NeurIPS 2024 Papers

In this paper, we study Adam in non-convex smooth scenarios with potential unbounded gradients and affine variance noise. We consider a general noise model which governs affine variance noise, bounded noise, and sub-Gaussian noise. We show that Adam with a specific hyper-parameter setup can find a stationary point with a $\mathcal{O}(\text{poly}(\log T)/\sqrt{T})$ rate in high probability under this general noise model where $T$ denotes total number iterations, matching the lower rate of stochastic first-order algorithms up to logarithm factors. We also provide a probabilistic convergence result for Adam under a generalized smooth condition which allows unbounded smoothness parameters and has been illustrated empirically to capture the smooth property of many practical objective functions more accurately.

We analyze the capabilities of Transformer language models in learning compositional discrete tasks. To this end, we evaluate training LLaMA models and prompting GPT-4 and Gemini on four tasks demanding to learn a composition of several discrete sub-tasks. In particular, we measure how well these models can reuse primitives observable in the sub-tasks to learn the composition task. Our results indicate that compositional learning in state-of-the-art Transformer language models is highly sample inefficient: LLaMA requires more data samples than relearning all sub-tasks from scratch to learn the compositional task; in-context prompting with few samples is unreliable and fails at executing the sub-tasks or correcting the errors in multi-round code generation. Further, by leveraging complexity theory, we support these findings with a theoretical analysis focused on the sample inefficiency of gradient descent in memorizing feedforward models. We open source our code at https://github.com/IBM/limitations-lm-algorithmic-compositional-learning.

Rewards are a critical aspect of formulating Reinforcement Learning (RL) problems; often, one may be interested in testing multiple reward functions, or the problem may naturally involve multiple rewards. In this study, we investigate the _Multi-Reward Best Policy Identification_ (MR-BPI) problem, where the goal is to determine the best policy for all rewards in a given set $\mathcal{R}$ with minimal sample complexity and a prescribed confidence level. We derive a fundamental instance-specific lower bound on the sample complexity required by any Probably Correct (PC) algorithm in this setting. This bound guides the design of an optimal exploration policy attaining minimal sample complexity. However, this lower bound involves solving a hard non-convex optimization problem. We address this challenge by devising a convex approximation, enabling the design of sample-efficient algorithms. We propose MR-NaS, a PC algorithm with competitive performance on hard-exploration tabular environments. Extending this approach to Deep RL (DRL), we also introduce DBMR-BPI, an efficient algorithm for model-free exploration in multi-reward settings.

Graph generation has been dominated by autoregressive models due to their simplicity and effectiveness, despite their sensitivity to ordering. Yet diffusion models have garnered increasing attention, as they offer comparable performance while being permutation-invariant. Current graph diffusion models generate graphs in a one-shot fashion, but they require extra features and thousands of denoising steps to achieve optimal performance. We introduce PARD, a Permutation-invariant Auto Regressive Diffusion model that integrates diffusion models with autoregressive methods. PARD harnesses the effectiveness and efficiency of the autoregressive model while maintaining permutation invariance without ordering sensitivity. Specifically, we show that contrary to sets, elements in a graph are not entirely un-ordered and there is a unique partial order for nodes and edges. With this partial order, PARD generates a graph in a block-by-block, autoregressive fashion, where each block’s probability is conditionally modeled by a shared diffusion model with an equivariant network. To ensure efficiency while being expressive, we further propose a higher-order graph transformer, which integrates transformer with PPGN (Maronet al., 2019). Like GPT, we extend the higher-order graph transformer to support parallel training of all blocks. Without any extra features, PARD achieves state-of-the-art performance on molecular and non-molecular datasets, and scales to large datasets like MOSES containing 1.9M molecules.

