks for learning rich representations, focusing on the setting where the number of tasks and the size of the agent’s network are simultaneously increased. For this purpose, we derive a new family of auxiliary tasks based on the successor measure. These tasks are easy to implement and have appealing theoretical properties. Combined with a suitable off-policy learning rule, the result is a representation learning algorithm that can be understood as extending Mahadevan & Maggioni (2007)’s proto-value functions to deep reinforcement learning – accordingly, we call the resulting object proto-value networks. Through a series of experiments on the Arcade Learning Environment, we demonstrate that proto-value networks produce rich features that may be used to obtain performance comparable to established algorithms, using only linear approximation and a small number (~4M) of interactions with the environment’s reward function.

Biological vision systems are unparalleled in their ability to learn visual representations without supervision. In machine learning, self-supervised learning (SSL) has led to major advances in forming object representations in an unsupervised fashion. Such systems learn representations invariant to augmentation operations over images, like cropping or flipping. In contrast, biological vision systems exploit the temporal structure of the visual experience during natural interactions with objects. This gives access to “augmentations” not commonly used in SSL, like watching the same object from multiple viewpoints or against different backgrounds. Here, we systematically investigate and compare the potential benefits of such time-based augmentations during natural interactions for learning object categories. Our results show that incorporating time-based augmentations achieves large performance gains over state-of-the-art image augmentations. Specifically, our analyses reveal that: 1) 3-D object manipulations drastically improve the learning of object categories; 2) viewing objects against changing backgrounds is important for learning to discard background-related information from the latent representation. Overall, we conclude that time-based augmentations during natural interactions with objects can substantially improve self-supervised learning, narrowing the gap between artificial and biological vision systems.

It is unclear how changing the learning rule of a deep neural network alters its learning dynamics and representations. To gain insight into the relationship between learned features, function approximation, and the learning rule, we analyze infinite-width deep networks trained with gradient descent (GD) and biologically-plausible alternatives including feedback alignment (FA), direct feedback alignment (DFA), and error modulated Hebbian learning (Hebb), as well as gated linear networks (GLN). We show that, for each of these learning rules, the evolution of the output function at infinite width is governed by a time varying effective neural tangent kernel (eNTK). In the lazy training limit, this eNTK is static and does not evolve, while in the rich mean-field regime this kernel's evolution can be determined self-consistently with dynamical mean field theory (DMFT). This DMFT enables comparisons of the feature and prediction dynamics induced by each of these learning rules. In the lazy limit, we find that DFA and Hebb can only learn using the last layer features, while full FA can utilize earlier layers with a scale determined by the initial correlation between feedforward and feedback weight matrices. In the rich regime, DFA and FA utilize a temporally evolving and depth-dependent NTK. Counterintuitively, we find that FA networks trained in the rich regime exhibit more feature learning if initialized with smaller correlation between the forward and backward pass weights. GLNs admit a very simple formula for their lazy limit kernel and preserve conditional Gaussianity of their preactivations under gating functions. Error modulated Hebb rules show very small task-relevant alignment of their kernels and perform most task relevant learning in the last layer.

Compositional representations of the world are a promising step towards enabling high-level scene understanding and efficient transfer to downstream tasks. Learning such representations for complex scenes and tasks remains an open challenge. Towards this goal, we introduce Neural Radiance Field Codebooks (NRC), a scalable method for learning object-centric representations through novel view reconstruction. NRC learns to reconstruct scenes from novel views using a dictionary of object codes which are decoded through a volumetric renderer. This enables the discovery of reoccurring visual and geometric patterns across scenes which are transferable to downstream tasks. We show that NRC representations transfer well to object navigation in THOR, outperforming 2D and 3D representation learning methods by 3.1\% success rate. We demonstrate that our approach is able to perform unsupervised segmentation for more complex synthetic (THOR) and real scenes (NYU Depth) better than prior methods (.101 ARI). Finally, we show that NRC improves on the task of depth ordering by 5.5% accuracy in THOR.