ICLR 2022 Papers

A variety of recent works, spanning pruning, lottery tickets, and training within random subspaces, have shown that deep neural networks can be trained using far fewer degrees of freedom than the total number of parameters. We analyze this phenomenon for random subspaces by first examining the success probability of hitting a training loss sublevel set when training within a random subspace of a given training dimensionality. We find a sharp phase transition in the success probability from $0$ to $1$ as the training dimension surpasses a threshold. This threshold training dimension increases as the desired final loss decreases, but decreases as the initial loss decreases. We then theoretically explain the origin of this phase transition, and its dependence on initialization and final desired loss, in terms of properties of the high-dimensional geometry of the loss landscape. In particular, we show via Gordon's escape theorem, that the training dimension plus the Gaussian width of the desired loss sublevel set, projected onto a unit sphere surrounding the initialization, must exceed the total number of parameters for the success probability to be large. In several architectures and datasets, we measure the threshold training dimension as a function of initialization and demonstrate that it is a small fraction of the total parameters, implying by our theory that successful training with so few dimensions is possible precisely because the Gaussian width of low loss sublevel sets is very large. Moreover, we compare this threshold training dimension to more sophisticated ways of reducing training degrees of freedom, including lottery tickets as well as a new, analogous method: lottery subspaces.

Frequently, population studies feature pyramidally-organized data represented using Hierarchical Bayesian Models (HBM) enriched with plates. These models can become prohibitively large in settings such as neuroimaging, where a sample is composed of a functional MRI signal measured on 300 brain locations, across 4 measurement sessions, and 30 subjects, resulting in around 1 million latent parameters. Such high dimensionality hampers the usage of modern, expressive flow-based techniques. To infer parameter posterior distributions in this challenging class of problems, we designed a novel methodology that automatically produces a variational family dual to a target HBM. This variational family, represented as a neural network, consists in the combination of an attention-based hierarchical encoder feeding summary statistics to a set of normalizing flows. Our automatically-derived neural network exploits exchangeability in the plate-enriched HBM and factorizes its parameter space. The resulting architecture reduces by orders of magnitude its parameterization with respect to that of a typical flow-based representation, while maintaining expressivity. Our method performs inference on the specified HBM in an amortized setup: once trained, it can readily be applied to a new data sample to compute the parameters' full posterior. We demonstrate the capability and scalability of our method on simulated data, as well as a challenging high-dimensional brain parcellation experiment. We also open up several questions that lie at the intersection between normalizing flows, SBI, structured Variational Inference, and inference amortization.

"The power of a generalization system follows directly from its biases" (Mitchell 1980). Today, CNNs are incredibly powerful generalisation systems---but to what degree have we understood how their inductive bias influences model decisions? We here attempt to disentangle the various aspects that determine how a model decides. In particular, we ask: what makes one model decide differently from another? In a meticulously controlled setting, we find that (1.) irrespective of the network architecture or objective (e.g. self-supervised, semi-supervised, vision transformers, recurrent models) all models end up with a similar decision boundary. (2.) To understand these findings, we analysed model decisions on the ImageNet validation set from epoch to epoch and image by image. We find that the ImageNet validation set, among others, suffers from dichotomous data difficulty (DDD): For the range of investigated models and their accuracies, it is dominated by 46.0% "trivial" and 11.5% "impossible" images (beyond label errors). Only 42.5% of the images could possibly be responsible for the differences between two models' decision boundaries. (3.) Only removing the "impossible" and "trivial" images allows us to see pronounced differences between models. (4.) Humans are highly accurate at predicting which images are "trivial" and "impossible" for CNNs (81.4%). This implies that in future comparisons of brains, machines and behaviour, much may be gained from investigating the decisive role of images and the distribution of their difficulties.