Synthetic face recognition (SFR) aims to generate synthetic face datasets that mimic the distribution of real face data, which allows for training face recognition models in a privacy-preserving manner. Despite the remarkable potential of diffusion models in image generation, current diffusion-based SFR models struggle with generalization to real-world faces. To address this limitation, we outline three key objectives for SFR: (1) promoting diversity across identities (inter-class diversity), (2) ensuring diversity within each identity by injecting various facial attributes (intra-class diversity), and (3) maintaining identity consistency within each identity group (intra-class identity preservation). Inspired by these goals, we introduce a diffusion-fueled SFR model termed $\text{ID}^3$. $\text{ID}^3$ employs an ID-preserving loss to generate diverse yet identity-consistent facial appearances. Theoretically, we show that minimizing this loss is equivalent to maximizing the lower bound of an adjusted conditional log-likelihood over ID-preserving data. This equivalence motivates an ID-preserving sampling algorithm, which operates over an adjusted gradient vector field, enabling the generation of fake face recognition datasets that approximate the distribution of real-world faces. Extensive experiments across five challenging benchmarks validate the advantages of $\text{ID}^3$.

Large language models (LLMs) have achieved significant success across various domains. However, training these LLMs typically involves substantial memory and computational costs during both forward and backward propagation. While parameter-efficient fine-tuning (PEFT) considerably reduces the training memory associated with parameters, it does not address the significant computational costs and activation memory. In this paper, we propose Dropping Backward Propagation (DropBP), a novel approach designed to reduce computational costs and activation memory while maintaining accuracy. DropBP randomly drops layers during backward propagation, which is essentially equivalent to training shallow submodules generated by undropped layers and residual connections. Additionally, DropBP calculates the sensitivity of each layer to assign an appropriate drop rate, thereby stabilizing the training process. DropBP is not only applicable to full fine-tuning but can also be orthogonally integrated with all types of PEFT by dropping layers during backward propagation. Specifically, DropBP can reduce training time by 44% with comparable accuracy to the baseline, accelerate convergence to the same perplexity by 1.5$\times$, and enable training with a sequence length 6.2$\times$ larger on a single NVIDIA-A100 GPU. Furthermore, our DropBP enabled a throughput increase of 79% on a NVIDIA A100 GPU and 117% on an Intel Gaudi2 HPU. The code is available at [https://github.com/WooSunghyeon/dropbp](https://github.com/WooSunghyeon/dropbp).

Unsupervised object detection using deep neural networks is typically a difficult problem with few to no guarantees about the learned representation. In this work we present the first unsupervised object detection method that is theoretically guaranteed to recover the true object positions up to quantifiable small shifts. We develop an unsupervised object detection architecture and prove that the learned variables correspond to the true object positions up to small shifts related to the encoder and decoder receptive field sizes, the object sizes, and the widths of the Gaussians used in the rendering process. We perform detailed analysis of how the error depends on each of these variables and perform synthetic experiments validating our theoretical predictions up to a precision of individual pixels. We also perform experiments on CLEVR-based data and show that, unlike current SOTA object detection methods (SAM, CutLER), our method's prediction errors always lie within our theoretical bounds. We hope that this work helps open up an avenue of research into object detection methods with theoretical guarantees.

Among approaches for provably safe reinforcement learning, Model Predictive Shielding (MPS) has proven effective at complex tasks in continuous, high-dimensional state spaces, by leveraging a *backup policy* to ensure safety when the learned policy attempts to take risky actions. However, while MPS can ensure safety both during and after training, it often hinders task progress due to the conservative and task-oblivious nature of backup policies. This paper introduces *Dynamic Model Predictive Shielding* (DMPS), which optimizes reinforcement learning objectives while maintaining provable safety. DMPS employs a local planner to dynamically select safe recovery actions that maximize both short-term progress as well as long-term rewards. Crucially, the planner and the neural policy play a synergistic role in DMPS. When planning recovery actions for ensuring safety, the planner utilizes the neural policy to estimate long-term rewards, allowing it to *observe* beyond its short-term planning horizon. Conversely, the neural policy under training learns from the recovery plans proposed by the planner, converging to policies that are both *high-performing* and *safe* in practice. This approach guarantees safety during and after training, with bounded recovery regret that decreases exponentially with planning horizon depth. Experimental results demonstrate that DMPS converges to policies that rarely require shield interventions after training and achieve higher rewards compared to several state-of-the-art baselines.

