ICLR 2024 Papers

We present a neural network architecture designed to naturally learn a positional embedding and overcome the spectral bias towards lower frequencies faced by conventional implicit neural representation networks. Our proposed architecture, SPDER, is a simple MLP that uses an activation function composed of a sinusoidal multiplied by a sublinear function, called the damping function. The sinusoidal enables the network to automatically learn the positional embedding of an input coordinate while the damping passes on the actual coordinate value by preventing it from being projected down to within a finite range of values. Our results indicate that SPDERs speed up training by 10 times and converge to losses 1,500 to 50,000 times lower than that of the state-of-the-art for image representation. SPDER is also state-of-the-art in audio representation. The superior representation capability allows SPDER to also excel on multiple downstream tasks such as image super-resolution and video frame interpolation. We provide intuition as to why SPDER significantly improves fitting compared to that of other INR methods while requiring no hyperparameter tuning or preprocessing. See code at https://github.com/katop1234/SPDER.

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward continuous denoising process, which can be described by a time-dependent vector field and is used as a generative model. In the original formulation of the diffusion model, this vector field is assumed to be the score function (i.e. it is the gradient of the log-probability at a given time in the diffusion process). Curiously, on the practical side, most studies on diffusion models implement this vector field as a neural network function and do not constrain it be the gradient of some energy function (that is, most studies do not constrain the vector field to be conservative). Even though some studies investigated empirically whether such a constraint will lead to a performance gain, they lead to contradicting results and failed to provide analytical results. Here, we provide three analytical results regarding the extent of the modeling freedom of this vector field. {Firstly, we propose a novel decomposition of vector fields into a conservative component and an orthogonal component which satisfies a given (gauge) freedom. Secondly, from this orthogonal decomposition, we show that exact density estimation and exact sampling is achieved when the conservative component is exactly equals to the true score and therefore conservativity is neither necessary nor sufficient to obtain exact density estimation and exact sampling. Finally, we show that when it comes to inferring local information of the data manifold, constraining the vector field to be conservative is desirable.

Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body --- two close positions in a higher-level mesh correspond to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods. Our code is available at https://github.com/yuyudeep/hcmt.

Recent large language models (LLMs) have witnessed significant advancement in various tasks, including mathematical reasoning and theorem proving. As these two tasks require strict and formal multi-step inference, they are appealing domains for exploring the reasoning ability of LLMs but still face important challenges. Previous studies such as Chain-of-Thought (CoT) have revealed the effectiveness of intermediate steps guidance. However, such step-wise annotation requires heavy labor, leading to insufficient training steps for current benchmarks. To fill this gap, this work introduces MUSTARD, a data generation framework that masters uniform synthesis of theorem and proof data of high quality and diversity. MUSTARD synthesizes data in three stages: (1) It samples a few mathematical concept seeds as the problem category. (2) Then, it prompts a generative language model with the sampled concepts to obtain both the problems and their step-wise formal solutions. (3) Lastly, the framework utilizes a proof assistant (e.g., Lean Prover) to filter the valid proofs. With the proposed MUSTARD, we present a theorem-and-proof benchmark MUSTARDSAUCE with 5,866 valid data points. Each data point contains an informal statement, an informal proof, and a translated formal proof that passes the prover validation. We perform extensive analysis and demonstrate that MUSTARD generates validated high-quality step-by-step data. We further apply the MUSTARDSAUCE for fine-tuning smaller language models. The fine-tuned Llama 2-7B achieves a 15.41% average relative performance gain in automated theorem proving, and 8.18% in math word problems. Codes and data are available at https://github.com/Eleanor-H/MUSTARD.

Forward- or reverse-mode automatic differentiation (AD) is a popular algorithm for computing the derivative of a function expressed by a program. AD always outputs the correct derivative if a program does not use any non-differentiable functions and control flows; however, it may return an arbitrary value otherwise. In this work, we investigate what AD computes for neural networks that may contain non-differentiable functions such as ReLU and maxpools. We first prove that AD always returns a generalized derivative called a Clarke subderivative for networks with pointwise activation functions, if the minibatch size is one and all non-differentiable neurons have distinct bias parameters. We show that the same conclusion does not hold otherwise, but does hold under some mild sufficient conditions. We also prove similar results for more general networks that can use maxpools and bias parameters shared across different neurons. We empirically check our sufficient conditions over popular network architectures and observe that AD almost always computes a Clarke subderivative in practical learning setups.

