NeurIPS 2023 Papers

Generative Models (GMs) have attracted considerable attention due to their tremendous success in various domains, such as computer vision where they are capable to generate impressive realistic-looking images. Likelihood-based GMs are attractive due to the possibility to generate new data by a single model evaluation. However, they typically achieve lower sample quality compared to state-of-the-art score-based Diffusion Models (DMs). This paper provides a significant step in the direction of addressing this limitation. The idea is to borrow one of the strengths of score-based DMs, which is the ability to perform accurate density estimation in low-density regions and to address manifold overfitting by means of data mollification. We propose a view of data mollification within likelihood-based GMs as a continuation method, whereby the optimization objective smoothly transitions from simple-to-optimize to the original target. Crucially, data mollification can be implemented by adding one line of code in the optimization loop, and we demonstrate that this provides a boost in generation quality of likelihood-based GMs, without computational overheads. We report results on real-world image data sets and UCI benchmarks with popular likelihood-based GMs, including variants of variational autoencoders and normalizing flows, showing large improvements in FID score and density estimation.

Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable invertible transformations. Therefore, once the manifold is properly aligned via a reconstruction loss, the probability density is tractable on the manifold and maximum likelihood can be used to optimize the network parameters. Naturally, the lower-dimensional representation of the data requires an injective-mapping. Recent approaches were able to enforce that the density aligns with the modelled manifold, while efficiently calculating the density volume-change term when embedding to the higher-dimensional space. However, unless the injective-mapping is analytically predefined, the learned manifold is not necessarily an \emph{efficient representation} of the data. Namely, the latent dimensions of such models frequently learn an entangled intrinsic basis, with degenerate information being stored in each dimension. Alternatively, if a locally orthogonal and/or sparse basis is to be learned, here coined canonical intrinsic basis, it can serve in learning a more compact latent space representation. Toward this end, we propose a canonical manifold learning flow method, where a novel optimization objective enforces the transformation matrix to have few prominent and non-degenerate basis functions. We demonstrate that by minimizing the off-diagonal manifold metric elements $\ell_1$-norm, we can achieve such a basis, which is simultaneously sparse and/or orthogonal. Canonical manifold flow yields a more efficient use of the latent space, automatically generating fewer prominent and distinct dimensions to represent data, and consequently a better approximation of target distributions than other manifold flow methods in most experiments we conducted, resulting in lower FID scores.

Advances in generative models have recently revolutionised machine learning. Meanwhile, in neuroscience, generative models have long been thought fundamental to animal intelligence. Understanding the biological mechanisms that support these processes promises to shed light on the relationship between biological and artificial intelligence. In animals, the hippocampal formation is thought to learn and use a generative model to support its role in spatial and non-spatial memory. Here we introduce a biologically plausible model of the hippocampal formation tantamount to a Helmholtz machine that we apply to a temporal stream of inputs. A novel component of our model is that fast theta-band oscillations (5-10 Hz) gate the direction of information flow throughout the network, training it akin to a high-frequency wake-sleep algorithm. Our model accurately infers the latent state of high-dimensional sensory environments and generates realistic sensory predictions. Furthermore, it can learn to path integrate by developing a ring attractor connectivity structure matching previous theoretical proposals and flexibly transfer this structure between environments. Whereas many models trade-off biological plausibility with generality, our model captures a variety of hippocampal cognitive functions under one biologically plausible local learning rule.

A conditional generative model is a method for sampling from a conditional distribution $p(y \mid x)$. For example, one may want to sample an image of a cat given the label ``cat''. A feed-forward conditional generative model is a function $g(x, z)$ that takes the input $x$ and a random seed $z$, and outputs a sample $y$ from $p(y \mid x)$. Ideally the distribution of outputs $(x, g(x, z))$ would be close in total variation to the ideal distribution $(x, y)$. Generalization bounds for other learning models require assumptions on the distribution of $x$, even in simple settings like linear regression with Gaussian noise. We show these assumptions are unnecessary in our model, for both linear regression and single-layer ReLU networks. Given samples $(x, y)$, we show how to learn a 1-layer ReLU conditional generative model in total variation. As our result has no assumption on the distribution of inputs $x$, if we are given access to the internal activations of a deep generative model, we can compose our 1-layer guarantee to progressively learn the deep model using a near-linear number of samples.

