NeurIPS 2024 论文列表

Conference on Neural Information Processing Systems

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4,562篇论文

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    4,06489.1%
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RA-PbRL: Provably Efficient Risk-Aware Preference-Based Reinforcement Learning

Yujie Zhao, Jose Efraim Aguilar Escamilla, Weyl Lu, Huazheng Wang

展开摘要

Reinforcement Learning from Human Feedback (RLHF) has recently surged in popularity, particularly for aligning large language models and other AI systems with human intentions. At its core, RLHF can be viewed as a specialized instance of Preference-based Reinforcement Learning (PbRL), where the preferences specifically originate from human judgments rather than arbitrary evaluators. Despite this connection, most existing approaches in both RLHF and PbRL primarily focus on optimizing a mean reward objective, neglecting scenarios that necessitate risk-awareness, such as AI safety, healthcare, and autonomous driving. These scenarios often operate under a one-episode-reward setting, which makes conventional risk-sensitive objectives inapplicable. To address this, we explore and prove the applicability of two risk-aware objectives to PbRL : nested and static quantile risk objectives. We also introduce Risk-AwarePbRL (RA-PbRL), an algorithm designed to optimize both nested and static objectives. Additionally, we provide a theoretical analysis of the regret upper bounds, demonstrating that they are sublinear with respect to the number of episodes, and present empirical results to support our findings. Our code is available in https://github.com/aguilarjose11/PbRLNeurips.

Poster
Unpacking DPO and PPO: Disentangling Best Practices for Learning from Preference Feedback

Hamish Ivison, Yizhong Wang, Jiacheng Liu, Zeqiu Wu, Valentina Pyatkin, Nathan Lambert, Noah A. Smith, Yejin Choi, Hannaneh Hajishirzi

展开摘要

Learning from preference feedback has emerged as an essential step for improving the generation quality and performance of modern language models (LMs). Despite its widespread use, the way preference-based learning is applied varies wildly, with differing data, learning algorithms, and evaluations used, making disentangling the impact of each aspect difficult. In this work, we identify four core aspects of preference-based learning: preference data, learning algorithm, reward model, and policy training prompts, systematically investigate the impact of these components on downstream model performance, and suggest a recipe for strong learning for preference feedback. Our findings indicate that all aspects are important for performance, with better preference data leading to the largest improvements, followed by the choice of learning algorithm, the use of improved reward models, and finally the use of additional unlabeled prompts for policy training. Notably, PPO outperforms DPO by up to 2.5% in math and 1.2% in general domains. High-quality preference data leads to improvements of up to 8% in instruction following and truthfulness. Despite significant gains of up to 5% in mathematical evaluation when scaling up reward models, we surprisingly observe marginal improvements in other categories.

Poster
Shape analysis for time series

Thibaut Germain, Samuel Gruffaz, Charles Truong, Alain Oliviero Durmus, Laurent Oudre

展开摘要

Analyzing inter-individual variability of physiological functions is particularly appealing in medical and biological contexts to describe or quantify health conditions. Such analysis can be done by comparing individuals to a reference one with time series as biomedical data. This paper introduces an unsupervised representation learning (URL) algorithm for time series tailored to inter-individual studies. The idea is to represent time series as deformations of a reference time series. The deformations are diffeomorphisms parameterized and learned by our method called TS-LDDMM. Once the deformations and the reference time series are learned, the vector representations of individual time series are given by the parametrization of their corresponding deformation. At the crossroads between URL for time series and shape analysis, the proposed algorithm handles irregularly sampled multivariate time series of variable lengths and provides shape-based representations of temporal data. In this work, we establish a representation theorem for the graph of a time series and derive its consequences on the LDDMM framework. We showcase the advantages of our representation compared to existing methods using synthetic data and real-world examples motivated by biomedical applications.

