ICLR 2024 论文列表

The behavior of neural networks still remains opaque, and a recently widely noted phenomenon is that networks often achieve similar performance when initialized with different random parameters. This phenomenon has attracted significant attention in measuring the similarity between features learned by distinct networks. However, feature similarity could be vague in describing the same feature since equivalent features hardly exist. In this paper, we expand the concept of equivalent feature and provide the definition of what we call *functionally equivalent features*. These features produce equivalent output under certain transformations. Using this definition, we aim to derive a more intrinsic metric for the so-called *feature complexity* regarding the redundancy of features learned by a neural network at each layer. We offer a formal interpretation of our approach through the lens of category theory, a well-developed area in mathematics. To quantify the feature complexity, we further propose an efficient algorithm named Iterative Feature Merging. Our experimental results validate our ideas and theories from various perspectives. We empirically demonstrate that the functionally equivalence widely exists among different features learned by the same neural network and we could reduce the number of parameters of the network without affecting the performance. We have also drawn several interesting empirical findings, including: 1) the larger the network, the more redundant features it learns; 2) in particular, we show how to prune the networks based on our finding using direct equivalent feature merging, without fine-tuning which is often needed in peer network pruning methods; 3) same structured networks with higher feature complexity achieve better performance; 4) through the layers of a neural network, the feature complexity first increase then decrease; 5) for the image classification task, a group of functionally equivalent features may correspond to a specific semantic meaning. Source code will be made publicly available.

Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the theoretical underpinnings remain far from mature. In this work, we develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models in discrete time, assuming access to $\ell_2$-accurate estimates of the (Stein) score functions. For a popular deterministic sampler (based on the probability flow ODE), we establish a convergence rate proportional to $1/T$ (with $T$ the total number of steps), improving upon past results; for another mainstream stochastic sampler (i.e., a type of the denoising diffusion probabilistic model), we derive a convergence rate proportional to $1/\sqrt{T}$, matching the state-of-the-art theory. Imposing only minimal assumptions on the target data distribution (e.g., no smoothness assumption is imposed), our results characterize how $\ell_2$ score estimation errors affect the quality of the data generation process. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach without resorting to toolboxes for SDEs and ODEs.

By employing neural networks (NN) to learn input-solution mappings and passing a new input through the learned mapping to obtain a solution instantly, recent studies have shown remarkable speed improvements over iterative algorithms for solving optimization problems. Meanwhile, they also highlight methodological challenges to be addressed. In particular, general non-convex problems often present multiple optimal solutions for identical inputs, signifying a complex, multi-valued input-solution mapping. Conventional learning techniques, primarily tailored to learn single-valued mappings, struggle to train NNs to accurately decipher multi-valued ones, leading to inferior solutions. We address this fundamental issue by developing a generative learning approach using a rectified flow (RectFlow) model built upon ordinary differential equations. In contrast to learning input-solution mapping, we learn the mapping from input to solution distribution, exploiting the universal approximation capability of the RectFlow model. Upon receiving a new input, we employ the trained RectFlow model to sample high-quality solutions from the input-dependent distribution it has learned. Our approach outperforms conceivable GAN and Diffusion models in terms of training stability and run-time complexity. We provide a detailed characterization of the optimality loss and runtime complexity associated with our generative approach. Simulation results for solving non-convex problems show that our method achieves significantly better solution optimality than recent NN schemes, with comparable feasibility and speedup performance.

We explore the problem of generating minority samples using diffusion models. The minority samples are instances that lie on low-density regions of a data manifold. Generating a sufficient number of such minority instances is important, since they often contain some unique attributes of the data. However, the conventional generation process of the diffusion models mostly yields majority samples (that lie on high-density regions of the manifold) due to their high likelihoods, making themselves ineffective and time-consuming for the minority generating task. In this work, we present a novel framework that can make the generation process of the diffusion models focus on the minority samples. We first highlight that Tweedie's denoising formula yields favorable results for majority samples. The observation motivates us to introduce a metric that describes the uniqueness of a given sample. To address the inherent preference of the diffusion models w.r.t. the majority samples, we further develop *minority guidance*, a sampling technique that can guide the generation process toward regions with desired likelihood levels. Experiments on benchmark real datasets demonstrate that our minority guidance can greatly improve the capability of generating high-quality minority samples over existing generative samplers. We showcase that the performance benefit of our framework persists even in demanding real-world scenarios such as medical imaging, further underscoring the practical significance of our work. Code is available at https://github.com/soobin-um/minority-guidance.