In generative compressed sensing (GCS), we want to recover a signal $\mathbf{x^*}\in\mathbb{R}^n$ from $m$ measurements ($m\ll n$) using a generative prior $\mathbf{x^*}\in G(\mathbb{B}_2^k(r))$, where $G$ is typically an $L$-Lipschitz continuous generative model and $\mathbb{B}_2^k(r)$ represents the radius-$r$ $\ell_2$-ball in $\mathbb{R}^k$. Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $\mathbf{x^*}$ rather than for all $\mathbf{x^*}$ simultaneously. In this paper, we build a unified framework to derive uniform recovery guarantees for nonlinear GCS where the observation model is nonlinear and possibly discontinuous or unknown. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index model as canonical examples. Specifically, using a single realization of the sensing ensemble and generalized Lasso, all $\mathbf{x^*}\in G(\mathbb{B}_2^k(r))$ can be recovered up to an $\ell_2$-error at most $\epsilon$ using roughly $\tilde{O}({k}/{\epsilon^2})$ samples, with omitted logarithmic factors typically being dominated by $\log L$. Notably, this almost coincides with existing non-uniform guarantees up to logarithmic factors, hence the uniformity costs very little. As part of our technical contributions, we introduce Lipschitz approximation to handle discontinuous observation models. We also develop a concentration inequality that produces tighter bound for product process whose index sets have low metric entropy. Experimental results are presented to corroborate our theory.

Combinatorial optimization (CO) problems are often NP-hard and thus out of reach for exact algorithms, making them a tempting domain to apply machine learning methods. The highly structured constraints in these problems can hinder either optimization or sampling directly in the solution space. On the other hand, GFlowNets have recently emerged as a powerful machinery to efficiently sample from composite unnormalized densities sequentially and have the potential to amortize such solution-searching processes in CO, as well as generate diverse solution candidates. In this paper, we design Markov decision processes (MDPs) for different combinatorial problems and propose to train conditional GFlowNets to sample from the solution space. Efficient training techniques are also developed to benefit long-range credit assignment. Through extensive experiments on a variety of different CO tasks with synthetic and realistic data, we demonstrate that GFlowNet policies can efficiently find high-quality solutions. Our implementation is open-sourced at https://github.com/zdhNarsil/GFlowNet-CombOpt.

Action-constrained reinforcement learning (ACRL) is a popular approach for solving safety-critical and resource-allocation related decision making problems. A major challenge in ACRL is to ensure agent taking a valid action satisfying constraints in each RL step. Commonly used approach of using a projection layer on top of the policy network requires solving an optimization program which can result in longer training time, slow convergence, and zero gradient problem. To address this, first we use a normalizing flow model to learn an invertible, differentiable mapping between the feasible action space and the support of a simple distribution on a latent variable, such as Gaussian. Second, learning the flow model requires sampling from the feasible action space, which is also challenging. We develop multiple methods, based on Hamiltonian Monte-Carlo and probabilistic sentential decision diagrams for such action sampling for convex and non-convex constraints. Third, we integrate the learned normalizing flow with the DDPG algorithm. By design, a well-trained normalizing flow will transform policy output into a valid action without requiring an optimization solver. Empirically, our approach results in significantly fewer constraint violations (upto an order-of-magnitude for several instances) and is multiple times faster on a variety of continuous control tasks.

Decision-making in personalized medicine such as cancer therapy or critical care must often make choices for dosage combinations, i.e., multiple continuous treatments. Existing work for this task has modeled the effect of multiple treatments independently, while estimating the joint effect has received little attention but comes with non-trivial challenges. In this paper, we propose a novel method for reliable off-policy learning for dosage combinations. Our method proceeds along three steps: (1) We develop a tailored neural network that estimates the individualized dose-response function while accounting for the joint effect of multiple dependent dosages. (2) We estimate the generalized propensity score using conditional normalizing flows in order to detect regions with limited overlap in the shared covariate-treatment space. (3) We present a gradient-based learning algorithm to find the optimal, individualized dosage combinations. Here, we ensure reliable estimation of the policy value by avoiding regions with limited overlap. We finally perform an extensive evaluation of our method to show its effectiveness. To the best of our knowledge, ours is the first work to provide a method for reliable off-policy learning for optimal dosage combinations.