Poster
A Practitioner's Guide to Real-World Continual Multimodal Pretraining

Vishaal Udandarao, Karsten Roth, Sebastian Dziadzio, Ameya Prabhu, Mehdi Cherti, Oriol Vinyals, Olivier J Henaff, Samuel Albanie, Zeynep Akata, Matthias Bethge

展开摘要

Multimodal foundation models serve numerous applications at the intersection of vision and language. Still, despite being pretrained on extensive data, they become outdated over time. To keep models updated, research into continual pretraining mainly explores scenarios with either (1) infrequent, indiscriminate updates on large-scale new data, or (2) frequent, sample-level updates. However, practical model deployment often operates in the gap between these two limit cases, as real-world applications demand adaptation to specific subdomains, tasks or concepts --- spread over the entire, varying life cycle of a model. In this work, we complement current perspectives on continual pretraining through a research test bed and offer comprehensive guidance for effective continual model updates in such scenarios. We first introduce FoMo-in-Flux, a continual multimodal pretraining benchmark with realistic compute constraints and practical deployment requirements, constructed over 63 datasets with diverse visual and semantic coverage. Using FoMo-in-Flux, we explore the complex landscape of practical continual pretraining through multiple perspectives: (1) data mixtures and stream orderings that emulate real-world deployment settings, (2) methods ranging from simple fine-tuning and traditional continual learning strategies to parameter-efficient updates and model merging, (3) meta-learning-rate schedules and mechanistic design choices, and (4) model and compute scaling. Together, our insights provide a practitioner's guide to continual multimodal pretraining for real-world deployment. Benchmark and code is provided here: https://github.com/ExplainableML/fomo_in_flux.

Poster
Federated Learning over Connected Modes

Dennis Grinwald, Philipp Wiesner, Shinichi Nakajima

展开摘要

Statistical heterogeneity in federated learning poses two major challenges: slow global training due to conflicting gradient signals, and the need of personalization for local distributions. In this work, we tackle both challenges by leveraging recent advances in \emph{linear mode connectivity} --- identifying a linearly connected low-loss region in the parameter space of neural networks, which we call solution simplex. We propose federated learning over connected modes (\textsc{Floco}), where clients are assigned local subregions in this simplex based on their gradient signals, and together learn the shared global solution simplex. This allows personalization of the client models to fit their local distributions within the degrees of freedom in the solution simplex and homogenizes the update signals for the global simplex training. Our experiments show that \textsc{Floco} accelerates the global training process, and significantly improves the local accuracy with minimal computational overhead in cross-silo federated learning settings.

Poster
SpatialRGPT: Grounded Spatial Reasoning in Vision-Language Models

An-Chieh Cheng, Hongxu Yin, Yang Fu, Qiushan Guo, Ruihan Yang, Jan Kautz, Xiaolong Wang, Sifei Liu

展开摘要

Vision Language Models (VLMs) have demonstrated remarkable performance in 2D vision and language tasks. However, their ability to reason about spatial arrangements remains limited. In this work, we introduce Spatial Region GPT (SpatialRGPT) to enhance VLMs’ spatial perception and reasoning capabilities. SpatialRGPT advances VLMs’ spatial understanding through two key innovations: (i) a data curation pipeline that enables effective learning of regional representation from 3D scene graphs, and (ii) a flexible ``plugin'' module for integrating depth information into the visual encoder of existing VLMs. During inference, when provided with user-specified region proposals, SpatialRGPT can accurately perceive their relative directions and distances. Additionally, we propose SpatialRGBT-Bench, a benchmark with ground-truth 3D annotations encompassing indoor, outdoor, and simulated environments, for evaluating 3D spatial cognition in Vision-Language Models (VLMs). Our results demonstrate that SpatialRGPT significantly enhances performance in spatial reasoning tasks, both with and without local region prompts. The model also exhibits strong generalization capabilities, effectively reasoning about complex spatial relations and functioning as a region-aware dense reward annotator for robotic tasks. Code, dataset, and benchmark are released at https://www.anjiecheng.me/SpatialRGPT.

Poster
Smoothed Energy Guidance: Guiding Diffusion Models with Reduced Energy Curvature of Attention

Susung Hong

展开摘要

Conditional diffusion models have shown remarkable success in visual content generation, producing high-quality samples across various domains, largely due to classifier-free guidance (CFG). Recent attempts to extend guidance to unconditional models have relied on heuristic techniques, resulting in suboptimal generation quality and unintended effects. In this work, we propose Smoothed Energy Guidance (SEG), a novel training- and condition-free approach that leverages the energy-based perspective of the self-attention mechanism to enhance image generation. By defining the energy of self-attention, we introduce a method to reduce the curvature of the energy landscape of attention and use the output as the unconditional prediction. Practically, we control the curvature of the energy landscape by adjusting the Gaussian kernel parameter while keeping the guidance scale parameter fixed. Additionally, we present a query blurring method that is equivalent to blurring the entire attention weights without incurring quadratic complexity in the number of tokens. In our experiments, SEG achieves a Pareto improvement in both quality and the reduction of side effects. The code is available at https://github.com/SusungHong/SEG-SDXL.