Originally formalized with symbolic representations, syntactic trees may also be effectively represented in the activations of large language models (LLMs). Indeed, a ''Structural Probe'' can find a subspace of neural activations, where syntactically-related words are relatively close to one-another. However, this syntactic code remains incomplete: the distance between the Structural Probe word embeddings can represent the \emph{existence} but not the type and direction of syntactic relations. Here, we hypothesize that syntactic relations are, in fact, coded by the relative direction between nearby embeddings. To test this hypothesis, we introduce a ''Polar Probe'' trained to read syntactic relations from both the distance and the direction between word embeddings. Our approach reveals three main findings. First, our Polar Probe successfully recovers the type and direction of syntactic relations, and substantially outperforms the Structural Probe by nearly two folds. Second, we confirm that this polar coordinate system exists in a low-dimensional subspace of the intermediate layers of many LLMs and becomes increasingly precise in the latest frontier models. Third, we demonstrate with a new benchmark that similar syntactic relations are coded similarly across the nested levels of syntactic trees. Overall, this work shows that LLMs spontaneously learn a geometry of neural activations that explicitly represents the main symbolic structures of linguistic theory.

Deploying deep neural networks for risk-sensitive tasks necessitates an uncertainty estimation mechanism. This paper introduces *hierarchical selective classification*, extending selective classification to a hierarchical setting. Our approach leverages the inherent structure of class relationships, enabling models to reduce the specificity of their predictions when faced with uncertainty. In this paper, we first formalize hierarchical risk and coverage, and introduce hierarchical risk-coverage curves. Next, we develop algorithms for hierarchical selective classification (which we refer to as "inference rules"), and propose an efficient algorithm that guarantees a target accuracy constraint with high probability. Lastly, we conduct extensive empirical studies on over a thousand ImageNet classifiers, revealing that training regimes such as CLIP, pretraining on ImageNet21k and knowledge distillation boost hierarchical selective performance.

A primary challenge for visual-based Reinforcement Learning (RL) is to generalize effectively across unseen environments. Although previous studies have explored different auxiliary tasks to enhance generalization, few adopt image reconstruction due to concerns about exacerbating overfitting to task-irrelevant features during training. Perceiving the pre-eminence of image reconstruction in representation learning, we propose SMG (\blue{S}eparated \blue{M}odels for \blue{G}eneralization), a novel approach that exploits image reconstruction for generalization. SMG introduces two model branches to extract task-relevant and task-irrelevant representations separately from visual observations via cooperatively reconstruction. Built upon this architecture, we further emphasize the importance of task-relevant features for generalization. Specifically, SMG incorporates two additional consistency losses to guide the agent's focus toward task-relevant areas across different scenarios, thereby achieving free from overfitting. Extensive experiments in DMC demonstrate the SOTA performance of SMG in generalization, particularly excelling in video-background settings. Evaluations on robotic manipulation tasks further confirm the robustness of SMG in real-world applications. Source code is available at \url{https://anonymous.4open.science/r/SMG/}.

Approximate nearest neighbor (ANN) search is a key component in many modern machine learning pipelines; recent use cases include retrieval-augmented generation (RAG) and vector databases. Clustering-based ANN algorithms, that use score computation methods based on product quantization (PQ), are often used in industrial-scale applications due to their scalability and suitability for distributed and disk-based implementations. However, they have slower query times than the leading graph-based ANN algorithms. In this work, we propose a new supervised score computation method based on the observation that inner product approximation is a multivariate (multi-output) regression problem that can be solved efficiently by reduced-rank regression. Our experiments show that on modern high-dimensional data sets, the proposed reduced-rank regression (RRR) method is superior to PQ in both query latency and memory usage. We also introduce LoRANN, a clustering-based ANN library that leverages the proposed score computation method. LoRANN is competitive with the leading graph-based algorithms and outperforms the state-of-the-art GPU ANN methods on high-dimensional data sets.