Learning Nash equilibria (NE) in games has garnered significant attention, particularly in the context of training Generative Adversarial Networks (GANs) and multi-agent Reinforcement Learning. The current state-of-the-art in efficiently learning games focuses on landscapes that meet the (weak) Minty property or games characterized by a unique function, often referred to as potential games. A significant challenge in this domain is that computing Nash equilibria is a computationally intractable task [Daskalakis et al. 2009]. In this paper we focus on bimatrix games (A,B) called rank-1. These are games in which the sum of the payoff matrices A+B is a rank 1 matrix; note that standard zero-sum games are rank 0. We show that optimistic gradient descent/ascent converges to an \epsilon-approximate NE after 1/\epsilon^2 log(1/\epsilon) iterates in rank-1 games. We achieve this by leveraging structural results about the NE landscape of rank-1 games Adsul et al. 2021. Notably, our approach bypasses the fact that these games do not satisfy the MVI property.

Fine-tuning on generalized tasks such as instruction following, code generation, and mathematics has been shown to enhance language models' performance on a range of tasks. Nevertheless, explanations of how such fine-tuning influences the internal computations in these models remain elusive. We study how fine-tuning affects the internal mechanisms implemented in language models. As a case study, we explore the property of entity tracking, a crucial facet of language comprehension, where models fine-tuned on mathematics have substantial performance gains. We identify a mechanism that enables entity tracking and show that (i) both the original model and its fine-tuned version implement entity tracking with the same circuit. In fact, the entity tracking circuit of the fine-tuned version performs better than the full original model. (ii) The circuits of all the models implement roughly the same functionality, that is entity tracking is performed by tracking the position of the correct entity in both the original model and its fine-tuned version. (iii) Performance boost in the fine-tuned model is primarily attributed to its improved ability to handle positional information. To uncover these findings, we employ two methods: DCM, which automatically detects model components responsible for specific semantics, and CMAP, a new approach for patching activations across models to reveal improved mechanisms. Our findings suggest that fine-tuning enhances, rather than fundamentally alters, the mechanistic operation of the model.

Recent works have empirically analyzed in-context learning and shown that transformers trained on synthetic linear regression tasks can learn to implement ridge regression, which is the Bayes-optimal predictor, given sufficient capacity (Akyurek et al., 2023), while one-layer transformers with linear self-attention and no MLP layer will learn to implement one step of gradient descent (GD) on a least-squares linear regression objective (von Oswald et al., 2022). However, the theory behind these observations remains poorly understood. We theoretically study transformers with a single layer of linear self-attention, trained on synthetic noisy linear regression data. First, we mathematically show that when the covariates are drawn from a standard Gaussian distribution, the one-layer transformer which minimizes the pre-training loss will implement a single step of GD on the least-squares linear regression objective. Then, we find that changing the distribution of the covariates and weight vector to a non-isotropic Gaussian distribution has a strong impact on the learned algorithm: the global minimizer of the pre-training loss now implements a single step of $\textit{pre-conditioned}$ GD. However, if only the distribution of the responses is changed, then this does not have a large effect on the learned algorithm: even when the response comes from a more general family of $\textit{nonlinear}$ functions, the global minimizer of the pre-training loss still implements a single step of GD on a least-squares linear regression objective.

Diffusion models may be viewed as hierarchical variational autoencoders (VAEs) with two improvements: parameter sharing for the conditionals in the generative process and efficient computation of the loss as independent terms over the hierarchy. We consider two changes to the diffusion model that retain these advantages while adding flexibility to the model. Firstly, we introduce a data and depth-dependent mean function in the diffusion process, which leads to a modified diffusion loss. Our proposed framework, DiffEnc, achieves a statistically significant improvement in likelihood on CIFAR-10. Secondly, we let the ratio of the noise variance of the reverse encoder process and the generative process be a free weight parameter rather than being fixed to one. This leads to theoretical insights: For a finite depth hierarchy, the evidence lower bound (ELBO) can be used as an objective for a weighted diffusion loss approach and for optimizing the noise schedule specifically for inference. For the infinite-depth hierarchy, on the other hand, the weight parameter has to be one to have a well-defined ELBO.