An intuitive way to search for images is to use queries composed of an example image and a complementary text. While the first provides rich and implicit context for the search, the latter explicitly calls for new traits, or specifies how some elements of the example image should be changed to retrieve the desired target image. Current approaches typically combine the features of each of the two elements of the query into a single representation, which can then be compared to the ones of the potential target images. Our work aims at shedding new light on the task by looking at it through the prism of two familiar and related frameworks: text-to-image and image-to-image retrieval. Taking inspiration from them, we exploit the specific relation of each query element with the targeted image and derive light-weight attention mechanisms which enable to mediate between the two complementary modalities. We validate our approach on several retrieval benchmarks, querying with images and their associated free-form text modifiers. Our method obtains state-of-the-art results without resorting to side information, multi-level features, heavy pre-training nor large architectures as in previous works.

Disentangled feature representation is essential for data-efficient learning. The feature space of deep models is inherently compositional. Existing $\beta$-VAE-based methods, which only apply disentanglement regularization to the resulting embedding space of deep models, cannot effectively regularize such compositional feature space, resulting in unsatisfactory disentangled results. In this paper, we formulate the compositional disentanglement learning problem from an information-theoretic perspective and propose a recursive disentanglement network (RecurD) that propagates regulatory inductive bias recursively across the compositional feature space during disentangled representation learning. Experimental studies demonstrate that RecurD outperforms $\beta$-VAE and several of its state-of-the-art variants on disentangled representation learning and enables more data-efficient downstream machine learning tasks.

Computational methods for predicting the interface contacts between proteins come highly sought after for drug discovery as they can significantly advance the accuracy of alternative approaches, such as protein-protein docking, protein function analysis tools, and other computational methods for protein bioinformatics. In this work, we present the Geometric Transformer, a novel geometry-evolving graph transformer for rotation and translation-invariant protein interface contact prediction, packaged within DeepInteract, an end-to-end prediction pipeline. DeepInteract predicts partner-specific protein interface contacts (i.e., inter-protein residue-residue contacts) given the 3D tertiary structures of two proteins as input. In rigorous benchmarks, DeepInteract, on challenging protein complex targets from the 13th and 14th CASP-CAPRI experiments as well as Docking Benchmark 5, achieves 14% and 1.1% top L/5 precision (L: length of a protein unit in a complex), respectively. In doing so, DeepInteract, with the Geometric Transformer as its graph-based backbone, outperforms existing methods for interface contact prediction in addition to other graph-based neural network backbones compatible with DeepInteract, thereby validating the effectiveness of the Geometric Transformer for learning rich relational-geometric features for downstream tasks on 3D protein structures.

We propose learning via retracing, a novel self-supervised approach for learning the state representation (and the associated dynamics model) for reinforcement learning tasks. In addition to the predictive (reconstruction) supervision in the forward direction, we propose to include "retraced" transitions for representation/model learning, by enforcing the cycle-consistency constraint between the original and retraced states, hence improve upon the sample efficiency of learning. Moreover, learning via retracing explicitly propagates information about future transitions backward for inferring previous states, thus facilitates stronger representation learning for the downstream reinforcement learning tasks. We introduce Cycle-Consistency World Model (CCWM), a concrete model-based instantiation of learning via retracing. Additionally we propose a novel adaptive "truncation" mechanism for counteracting the negative impacts brought by "irreversible" transitions such that learning via retracing can be maximally effective. Through extensive empirical studies on visual-based continuous control benchmarks, we demonstrate that CCWM achieves state-of-the-art performance in terms of sample efficiency and asymptotic performance, whilst exhibiting behaviours that are indicative of stronger representation learning.