While neural networks can enjoy an outstanding flexibility and exhibit unprecedented performance, the mechanism behind their behavior is still not well-understood. To tackle this fundamental challenge, researchers have tried to restrict and manipulate some of their properties in order to gain new insights and better control on them. Especially, throughout the past few years, the concept of *bi-Lipschitzness* has been proved as a beneficial inductive bias in many areas. However, due to its complexity, the design and control of bi-Lipschitz architectures are falling behind, and a model that is precisely designed for bi-Lipschitzness realizing a direct and simple control of the constants along with solid theoretical analysis is lacking. In this work, we investigate and propose a novel framework for bi-Lipschitzness that can achieve such a clear and tight control based on convex neural networks and the Legendre-Fenchel duality. Its desirable properties are illustrated with concrete experiments to illustrate its broad range of applications.

In this paper, we propose a provably efficient natural policy gradient algorithm called Spectral Dynamic Embedding Policy Optimization (\SDEPO) for two-player zero-sum stochastic Markov games with continuous state space and finite action space. In the policy evaluation procedure of our algorithm, a novel kernel embedding method is employed to construct a finite-dimensional linear approximations to the state-action value function. We explicitly analyze the approximation error in policy evaluation, and show that \SDEPO\ achieves an $\tilde{O}(\frac{1}{(1-\gamma)^3\epsilon})$ last-iterate convergence to the $\epsilon-$optimal Nash equilibrium, which is independent of the cardinality of the state space. The complexity result matches the best-known results for global convergence of policy gradient algorithms for single agent setting. Moreover, we also propose a practical variant of \SDEPO\ to deal with continuous action space and empirical results demonstrate the practical superiority of the proposed method.

The learnware paradigm aims to enable users to leverage numerous existing well-trained models instead of building machine learning models from scratch. In this paradigm, developers worldwide can submit their well-trained models spontaneously into a learnware dock system, and the system helps developers generate specification for each model to form a learnware. As the key component, a specification should characterize the capabilities of the model, enabling it to be adequately identified and reused, while preserving the developer's original data. Recently, the RKME (Reduced Kernel Mean Embedding) specification was proposed and most commonly utilized. This paper provides a theoretical analysis of RKME specification about its preservation ability for developer's training data. By modeling it as a geometric problem on manifolds and utilizing tools from geometric analysis, we prove that the RKME specification is able to disclose none of the developer's original data and possesses robust defense against common inference attacks, while preserving sufficient information for effective learnware identification.

Deep learning succeeds by doing hierarchical feature learning, yet tuning hyper-parameters (HP) such as initialization scales, learning rates etc., only give indirect control over this behavior. In this paper, we introduce a key notion to predict and control feature learning: the angle $\theta_\ell$ between the feature updates and the backward pass (at layer index $\ell$). We show that the magnitude of feature updates after one GD step, at any training time, can be expressed via a simple and general *feature speed formula* in terms of this angle $\theta_\ell$, the loss decay, and the magnitude of the backward pass. This angle $\theta_\ell$ is controlled by the conditioning of the layer-to-layer Jacobians and at random initialization, it is determined by the spectrum of a certain kernel, which coincides with the Neural Tangent Kernel when $\ell=\text{depth}$. Given $\theta_\ell$, the feature speed formula provides us with rules to adjust HPs (scales and learning rates) so as to satisfy certain dynamical properties, such as feature learning and loss decay. We investigate the implications of our approach for ReLU MLPs and ResNets in the large width-then-depth limit. Relying on prior work, we show that in ReLU MLPs with iid initialization, the angle degenerates with depth as $\cos(\theta_\ell)=\Theta(1/\sqrt{\ell})$. In contrast, ResNets with branch scale $O(1/\sqrt{\text{depth}})$ maintain a non-degenerate angle $\cos(\theta_\ell)=\Theta(1)$. We use these insights to recover key properties of known HP scalings (such as $\mu$P), and also introduce a new HP scaling for large depth ReLU MLPs with favorable theoretical properties.