We introduce a new diffusion-based approach for shape completion on 3D range scans. Compared with prior deterministic and probabilistic methods, we strike a balance between realism, multi-modality, and high fidelity. We propose DiffComplete by casting shape completion as a generative task conditioned on the incomplete shape. Our key designs are two-fold. First, we devise a hierarchical feature aggregation mechanism to inject conditional features in a spatially-consistent manner. So, we can capture both local details and broader contexts of the conditional inputs to control the shape completion. Second, we propose an occupancy-aware fusion strategy in our model to enable the completion of multiple partial shapes and introduce higher flexibility on the input conditions. DiffComplete sets a new SOTA performance (e.g., 40% decrease on $l_1$ error) on two large-scale 3D shape completion benchmarks. Our completed shapes not only have a realistic outlook compared with the deterministic methods but also exhibit high similarity to the ground truths compared with the probabilistic alternatives. Further, DiffComplete has strong generalizability on objects of entirely unseen classes for both synthetic and real data, eliminating the need for model re-training in various applications.

Generative diffusion models have recently emerged as a leading approach for generating high-dimensional data. In this paper, we show that the dynamics of these models exhibit a spontaneous symmetry breaking that divides the generative dynamics into two distinct phases: 1) A linear steady-state dynamics around a central fixed-point and 2) an attractor dynamics directed towards the data manifold. These two "phases'' are separated by the change in stability of the central fixed-point, with the resulting window of instability being responsible for the diversity of the generated samples. Using both theoretical and empirical evidence, we show that an accurate simulation of the early dynamics does not significantly contribute to the final generation, since early fluctuations are reverted to the central fixed point. To leverage this insight, we propose a Gaussian late initialization scheme, which significantly improves model performance, achieving up to 3x FID improvements on fast samplers, while also increasing sample diversity (e.g., racial composition of generated CelebA images). Our work offers a new way to understand the generative dynamics of diffusion models that has the potential to bring about higher performance and less biased fast-samplers.

Many recent works in simulation-based inference (SBI) rely on deep generative models to approximate complex, high-dimensional posterior distributions. However, evaluating whether or not these approximations can be trusted remains a challenge. Most approaches evaluate the posterior estimator only in expectation over the observation space. This limits their interpretability and is not sufficient to identify for which observations the approximation can be trusted or should be improved. Building upon the well-known classifier two-sample test (C2ST), we introduce $\ell$-C2ST, a new method that allows for a local evaluation of the posterior estimator at any given observation. It offers theoretically grounded and easy to interpret -- e.g. graphical -- diagnostics, and unlike C2ST, does not require access to samples from the true posterior. In the case of normalizing flow-based posterior estimators, $\ell$-C2ST can be specialized to offer better statistical power, while being computationally more efficient. On standard SBI benchmarks, $\ell$-C2ST provides comparable results to C2ST and outperforms alternative local approaches such as coverage tests based on highest predictive density (HPD). We further highlight the importance of local evaluation and the benefit of interpretability of $\ell$-C2ST on a challenging application from computational neuroscience.

In this paper, we make a bold attempt toward an ambitious task: given a pre-trained classifier, we aim to reconstruct an image generator, without relying on any data samples. From a black-box perspective, this challenge seems intractable, since it inevitably involves identifying the inverse function for a classifier, which is, by nature, an information extraction process. As such, we resort to leveraging the knowledge encapsulated within the parameters of the neural network. Grounded on the theory of Maximum-Margin Bias of gradient descent, we propose a novel learning paradigm, in which the generator is trained to ensure that the convergence conditions of the network parameters are satisfied over the generated distribution of the samples. Empirical validation from various image generation tasks substantiates the efficacy of our strategy.

Normalizing flows are a class of deep generative models that are especially interesting for modeling probability distributions in physics, where the exact likelihood of flows allows reweighting to known target energy functions and computing unbiased observables. For instance, Boltzmann generators tackle the long-standing sampling problem in statistical physics by training flows to produce equilibrium samples of many-body systems such as small molecules and proteins. To build effective models for such systems, it is crucial to incorporate the symmetries of the target energy into the model, which can be achieved by equivariant continuous normalizing flows (CNFs). However, CNFs can be computationally expensive to train and generate samples from, which has hampered their scalability and practical application. In this paper, we introduce equivariant flow matching, a new training objective for equivariant CNFs that is based on the recently proposed optimal transport flow matching. Equivariant flow matching exploits the physical symmetries of the target energy for efficient, simulation-free training of equivariant CNFs. We demonstrate the effectiveness of flow matching on rotation and permutation invariant many-particle systems and a small molecule, alanine dipeptide, where for the first time we obtain a Boltzmann generator with significant sampling efficiency without relying on tailored internal coordinate featurization. Our results show that the equivariant flow matching objective yields flows with shorter integration paths, improved sampling efficiency, and higher scalability compared to existing methods.