The availability of both anatomical connectivity and brain-wide neural activity measurements in C. elegans make the worm a promising system for learning detailed, mechanistic models of an entire nervous system in a data-driven way. However, one faces several challenges when constructing such a model. We often do not have direct experimental access to important modeling details such as single-neuron dynamics and the signs and strengths of the synaptic connectivity. Further, neural activity can only be measured in a subset of neurons, often indirectly via calcium imaging, and significant trial-to-trial variability has been observed. To address these challenges, we introduce a connectome-constrained latent variable model (CC-LVM) of the unobserved voltage dynamics of the entire C. elegans nervous system and the observed calcium signals. We used the framework of variational autoencoders to fit parameters of the mechanistic simulation constituting the generative model of the LVM to calcium imaging observations. A variational approximate posterior distribution over latent voltage traces for all neurons is efficiently inferred using an inference network, and constrained by a prior distribution given by the biophysical simulation of neural dynamics. We applied this model to an experimental whole-brain dataset, and found that connectomic constraints enable our LVM to predict the activity of neurons whose activity were withheld significantly better than models unconstrained by a connectome. We explored models with different degrees of biophysical detail, and found that models with realistic conductance-based synapses provide markedly better predictions than current-based synapses for this system.

We strive to learn a model from a set of source domains that generalizes well to unseen target domains. The main challenge in such a domain generalization scenario is the unavailability of any target domain data during training, resulting in the learned model not being explicitly adapted to the unseen target domains. We propose learning to generalize across domains on single test samples. We leverage a meta-learning paradigm to learn our model to acquire the ability of adaptation with single samples at training time so as to further adapt itself to each single test sample at test time. We formulate the adaptation to the single test sample as a variational Bayesian inference problem, which incorporates the test sample as a conditional into the generation of model parameters. The adaptation to each test sample requires only one feed-forward computation at test time without any fine-tuning or self-supervised training on additional data from the unseen domains. Extensive ablation studies demonstrate that our model learns the ability to adapt models to each single sample by mimicking domain shifts during training. Further, our model achieves at least comparable -- and often better -- performance than state-of-the-art methods on multiple benchmarks for domain generalization.

We study COMP-AMS, a distributed optimization framework based on gradient averaging and adaptive AMSGrad algorithm. Gradient compression with error feedback is applied to reduce the communication cost in the gradient transmission process. Our convergence analysis of COMP-AMS shows that such compressed gradient averaging strategy yields same convergence rate as standard AMSGrad, and also exhibits the linear speedup effect w.r.t. the number of local workers. Compared with recently proposed protocols on distributed adaptive methods, COMP-AMS is simple and convenient. Numerical experiments are conducted to justify the theoretical findings, and demonstrate that the proposed method can achieve same test accuracy as the full-gradient AMSGrad with substantial communication savings. With its simplicity and efficiency, COMP-AMS can serve as a useful distributed training framework for adaptive methods.

Graph neural networks achieve high accuracy in link prediction by jointly leveraging graph topology and node attributes. Topology, however, is represented indirectly; state-of-the-art methods based on subgraph classification label nodes with distance to the target link, so that, although topological information is present, it is tempered by pooling. This makes it challenging to leverage features like loops and motifs associated with network formation mechanisms. We propose a link prediction algorithm based on a new pooling scheme called WalkPool. WalkPool combines the expressivity of topological heuristics with the feature-learning ability of neural networks. It summarizes a putative link by random walk probabilities of adjacent paths. Instead of extracting transition probabilities from the original graph, it computes the transition matrix of a ``predictive'' latent graph by applying attention to learned features; this may be interpreted as feature-sensitive topology fingerprinting. WalkPool can leverage unsupervised node features or be combined with GNNs and trained end-to-end. It outperforms state-of-the-art methods on all common link prediction benchmarks, both homophilic and heterophilic, with and without node attributes. Applying WalkPool to a set of unsupervised GNNs significantly improves prediction accuracy, suggesting that it may be used as a general-purpose graph pooling scheme.