Poster
Hamiltonian Score Matching and Generative Flows

Peter Holderrieth, Yilun Xu, Tommi Jaakkola

展开摘要

Classical Hamiltonian mechanics has been widely used in machine learning in the form of Hamiltonian Monte Carlo for applications with predetermined force fields. In this paper, we explore the potential of deliberately designing force fields for Hamiltonian systems, introducing Hamiltonian velocity predictors (HVPs) as a core tool for constructing energy-based and generative models. We present two innovations: Hamiltonian Score Matching (HSM), which utilizes score functions to augment data by simulating Hamiltonian trajectories, and Hamiltonian Generative Flows (HGFs), a novel generative model that encompasses diffusion models and OT-flow matching as HGFs with zero force fields. We showcase the extended design space of force fields by introducing Oscillation HGFs, a generative model inspired by harmonic oscillators. Our experiments demonstrate that HSM and HGFs rival leading score-matching and generative modeling techniques. Overall, our work systematically elucidates the synergy between Hamiltonian dynamics, force fields, and generative models, thereby opening new avenues for applications of machine learning in physical sciences and dynamical systems.

Poster
PowerPM: Foundation Model for Power Systems

Shihao Tu, Yupeng Zhang, Jing Zhang, Zhendong Fu, Yin Zhang, Yang Yang

展开摘要

The proliferation of abundant electricity time series (ETS) data presents numerous opportunities for various applications within power systems, including demand-side management, grid stability, and consumer behavior analysis. Deep learning models have advanced ETS modeling by effectively capturing sequence dependence. However, learning a generic representation of ETS data for various applications is challenging due to the inherently complex hierarchical structure of ETS data. Moreover, ETS data exhibits intricate temporal dependencies and is susceptible to the influence of exogenous variables. Furthermore, different instances exhibit diverse electricity consumption behavior. In this paper, we propose a foundation model PowerPM for ETS data, providing a large-scale, off-the-shelf model for power systems. PowerPM consists of a temporal encoder and a hierarchical encoder. The temporal encoder captures temporal dependencies within ETS data, taking into account exogenous variables. The hierarchical encoder models correlations between different levels of hierarchy. Furthermore, PowerPM leverages a novel self-supervised pre-training framework consisting of masked ETS modeling and dual-view contrastive learning. This framework enables PowerPM to capture temporal dependency within ETS windows and aware the discrepancy across ETS windows, providing two different perspectives to learn generic representation. Our experiments span five real-world scenario datasets, including both private and public data. Through pre-training on massive ETS data, PowerPM achieves SOTA performance on diverse downstream tasks within the private dataset. Notably, when transferred to public datasets, PowerPM retains its edge, showcasing its remarkable generalization ability across various tasks and domains. Moreover, ablation studies and few-shot experiments further substantiate the effectiveness of our model.

Poster
Architect: Generating Vivid and Interactive 3D Scenes with Hierarchical 2D Inpainting

Yian Wang, Xiaowen Qiu, Jiageng Liu, Zhehuan Chen, Jiting Cai, Yufei Wang, Tsun-Hsuan Wang, Zhou Xian, Chuang Gan