This paper considers the problem for finding the $(\delta,\epsilon)$-Goldstein stationary point of Lipschitz continuous objective, which is a rich function class to cover a great number of important applications. We construct a novel zeroth-order quantum estimator for the gradient of the smoothed surrogate. Based on such estimator, we propose a novel quantum algorithm that achieves a query complexity of $\tilde{\mathcal{O}}(d^{3/2}\delta^{-1}\epsilon^{-3})$ on the stochastic function value oracle, where $d$ is the dimension of the problem. We also enhance the query complexity to $\tilde{\mathcal{O}}(d^{3/2}\delta^{-1}\epsilon^{-7/3})$ by introducing a variance reduction variant. Our findings demonstrate the clear advantages of utilizing quantum techniques for non-convex non-smooth optimization, as they outperform the optimal classical methods on the dependency of $\epsilon$ by a factor of $\epsilon^{-2/3}$.

In linear bandits, how can a learner effectively learn when facing corrupted rewards? While significant work has explored this question, a holistic understanding across different adversarial models and corruption measures is lacking, as is a full characterization of the minimax regret bounds. In this work, we compare two types of corruptions commonly considered: strong corruption, where the corruption level depends on the learner’s chosen action, and weak corruption, where the corruption level does not depend on the learner’s chosen action. We provide a unified framework to analyze these corruptions. For stochastic linear bandits, we fully characterize the gap between the minimax regret under strong and weak corruptions. We also initiate the study of corrupted adversarial linear bandits, obtaining upper and lower bounds with matching dependencies on the corruption level. Next, we reveal a connection between corruption-robust learning and learning with gap-dependent misspecification—a setting first studied by Liu et al. (2023a), where the misspecification level of an action or policy is proportional to its suboptimality. We present a general reduction that enables any corruption-robust algorithm to handle gap-dependent misspecification. This allows us to recover the results of Liu et al. (2023a) in a black-box manner and significantly generalize them to settings like linear MDPs, yielding the first results for gap-dependent misspecification in reinforcement learning. However, this general reduction does not attain the optimal rate for gap-dependent misspecification. Motivated by this, we develop a specialized algorithm that achieves optimal bounds for gap-dependent misspecification in linear bandits, thus answering an open question posed by Liu et al. (2023a).

Artificial general intelligence on graphs has shown significant advancements across various applications, yet the traditional `Pre-train \& Fine-tune' paradigm faces inefficiencies and negative transfer issues, particularly in complex and few-shot settings. Graph prompt learning emerges as a promising alternative, leveraging lightweight prompts to manipulate data and fill the task gap by reformulating downstream tasks to the pretext. However, several critical challenges still remain: how to unify diverse graph prompt models, how to evaluate the quality of graph prompts, and to improve their usability for practical comparisons and selection. In response to these challenges, we introduce the first comprehensive benchmark for graph prompt learning. Our benchmark integrates **SIX** pre-training methods and **FIVE** state-of-the-art graph prompt techniques, evaluated across **FIFTEEN** diverse datasets to assess performance, flexibility, and efficiency. We also present 'ProG', an easy-to-use open-source library that streamlines the execution of various graph prompt models, facilitating objective evaluations. Additionally, we propose a unified framework that categorizes existing graph prompt methods into two main approaches: prompts as graphs and prompts as tokens. This framework enhances the applicability and comparison of graph prompt techniques. The code is available at: https://github.com/sheldonresearch/ProG.