How to extract as much learning signal from each trajectory data has been a key problem in reinforcement learning (RL), where sample inefficiency has posed serious challenges for practical applications. Recent works have shown that using expressive policy function approximators and conditioning on future trajectory information -- such as future states in hindsight experience replay (HER) or returns-to-go in Decision Transformer (DT) -- enables efficient learning of multi-task policies, where at times online RL is fully replaced by offline behavioral cloning (BC), e.g. sequence modeling. We demonstrate that all these approaches are doing hindsight information matching (HIM) -- training policies that can output the rest of trajectory that matches some statistics of future state information. We present Generalized Decision Transformer (GDT) for solving any HIM problem, and show how different choices for the feature function and the anti-causal aggregator not only recover DT as a special case, but also lead to novel Categorical DT (CDT) and Bi-directional DT (BDT) for matching different statistics of the future. For evaluating CDT and BDT, we define offline multi-task state-marginal matching (SMM) and imitation learning (IL) as two generic HIM problems, propose a Wasserstein distance loss as a metric for both, and empirically study them on MuJoCo continuous control benchmarks. Categorical DT, which simply replaces anti-causal summation with anti-causal binning in DT, enables arguably the first effective offline multi-task SMM algorithm that generalizes well to unseen (and even synthetic) multi-modal reward or state-feature distributions. Bi-directional DT, which uses an anti-causal second transformer as the aggregator, can learn to model any statistics of the future and outperforms DT variants in offline multi-task IL, i.e. one-shot IL. Our generalized formulations from HIM and GDT greatly expand the role of powerful sequence modeling architectures in modern RL.

The ability to learn reward functions plays an important role in enabling the deployment of intelligent agents in the real world. However, $\textit{comparing}$ reward functions, for example as a means of evaluating reward learning methods, presents a challenge. Reward functions are typically compared by considering the behavior of optimized policies, but this approach conflates deficiencies in the reward function with those of the policy search algorithm used to optimize it. To address this challenge, Gleave et al. (2020) propose the Equivalent-Policy Invariant Comparison (EPIC) distance. EPIC avoids policy optimization, but in doing so requires computing reward values at transitions that may be impossible under the system dynamics. This is problematic for learned reward functions because it entails evaluating them outside of their training distribution, resulting in inaccurate reward values that we show can render EPIC ineffective at comparing rewards. To address this problem, we propose the Dynamics-Aware Reward Distance (DARD), a new reward pseudometric. DARD uses an approximate transition model of the environment to transform reward functions into a form that allows for comparisons that are invariant to reward shaping while only evaluating reward functions on transitions close to their training distribution. Experiments in simulated physical domains demonstrate that DARD enables reliable reward comparisons without policy optimization and is significantly more predictive than baseline methods of downstream policy performance when dealing with learned reward functions.

Distributional Reinforcement Learning (RL) differs from traditional RL by estimating the distribution over returns to capture the intrinsic uncertainty of MDPs. One key challenge in distributional RL lies in how to parameterize the quantile function when minimizing the Wasserstein metric of temporal differences. Existing algorithms use step functions or piecewise linear functions. In this paper, we propose to learn smooth continuous quantile functions represented by monotonic rational-quadratic splines, which also naturally solve the quantile crossing problem. Experiments in stochastic environments show that a dense estimation for quantile functions enhances distributional RL in terms of faster empirical convergence and higher rewards in most cases.

3D object detection is a fundamental and challenging task for 3D scene understanding, and the monocular-based methods can serve as an economical alternative to the stereo-based or LiDAR-based methods. However, accurately locating objects in the 3D space from a single image is extremely difficult due to the lack of spatial cues. To mitigate this issue, we propose a simple and effective scheme to introduce the spatial information from LiDAR signals to the monocular 3D detectors, without introducing any extra cost in the inference phase. In particular, we first project the LiDAR signals into the image plane and align them with the RGB images. After that, we use the resulting data to train a 3D detector (LiDAR Net) using the same architecture as the baseline model. Finally, this LiDAR Net can serve as the teacher to transfer the learned knowledge to the baseline model. Experimental results show that the proposed method can significantly boost the performance of the baseline model and ranks the $1^{st}$ place among all monocular-based methods on the KITTI benchmark. Besides, extensive ablation studies are conducted, which further prove the effectiveness of each part of our designs and illustrate what the baseline model has learned from the LiDAR Net.