Arguably one of the thorniest problems in game theory is that of equilibrium selection. Specifically, in the presence of multiple equilibria do self-interested learning dynamics typically select the socially optimal ones? We study a rich class of continuous-time no-regret dynamics in potential games (PGs). Our class of dynamics, *Q-Replicator Dynamics* (QRD), include gradient descent (GD), log-barrier and replicator dynamics (RD) as special cases. We start by establishing *pointwise convergence* of all QRD to Nash equilibria in almost all PGs. In the case of GD, we show a tight average case performance within a factor of two of optimal, for a class of symmetric $2\times2$ potential games with unbounded Price of Anarchy (PoA). Despite this positive result, we show that GD is not always the optimal choice even in this restricted setting. Specifically, GD outperforms RD, if and only if *risk-* and *payoff-dominance* equilibria coincide. Finally, we experimentally show how these insights extend to all QRD dynamics and that unbounded gaps between average case performance and PoA analysis are common even in larger settings.

Recent studies have introduced a new class of generative models for synthesizing implicit neural representations (INRs) that capture arbitrary continuous signals in various domains. These models opened the door for domain-agnostic generative models, but they often fail to achieve high-quality generation. We observed that the existing methods generate the weights of neural networks to parameterize INRs and evaluate the network with fixed positional embeddings (PEs). Arguably, this architecture limits the expressive power of generative models and results in low-quality INR generation. To address this limitation, we propose Domain-agnostic Latent Diffusion Model for INRs (DDMI) that generates adaptive positional embeddings instead of neural networks' weights. Specifically, we develop a Discrete-to-continuous space Variational AutoEncoder (D2C-VAE) that seamlessly connects discrete data and continuous signal functions in the shared latent space. Additionally, we introduce a novel conditioning mechanism for evaluating INRs with the hierarchically decomposed PEs to further enhance expressive power. Extensive experiments across four modalities, \eg, 2D images, 3D shapes, Neural Radiance Fields, and videos, with seven benchmark datasets, demonstrate the versatility of DDMI and its superior performance compared to the existing INR generative models. Code is available at \href{https://github.com/mlvlab/DDMI}{https://github.com/mlvlab/DDMI}.

In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and capturing both global and local graph structures simultaneously. To overcome these issues, we introduce a method that generates a graph by progressively expanding a single node to a target graph. In each step, nodes and edges are added in a localized manner through denoising diffusion, building first the global structure, and then refining the local details. The local generation avoids modeling the entire joint distribution over all node pairs, achieving substantial computational savings with subquadratic runtime relative to node count while maintaining high expressivity through multiscale generation. Our experiments show that our model achieves state-of-the-art performance on well-established benchmark datasets while successfully scaling to graphs with at least 5000 nodes. Our method is also the first to successfully extrapolate to graphs outside of the training distribution, showcasing a much better generalization capability over existing methods.

We present a scalable method to build a high quality instruction following language model by automatically labelling human-written text with corresponding instructions. Our approach, named instruction backtranslation, starts with a language model finetuned on a small amount of seed data, and a given web corpus. The seed model is used to construct training examples by generating instruction prompts for web documents (self-augmentation), and then selecting high quality examples from among these candidates (self-curation). This data is then used to finetune a stronger model. Finetuning LLaMa on two iterations of our approach yields a model that outperforms all other LLaMa-based models on the Alpaca leaderboard not relying on distillation data, demonstrating highly effective self-alignment.