Adaptive regularization based optimization methods such as full-matrix Adagrad which use gradient second-moment information hold significant potential for fast convergence in deep neural network (DNN) training, but are memory intensive and computationally demanding for large neural nets. We develop a technique called Combining AxeS PReconditioners (CASPR), which optimizes matrix-shaped DNN parameters by finding different preconditioners for each mode/axis of the parameter and combining them using a Kronecker-sum based approximation. We show tighter convergence guarantees in stochastic optimization compared to a Kronecker product based preconditioner, Shampoo, which arises as a special case of CASPR. Furthermore, our experiments demonstrates that CASPR approximates the gradient second-moment matrix in full-matrix Adagrad more accurately, and shows significant improvement in training and generalization performance compared to existing practical adaptive regularization based methods such as Shampoo and Adam in a variety of tasks including graph neural network on OGBG-molpcba, Transformer on a universal dependencies dataset and auto-regressive large language modeling on C4 dataset.

We propose to replace vector quantization (VQ) in the latent representation of VQ-VAEs with a simple scheme termed finite scalar quantization (FSQ), where we project the VAE representation down to a few dimensions (typically less than 10). Each dimension is quantized to a small set of fixed values, leading to an (implicit) codebook given by the product of these sets. By appropriately choosing the number of dimensions and values each dimension can take, we obtain the same codebook size as in VQ. On top of such discrete representations, we can train the same models that have been trained on VQ-VAE representations. For example, autoregressive and masked transformer models for image generation, multimodal generation, and dense prediction computer vision tasks. Concretely, we employ FSQ with MaskGIT for image generation, and with UViM for depth estimation, colorization, and panoptic segmentation. Despite the much simpler design of FSQ, we obtain competitive performance in all these tasks. We emphasize that FSQ does not suffer from codebook collapse and does not need the complex machinery employed in VQ (commitment losses, codebook reseeding, code splitting, entropy penalties, etc.) to learn expressive discrete representations.

The proliferation of face forgery techniques has raised significant concerns within society, thereby motivating the development of face forgery detection methods. These methods aim to distinguish forged faces from genuine ones and have proven effective in practical applications. However, this paper introduces a novel and previously unrecognized threat in face forgery detection scenarios caused by backdoor attack. By embedding backdoors into models and incorporating specific trigger patterns into the input, attackers can deceive detectors into producing erroneous predictions for forged faces. To achieve this goal, this paper proposes \emph{Poisoned Forgery Face} framework, which enables clean-label backdoor attacks on face forgery detectors. Our approach involves constructing a scalable trigger generator and utilizing a novel convolving process to generate translation-sensitive trigger patterns. Moreover, we employ a relative embedding method based on landmark-based regions to enhance the stealthiness of the poisoned samples. Consequently, detectors trained on our poisoned samples are embedded with backdoors. Notably, our approach surpasses SoTA backdoor baselines with a significant improvement in attack success rate (+16.39\% BD-AUC) and reduction in visibility (-12.65\% $L_\infty$). Furthermore, our attack exhibits promising performance against backdoor defenses. We anticipate that this paper will draw greater attention to the potential threats posed by backdoor attacks in face forgery detection scenarios. Our codes will be made available at \url{https://github.com/JWLiang007/PFF}.

Quantum kernels hold great promise for offering computational advantages over classical learners, with the effectiveness of these kernels closely tied to the design of the feature map. However, the challenge of designing effective quantum feature maps for real-world datasets, particularly in the absence of sufficient prior information, remains a significant obstacle. In this study, we present a data-driven approach that automates the design of problem-specific quantum feature maps. Our approach leverages feature-selection techniques to handle high-dimensional data on near-term quantum machines with limited qubits, and incorporates a deep neural predictor to efficiently evaluate the performance of various candidate quantum kernels. Through extensive numerical simulations on different datasets, we demonstrate the superiority of our proposal over prior methods, especially for the capability of eliminating the kernel concentration issue and identifying the feature map with prediction advantages. Our work not only unlocks the potential of quantum kernels for enhancing real-world tasks, but also highlights the substantial role of deep learning in advancing quantum machine learning.