We introduce Synthetic Environments (SEs) and Reward Networks (RNs), represented by neural networks, as proxy environment models for training Reinforcement Learning (RL) agents. We show that an agent, after being trained exclusively on the SE, is able to solve the corresponding real environment. While an SE acts as a full proxy to a real environment by learning about its state dynamics and rewards, an RN is a partial proxy that learns to augment or replace rewards. We use bi-level optimization to evolve SEs and RNs: the inner loop trains the RL agent, and the outer loop trains the parameters of the SE / RN via an evolution strategy. We evaluate our proposed new concept on a broad range of RL algorithms and classic control environments. In a one-to-one comparison, learning an SE proxy requires more interactions with the real environment than training agents only on the real environment. However, once such an SE has been learned, we do not need any interactions with the real environment to train new agents. Moreover, the learned SE proxies allow us to train agents with fewer interactions while maintaining the original task performance. Our empirical results suggest that SEs achieve this result by learning informed representations that bias the agents towards relevant states. Moreover, we find that these proxies are robust against hyperparameter variation and can also transfer to unseen agents.

We consider the problem of generating 3D molecular geometries from scratch. While multiple methods have been developed for generating molecular graphs, generating 3D molecular geometries from scratch is largely under-explored. In this work, we propose G-SphereNet, a novel autoregressive flow model for generating 3D molecular geometries. G-SphereNet employs a flexible sequential generation scheme by placing atoms in 3D space step-by-step. Instead of generating 3D coordinates directly, we propose to determine 3D positions of atoms by generating distances, angles and torsion angles, thereby ensuring both invariance and equivariance properties. In addition, we propose to use spherical message passing and attention mechanism for conditional information extraction. Experimental results show that G-SphereNet outperforms previous methods on random molecular geometry generation and targeted molecule discovery tasks. Our code is publicly available as part of the DIG package (https://github.com/divelab/DIG).

Recovering sparse parameters from observational data is a fundamental problem in machine learning with wide applications. Many classic algorithms can solve this problem with theoretical guarantees, but their performances rely on choosing the correct hyperparameters. Besides, hand-designed algorithms do not fully exploit the particular problem distribution of interest. In this work, we propose a deep learning method for algorithm learning called PLISA (Provable Learning-based Iterative Sparse recovery Algorithm). PLISA is designed by unrolling a classic path-following algorithm for sparse recovery, with some components being more flexible and learnable. We theoretically show the improved recovery accuracy achievable by PLISA. Furthermore, we analyze the empirical Rademacher complexity of PLISA to characterize its generalization ability to solve new problems outside the training set. This paper contains novel theoretical contributions to the area of learning-based algorithms in the sense that (i) PLISA is generically applicable to a broad class of sparse estimation problems, (ii) generalization analysis has received less attention so far, and (iii) our analysis makes novel connections between the generalization ability and algorithmic properties such as stability and convergence of the unrolled algorithm, which leads to a tighter bound that can explain the empirical observations. The techniques could potentially be applied to analyze other learning-based algorithms in the literature.

We consider offline imitation learning (IL), which aims to mimic the expert's behavior from its demonstration without further interaction with the environment. One of the main challenges in offline IL is to deal with the narrow support of the data distribution exhibited by the expert demonstrations that cover only a small fraction of the state and the action spaces. As a result, offline IL algorithms that rely only on expert demonstrations are very unstable since the situation easily deviates from those in the expert demonstrations. In this paper, we assume additional demonstration data of unknown degrees of optimality, which we call imperfect demonstrations. Under this setting, we propose DemoDICE, which effectively utilizes imperfect demonstrations by matching the stationary distribution of a policy with experts' distribution while penalizing its deviation from the overall demonstrations. Compared with the recent IL algorithms that adopt adversarial minimax training objectives, we substantially stabilize overall learning process by reducing minimax optimization to a direct convex optimization in a principled manner. Using extensive tasks, we show that DemoDICE achieves promising results in the offline IL from expert and imperfect demonstrations.