Achieving a balance between image quality (precision) and diversity (recall) is a significant challenge in the domain of generative models. Current state-of-the-art models primarily rely on optimizing heuristics, such as the Fr\'echet Inception Distance. While recent developments have introduced principled methods for evaluating precision and recall, they have yet to be successfully integrated into the training of generative models. Our main contribution is a novel training method for generative models, such as Generative Adversarial Networks and Normalizing Flows, which explicitly optimizes a user-defined trade-off between precision and recall. More precisely, we show that achieving a specified precision-recall trade-off corresponds to minimizing a unique $f$-divergence from a family we call the \mbox{\em PR-divergences}. Conversely, any $f$-divergence can be written as a linear combination of PR-divergences and corresponds to a weighted precision-recall trade-off. Through comprehensive evaluations, we show that our approach improves the performance of existing state-of-the-art models like BigGAN in terms of either precision or recall when tested on datasets such as ImageNet.

In this work, we deepen on the use of normalizing flows for causal reasoning. Specifically, we first leverage recent results on non-linear ICA to show that causal models are identifiable from observational data given a causal ordering, and thus can be recovered using autoregressive normalizing flows (NFs). Second, we analyze different design and learning choices for *causal normalizing flows* to capture the underlying causal data-generating process. Third, we describe how to implement the *do-operator* in causal NFs, and thus, how to answer interventional and counterfactual questions. Finally, in our experiments, we validate our design and training choices through a comprehensive ablation study; compare causal NFs to other approaches for approximating causal models; and empirically demonstrate that causal NFs can be used to address real-world problems—where the presence of mixed discrete-continuous data and partial knowledge on the causal graph is the norm. The code for this work can be found at https://github.com/psanch21/causal-flows.

Prevailing theories of perception hypothesize that the brain implements perception via Bayesian inference in a generative model of the world. One prominent theory, the Neural Sampling Code (NSC), posits that neuronal responses to a stimulus represent samples from the posterior distribution over latent world state variables that cause the stimulus. Although theoretically elegant, NSC does not specify the exact form of the generative model or prescribe how to link the theory to recorded neuronal activity. Previous works assume simple generative models and test their qualitative agreement with neurophysiological data. Currently, there is no precise alignment of the normative theory with neuronal recordings, especially in response to natural stimuli, and a quantitative, experimental evaluation of models under NSC has been lacking. Here, we propose a novel formalization of NSC, that (a) allows us to directly fit NSC generative models to recorded neuronal activity in response to natural images, (b) formulate richer and more flexible generative models, and (c) employ standard metrics to quantitatively evaluate different generative models under NSC. Furthermore, we derive a stimulus-conditioned predictive model of neuronal responses from the trained generative model using our formalization that we compare to neural system identification models. We demonstrate our approach by fitting and comparing classical- and flexible deep learning-based generative models on population recordings from the macaque primary visual cortex (V1) to natural images, and show that the flexible models outperform classical models in both their generative- and predictive-model performance. Overall, our work is an important step towards a quantitative evaluation of NSC. It provides a framework that lets us \textit{learn} the generative model directly from neuronal population recordings, paving the way for an experimentally-informed understanding of probabilistic computational principles underlying perception and behavior.

Coupling normalizing flows allow for fast sampling and density evaluation, making them the tool of choice for probabilistic modeling of physical systems. However, the standard coupling architecture precludes endowing flows that operate on the Cartesian coordinates of atoms with the SE(3) and permutation invariances of physical systems. This work proposes a coupling flow that preserves SE(3) and permutation equivariance by performing coordinate splits along additional augmented dimensions. At each layer, the flow maps atoms' positions into learned SE(3) invariant bases, where we apply standard flow transformations, such as monotonic rational-quadratic splines, before returning to the original basis. Crucially, our flow preserves fast sampling and density evaluation, and may be used to produce unbiased estimates of expectations with respect to the target distribution via importance sampling. When trained on the DW4, LJ13, and QM9-positional datasets, our flow is competitive with equivariant continuous normalizing flows and diffusion models, while allowing sampling more than an order of magnitude faster. Moreover, to the best of our knowledge, we are the first to learn the full Boltzmann distribution of alanine dipeptide by only modeling the Cartesian positions of its atoms. Lastly, we demonstrate that our flow can be trained to approximately sample from the Boltzmann distribution of the DW4 and LJ13 particle systems using only their energy functions.