Excitatory point processes (i.e., event flows) occurring over dynamic graphs (i.e., evolving topologies) provide a fine-grained model to capture how discrete events may spread over time and space. How to effectively steer the event flows by modifying the dynamic graph structures presents an interesting problem, motivated by curbing the spread of infectious diseases through strategically locking down cities to mitigating traffic congestion via traffic light optimization. To address the intricacies of planning and overcome the high dimensionality inherent to such decision-making problems, we design an Amortized Network Interventions (ANI) framework, allowing for the pooling of optimal policies from history and other contexts while ensuring a permutation equivalent property. This property enables efficient knowledge transfer and sharing across diverse contexts. Each task is solved by an H-step lookahead model-based reinforcement learning, where neural ODEs are introduced to model the dynamics of the excitatory point processes. Instead of simulating rollouts from the dynamics model, we derive an analytical mean-field approximation for the event flows given the dynamics, making the online planning more efficiently solvable. We empirically illustrate that this ANI approach substantially enhances policy learning for unseen dynamics and exhibits promising outcomes in steering event flows through network intervention using synthetic and real COVID datasets.

Recently, GPT-4 has become the de facto evaluator for long-form text generated by large language models (LLMs). However, for practitioners and researchers with large and custom evaluation tasks, GPT-4 is unreliable due to its closed-source nature, uncontrolled versioning, and prohibitive costs. In this work, we propose PROMETHEUS a fully open-source LLM that is on par with GPT-4’s evaluation capabilities when the appropriate reference materials (reference answer, score rubric) are accompanied. For this purpose, we construct a new dataset – FEEDBACK COLLECTION – that consists of 1K fine-grained score rubrics, 20K instructions, and 100K natural language feedback generated by GPT-4. Using the FEEDBACK COLLECTION, we train PROMETHEUS, a 13B evaluation-specific LLM that can assess any given response based on novel and unseen score rubrics and reference materials provided by the user. Our dataset’s versatility and diversity make our model generalize to challenging real-world criteria, such as prioritizing conciseness, child-readability, or varying levels of formality. We show that PROMETHEUS shows a stronger correlation with GPT-4 evaluation compared to ChatGPT on seven evaluation benchmarks (Two Feedback Collection testsets, MT Bench, Vicuna Bench, Flask Eval, MT Bench Human Judgment, and HHH Alignment), showing the efficacy of our model and dataset design. During human evaluation with hand-crafted score rubrics, PROMETHEUS shows a Pearson correlation of 0.897 with human evaluators, which is on par with GPT-4-0613 (0.882), and greatly outperforms ChatGPT (0.392). Remarkably, when assessing the quality of the generated feedback, PROMETHEUS demonstrates a win rate of 58.62% when compared to GPT-4 evaluation and a win rate of 79.57% when compared to ChatGPT evaluation. Our findings suggests that by adding reference materials and training on GPT-4 feedback, we can obtain effective open-source evaluator LMs.

Hyperspectral imaging (HSI) technology captures spectral information across a broad wavelength range, providing richer pixel features compared to traditional color images with only three channels. Although pixel classification in HSI has been extensively studied, especially using graph convolution neural networks (GCNs), quantifying epistemic and aleatoric uncertainties associated with the HSI classification (HSIC) results remains an unexplored area. These two uncertainties are effective for out-of-distribution (OOD) and misclassification detection, respectively. In this paper, we adapt two advanced uncertainty quantification models, evidential GCNs (EGCN) and graph posterior networks (GPN), designed for node classifications in graphs, into the realm of HSIC. We first reveal theoretically that a popular uncertainty cross-entropy (UCE) loss function is insufficient to produce good epistemic uncertainty when learning EGCNs. To mitigate the limitations, we propose two regularization terms. One leverages the inherent property of HSI data where each feature vector is a linear combination of the spectra signatures of the confounding materials, while the other is the total variation (TV) regularization to enforce the spatial smoothness of the evidence with edge-preserving. We demonstrate the effectiveness of the proposed regularization terms on both EGCN and GPN on three real-world HSIC datasets for OOD and misclassification detection tasks. The code is available at GitHub.