展开摘要

Creating large-scale interactive 3D environments is essential for the development of Robotics and Embodied AI research. However, generating diverse embodied environments with realistic detail and considerable complexity remains a significant challenge. Current methods, including manual design, procedural generation, diffusion-based scene generation, and large language model (LLM) guided scene design, are hindered by limitations such as excessive human effort, reliance on predefined rules or training datasets, and limited 3D spatial reasoning ability. Since pre-trained 2D image generative models better capture scene and object configuration than LLMs, we address these challenges by introducing $\textit{Architect}$, a generative framework that creates complex and realistic 3D embodied environments leveraging diffusion-based 2D image inpainting. In detail, we utilize foundation visual perception models to obtain each generated object from the image and leverage pre-trained depth estimation models to lift the generated 2D image to 3D space. While there are still challenges that the camera parameters and scale of depth are still absent in the generated image, we address those problems by ''controlling'' the diffusion model by $\textit{hierarchical inpainting}$. Specifically, having access to ground-truth depth and camera parameters in simulation, we first render a photo-realistic image of only the background. Then, we inpaint the foreground in this image, passing the geometric cues to the inpainting model in the background, which informs the camera parameters. This process effectively controls the camera parameters and depth scale for the generated image, facilitating the back-projection from 2D image to 3D point clouds. Our pipeline is further extended to a hierarchical and iterative inpainting process to continuously generate the placement of large furniture and small objects to enrich the scene. This iterative structure brings the flexibility for our method to generate or refine scenes from various starting points, such as text, floor plans, or pre-arranged environments. Experimental results demonstrate that $\textit{Architect}$ outperforms existing methods in producing realistic and complex environments, making it highly suitable for Embodied AI and robotics applications.

Poster
Explicit Eigenvalue Regularization Improves Sharpness-Aware Minimization

Haocheng Luo, Tuan Truong, Tung Pham, Mehrtash Harandi, Dinh Phung, Trung Le

展开摘要

Sharpness-Aware Minimization (SAM) has attracted significant attention for its effectiveness in improving generalization across various tasks. However, its underlying principles remain poorly understood. In this work, we analyze SAM’s training dynamics using the maximum eigenvalue of the Hessian as a measure of sharpness and propose a third-order stochastic differential equation (SDE), which reveals that the dynamics are driven by a complex mixture of second- and third-order terms. We show that alignment between the perturbation vector and the top eigenvector is crucial for SAM’s effectiveness in regularizing sharpness, but find that this alignment is often inadequate in practice, which limits SAM's efficiency. Building on these insights, we introduce Eigen-SAM, an algorithm that explicitly aims to regularize the top Hessian eigenvalue by aligning the perturbation vector with the leading eigenvector. We validate the effectiveness of our theory and the practical advantages of our proposed approach through comprehensive experiments. Code is available at https://github.com/RitianLuo/EigenSAM.

Poster
What Makes and Breaks Safety Fine-tuning? A Mechanistic Study

Samyak Jain, Ekdeep Singh Lubana, Kemal Oksuz, Tom Joy, Philip Torr, Amartya Sanyal, Puneet K. Dokania

展开摘要

Safety fine-tuning helps align Large Language Models (LLMs) with human preferences for their safe deployment. To better understand the underlying factors that make models safe via safety fine-tuning, we design a synthetic data generation framework that captures salient aspects of an unsafe input by modeling the interaction between the task the model is asked to perform (e.g., “design”) versus the specific concepts the task is asked to be performed upon (e.g., a “cycle” vs. a “bomb”). Using this, we investigate three well-known safety fine-tuning methods—supervised safety fine-tuning, direct preference optimization, and unlearning—and provide significant evidence demonstrating that these methods minimally transform MLP weights to specifically align unsafe inputs into its weights’ null space. This yields a clustering of inputs based on whether the model deems them safe or not. Correspondingly, when an adversarial input (e.g., a jailbreak) is provided, its activations are closer to safer samples, leading to the model processing such an input as if it were safe. Code is available at https://github.com/fiveai/understanding_safety_finetuning.

Poster
Binary Search with Distributional Predictions

Michael Dinitz, Sungjin Im, Thomas Lavastida, Benjamin Moseley, Aidin Niaparast, Sergei Vassilvitskii

展开摘要

Algorithms with (machine-learned) predictions is a powerful framework for combining traditional worst-case algorithms with modern machine learning. However, the vast majority of work in this space assumes that the prediction itself is non-probabilistic, even if it is generated by some stochastic process (such as a machine learning system). This is a poor fit for modern ML, particularly modern neural networks, which naturally generate a *distribution*. We initiate the study of algorithms with *distributional* predictions, where the prediction itself is a distribution. We focus on one of the simplest yet fundamental settings: binary search (or searching a sorted array). This setting has one of the simplest algorithms with a point prediction, but what happens if the prediction is a distribution? We show that this is a richer setting: there are simple distributions where using the classical prediction-based algorithm with any single prediction does poorly. Motivated by this, as our main result, we give an algorithm with query complexity $O(H(p) + \log \eta)$, where $H(p)$ is the entropy of the true distribution $p$ and $\eta$ is the earth mover's distance between $p$ and the predicted distribution $\hat p$. This also yields the first *distributionally-robust* algorithm for the classical problem of computing an optimal binary search tree given a distribution over target keys. We complement this with a lower bound showing that this query complexity is essentially optimal (up to constants), and experiments validating the practical usefulness of our algorithm.