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each task. Most inverse tasks can be formulated as inferring a posterior distribution over data (e.g., a full image) given a measurement (e.g., a masked image). This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. To cope with this challenge, we propose a variational approach that by design seeks to approximate the true posterior distribution. We show that our approach naturally leads to regularization by denoising diffusion process (RED-diff) where denoisers at different timesteps concurrently impose different structural constraints over the image. To gauge the contribution of denoisers from different timesteps, we propose a weighting mechanism based on signal-to-noise-ratio (SNR). Our approach provides a new variational perspective for solving inverse problems with diffusion models, allowing us to formulate sampling as stochastic optimization, where one can simply apply off-the-shelf solvers with lightweight iterates. Our experiments for various linear and nonlinear image restoration tasks demonstrate the strengths of our method compared with state-of-the-art sampling-based diffusion models. The code is available online \footnote{\url{https://github.com/NVlabs/RED-diff}}.

Diffusion or flow-based models are powerful generative paradigms that are notoriously hard to sample as samples are defined as solutions to high-dimensional Ordinary or Stochastic Differential Equations (ODEs/SDEs) which require a large Number of Function Evaluations (NFE) to approximate well. Existing methods to alleviate the costly sampling process include model distillation and designing dedicated ODE solvers. However, distillation is costly to train and sometimes can deteriorate quality, while dedicated solvers still require relatively large NFE to produce high quality samples. In this paper we introduce ``Bespoke solvers'', a novel framework for constructing custom ODE solvers tailored to the ODE of a given pre-trained flow model. Our approach optimizes an order consistent and parameter-efficient solver (e.g., with 80 learnable parameters), is trained for roughly 1\% of the GPU time required for training the pre-trained model, and significantly improves approximation and generation quality compared to dedicated solvers. For example, a Bespoke solver for a CIFAR10 model produces samples with Fréchet Inception Distance (FID) of 2.73 with 10 NFE, and gets to 1\% of the Ground Truth (GT) FID (2.59) for this model with only 20 NFE. On the more challenging ImageNet-64$\times$64, Bespoke samples at 2.2 FID with 10 NFE, and gets within 2\% of GT FID (1.71) with 20 NFE.

We present ``Magic123'', a two-stage coarse-to-fine approach for high-quality, textured 3D mesh generation from a single image in the wild using *both 2D and 3D priors*. In the first stage, we optimize a neural radiance field to produce a coarse geometry. In the second stage, we adopt a memory-efficient differentiable mesh representation to yield a high-resolution mesh with a visually appealing texture. In both stages, the 3D content is learned through reference-view supervision and novel-view guidance by a joint 2D and 3D diffusion prior. We introduce a trade-off parameter between the 2D and 3D priors to control the details and 3D consistencies of the generation. Magic123 demonstrates a significant improvement over previous image-to-3D techniques, as validated through extensive experiments on diverse synthetic and real-world images.

We show that language model finetuning can be improved, sometimes dramatically, with a simple augmentation. NEFTune adds noise to the embedding vectors during training. Standard finetuning of LLaMA-2-7B using Alpaca achieves $29.79$\% on AlpacaEval, which rises to $64.69$\% using noisy embeddings. NEFTune also improves over strong baselines on modern instruction datasets. Models trained with Evol-Instruct see a $10$\% improvement, with ShareGPT an $8$\% improvement, and with OpenPlatypus an $8$\% improvement. Even powerful models further refined with RLHF such as LLaMA-2-Chat benefit from additional training with NEFTune. Particularly, we see these improvements on the conversational abilities of the instruction model and not on traditional tasks like those on the OpenLLM Leaderboard, where performance is the same.

Classifier-free guidance (CFG) is a pivotal technique for balancing the diversity and fidelity of samples in conditional diffusion models. This approach involves utilizing a single model to jointly optimize the conditional score predictor and unconditional score predictor, eliminating the need for additional classifiers. It delivers impressive results and can be employed for continuous and discrete condition representations. However, when the condition is continuous, it prompts the question of whether the trade-off can be further enhanced. Our proposed inner classifier-free guidance (ICFG) provides an alternative perspective on the CFG method when the condition has a specific structure, demonstrating that CFG represents a first-order case of ICFG. Additionally, we offer a second-order implementation, highlighting that even without altering the training policy, our second-order approach can introduce new valuable information and achieve an improved balance between fidelity and diversity for Stable Diffusion.