Large language models (LLMs) have revolutionized natural language processing tasks. However, their practical deployment is hindered by their immense memory and computation requirements. Although recent post-training quantization (PTQ) methods are effective in reducing memory footprint and improving the computational efficiency of LLM, they hand-craft quantization parameters, leading to low performance, especially in extremely low-bit quantization. To tackle this issue, we introduce an Omnidirectionally calibrated Quantization ($\textbf{OmniQuant}$) technique for LLMs, which achieves good performance in diverse quantization settings while maintaining the computational efficiency of PTQ by efficiently optimizing various quantization parameters. OmniQuant comprises two innovative components including Learnable Weight Clipping (LWC) and Learnable Equivalent Transformation (LET). LWC modulates the extreme values of weights by optimizing the clipping threshold. Meanwhile, LET tackles activation outliers by shifting the challenge of quantization from activations to weights. Operating within a differentiable framework using block-wise error minimization, OmniQuant can optimize the quantization process efficiently for both weight-only and weight-activation quantization. For instance, the LLaMA-2 model family size 7-70B can be processed with OmniQuant on a single A100-40G GPU within 1-16 hours using 128 samples. Extensive experiments validate OmniQuant's superior performance across diverse quantization configurations such as W4A4 (4-bit weight, 4-bit activation), W6A6, W4A16, W3A16, and W2A16. Additionally, OmniQuant demonstrates effectiveness in instruction-tuned models and delivers notable improvements in inference speed and memory reduction on real devices. Codes are available at \url{https://github.com/OpenGVLab/OmniQuant}.

Two lines of work are taking the central stage in AI research. On the one hand, the community is making increasing efforts to build models that discard spurious correlations and generalize better in novel test environments. Unfortunately, the hard lesson so far is that no proposal convincingly outperforms a simple empirical risk minimization baseline. On the other hand, large language models (LLMs) have erupted as algorithms able to learn in-context, generalizing on-the-fly to eclectic contextual circumstances that users enforce by means of prompting. In this paper, we argue that context is environment, and posit that in-context learning holds the key to better domain generalization. Via extensive theory and experiments, we show that paying attention to context$\unicode{x2013}\unicode{x2013}$unlabeled examples as they arrive$\unicode{x2013}\unicode{x2013}$allows our proposed In-Context Risk Minimization (ICRM) algorithm to zoom-in on the test environment risk minimizer, leading to significant out-of-distribution performance improvements. Furthermore, training with context helps the model learn a better featurizer. From all of this, two messages are worth taking home. Researchers in domain generalization should consider environment as context, and harness the adaptive power of in-context learning. Researchers in LLMs should consider context as environment, to better structure data towards generalization. Code is available at https://github.com/facebookresearch/ICRM.

Link prediction, a fundamental task on graphs, has proven indispensable in various applications, e.g., friend recommendation, protein analysis, and drug interaction prediction. However, since datasets span a multitude of domains, they could have distinct underlying mechanisms of link formation. Evidence in existing literature underscores the absence of a universally best algorithm suitable for all datasets. In this paper, we endeavor to explore principles of link prediction across diverse datasets from a data-centric perspective. We recognize three fundamental factors critical to link prediction: local structural proximity, global structural proximity, and feature proximity. We then unearth relationships among those factors where (i) global structural proximity only shows effectiveness when local structural proximity is deficient. (ii) The incompatibility can be found between feature and structural proximity. Such incompatibility leads to GNNs for Link Prediction (GNN4LP) consistently underperforming on edges where the feature proximity factor dominates. Inspired by these new insights from a data perspective, we offer practical instruction for GNN4LP model design and guidelines for selecting appropriate benchmark datasets for more comprehensive evaluations.