Poster
Large language model validity via enhanced conformal prediction methods

John Cherian, Isaac Gibbs, Emmanuel Candes

展开摘要

We develop new conformal inference methods for obtaining validity guarantees on the output of large language models (LLMs). Prior work in conformal language modeling identifies a subset of the text that satisfies a high-probability guarantee of correctness. These methods work by filtering claims from the LLM's original response if a scoring function evaluated on the claim fails to exceed a threshold calibrated via split conformal prediction. Existing methods in this area suffer from two deficiencies. First, the guarantee stated is not conditionally valid. The trustworthiness of the filtering step may vary based on the topic of the response. Second, because the scoring function is imperfect, the filtering step can remove many valuable and accurate claims. We address both of these challenges via two new conformal methods. First, we generalize the conditional conformal procedure of Gibbs et al. (2023) in order to adaptively issue weaker guarantees when they are required to preserve the utility of the output. Second, we show how to systematically improve the quality of the scoring function via a novel algorithm for differentiating through the conditional conformal procedure. We demonstrate the efficacy of our approach on biography and medical question-answering datasets.

Poster
SimGen: Simulator-conditioned Driving Scene Generation

Yunsong Zhou, Michael Simon, Zhenghao Peng, Sicheng Mo, Hongzi Zhu, Minyi Guo, Bolei Zhou

展开摘要

Controllable synthetic data generation can substantially lower the annotation cost of training data. Prior works use diffusion models to generate driving images conditioned on the 3D object layout. However, those models are trained on small-scale datasets like nuScenes, which lack appearance and layout diversity. Moreover, overfitting often happens, where the trained models can only generate images based on the layout data from the validation set of the same dataset. In this work, we introduce a simulator-conditioned scene generation framework called SimGen that can learn to generate diverse driving scenes by mixing data from the simulator and the real world. It uses a novel cascade diffusion pipeline to address challenging sim-to-real gaps and multi-condition conflicts. A driving video dataset DIVA is collected to enhance the generative diversity of SimGen, which contains over 147.5 hours of real-world driving videos from 73 locations worldwide and simulated driving data from the MetaDrive simulator. SimGen achieves superior generation quality and diversity while preserving controllability based on the text prompt and the layout pulled from a simulator. We further demonstrate the improvements brought by SimGen for synthetic data augmentation on the BEV detection and segmentation task and showcase its capability in safety-critical data generation.

Poster
Poseidon: Efficient Foundation Models for PDEs

Maximilian Herde, Bogdan Raonic, Tobias Rohner, Roger Käppeli, Roberto Molinaro, Emmanuel de Bezenac, Siddhartha Mishra

展开摘要

We introduce Poseidon, a foundation model for learning the solution operators of PDEs. It is based on a multiscale operator transformer, with time-conditioned layer norms that enable continuous-in-time evaluations. A novel training strategy leveraging the semi-group property of time-dependent PDEs to allow for significant scaling-up of the training data is also proposed. Poseidon is pretrained on a diverse, large scale dataset for the governing equations of fluid dynamics. It is then evaluated on a suite of 15 challenging downstream tasks that include a wide variety of PDE types and operators. We show that Poseidon exhibits excellent performance across the board by outperforming baselines significantly, both in terms of sample efficiency and accuracy. Poseidon also generalizes very well to new physics that is not seen during pretraining. Moreover, Poseidon scales with respect to model and data size, both for pretraining and for downstream tasks. Taken together, our results showcase the surprising ability of Poseidon to learn effective representations from a very small set of PDEs during pretraining in order to generalize well to unseen and unrelated PDEs downstream, demonstrating its potential as an effective, general purpose PDE foundation model. Finally, the Poseidon model as well as underlying pretraining and downstream datasets are open sourced, with code being available at https://github.com/camlab-ethz/poseidon and pretrained models and datasets at https://huggingface.co/camlab-ethz.

Poster
HumanSplat: Generalizable Single-Image Human Gaussian Splatting with Structure Priors

Panwang Pan, Zhuo Su, Chenguo Lin, Zhen Fan, Yongjie Zhang, Zeming Li, Tingting Shen, Yadong Mu, Yebin Liu

展开摘要

Despite recent advancements in high-fidelity human reconstruction techniques, the requirements for densely captured images or time-consuming per-instance optimization significantly hinder their applications in broader scenarios. To tackle these issues, we present **HumanSplat**, which predicts the 3D Gaussian Splatting properties of any human from a single input image in a generalizable manner. Specifically, HumanSplat comprises a 2D multi-view diffusion model and a latent reconstruction Transformer with human structure priors that adeptly integrate geometric priors and semantic features within a unified framework. A hierarchical loss that incorporates human semantic information is devised to achieve high-fidelity texture modeling and impose stronger constraints on the estimated multiple views. Comprehensive experiments on standard benchmarks and in-the-wild images demonstrate that HumanSplat surpasses existing state-of-the-art methods in achieving photorealistic novel-view synthesis. Project page: https://humansplat.github.io.

Poster
SpecExec: Massively Parallel Speculative Decoding For Interactive LLM Inference on Consumer Devices

Ruslan Svirschevski, Avner May, Zhuoming Chen, Beidi Chen, Zhihao Jia, Max Ryabinin

展开摘要

As large language models gain widespread adoption, running them efficiently becomes a crucial task. Recent works on LLM inference use speculative decoding to achieve extreme speedups. However, most of these works implicitly design their algorithms for high-end datacenter hardware. In this work, we ask the opposite question: how fast can we run LLMs on consumer machines? Consumer GPUs can no longer fit the largest available models and must offload them to RAM or SSD. With parameter offloading, hundreds or thousands of tokens can be processed in batches within the same time as just one token, making it a natural fit for speculative decoding. We propose SpecExec (Speculative Execution), a simple parallel decoding method that can generate up to 20 tokens per target model iteration for popular LLM families. SpecExec takes the most probable continuations from the draft model to build a "cache" tree for the target model, which then gets validated in a single pass. Using SpecExec, we demonstrate inference of 50B+ parameter LLMs on consumer GPUs with RAM offloading at 4--6 tokens per second with 4-bit quantization or 2--3 tokens per second with 16-bit weights. Our code is available at https://github.com/yandex-research/specexec .

Poster
RAGChecker: A Fine-grained Framework for Diagnosing Retrieval-Augmented Generation

Dongyu Ru, Lin Qiu, Xiangkun Hu, Tianhang Zhang, Peng Shi, Shuaichen Chang, Cheng Jiayang, Cunxiang Wang, Shichao Sun, Huanyu Li, Zizhao Zhang, Binjie Wang, Jiarong Jiang, Tong He, Zhiguo Wang, Pengfei Liu, Yue Zhang, Zheng Zhang

展开摘要

Despite Retrieval-Augmented Generation (RAG) has shown promising capability in leveraging external knowledge, a comprehensive evaluation of RAG systems is still challenging due to the modular nature of RAG, evaluation of long-form responses and reliability of measurements. In this paper, we propose a fine-grained evaluation framework, RAGChecker, that incorporates a suite of diagnostic metrics for both the retrieval and generation modules. Meta evaluation verifies that RAGChecker has significantly better correlations with human judgments than other evaluation metrics. Using RAGChecker, we evaluate 8 RAG systems and conduct an in-depth analysis of their performance, revealing insightful patterns and trade-offs in the design choices of RAG architectures. The metrics of RAGChecker can guide researchers and practitioners in developing more effective RAG systems.

Poster
On the Stability and Generalization of Meta-Learning

Yunjuan Wang, Raman Arora

展开摘要

We focus on developing a theoretical understanding of meta-learning. Given multiple tasks drawn i.i.d. from some (unknown) task distribution, the goal is to find a good pre-trained model that can be adapted to a new, previously unseen, task with little computational and statistical overhead. We introduce a novel notion of stability for meta-learning algorithms, namely *uniform meta-stability*. We instantiate two uniformly meta-stable learning algorithms based on regularized empirical risk minimization and gradient descent and give explicit generalization bounds for convex learning problems with smooth losses and for weakly convex learning problems with non-smooth losses. Finally, we extend our results to stochastic and adversarially robust variants of our meta-learning algorithm.

Poster