Self-supervised pre-training, where large corpora of unlabeled data are used to learn representations for downstream fine-tuning, has become a cornerstone of modern machine learning. While a growing body of theoretical work has begun to analyze this paradigm, existing bounds leave open the question of how sharp the current rates are, and whether they accurately capture the complex interaction between pre-training and fine-tuning. In this paper, we address this gap by developing an asymptotic theory of pre-training via two-stage M-estimation. A key challenge is that the pre-training estimator is often identifiable only up to a group symmetry, a feature common in representation learning that requires careful treatment. We address this issue using tools from Riemannian geometry to study the intrinsic parameters of the pre-training representation, which we link with the downstream predictor through a notion of orbit-invariance, precisely characterizing the limiting distribution of the downstream test risk. We apply our main result to several case studies, including spectral pre-training, factor models, and Gaussian mixture models, and obtain substantial improvements in problem-specific factors over prior art when applicable.

Vision and diverse languages are important information sources in our living world.

To answer this question, we begin by revisiting the forward procedure of ViTs. A sequence of positional embeddings (PEs) [51] is added to patch embeddings to preserve position information. Intuitively, simply discarding these PEs and requesting the model to reconstruct the position for each patch naturally becomes a qualified location-aware pretext task.

Figure 2: These two graphs cannot be distinguished by 1-WL-test. The COMBINE step takes the result of AGGREGATE and the previous representation of current node asinput. Wereduce theFFN inner-layer dimension of4din [47] tod, which does not appreciably hurt the performance but significantly save the parameters. The embedding dropout ratio is set to 0.1 by default in many previous Transformer works[11,34]. The rest of hyper-parameters remain unchanged. Table 8 summarizes the hyper-parameters used for fine-tuning Graphormer on OGBGMolPCBA.

Pre-training is crucial in 3D-related fields such as autonomous driving where point cloud annotation is costly and challenging. Many recent studies on point cloud pre-training, however, have overlooked the issue of incompleteness, where only a fraction of the points are captured by LiDAR, leading to ambiguity during the training phase. On the other hand, images offer more comprehensive information and richer semantics that can bolster point cloud encoders in addressing the incompleteness issue inherent in point clouds. Yet, incorporating images into point cloud pre-training presents its own challenges due to occlusions, potentially causing misalignments between points and pixels. In this work, we propose PRED, a novel image-assisted pre-training framework for outdoor point clouds in an occlusion-aware manner. The main ingredient of our framework is a Birds-Eye-View (BEV) feature map conditioned semantic rendering, leveraging the semantics of images for supervision through neural rendering. We further enhance our model's performance by incorporating point-wise masking with a high mask ratio (95%). Extensive experiments demonstrate PRED's superiority over prior point cloud pre-training methods, providing significant improvements on various large-scale datasets for 3D perception tasks. Codes will be available at https://github.com/PRED4pc/PRED.

We empirically investigate how pre-training on data of different modalities, such as language and vision, affects fine-tuning of Transformer-based models to Mujoco offline reinforcement learning tasks. Analysis of the internal representation reveals that the pre-trained Transformers acquire largely different representations before and after pre-training, but acquire less information of data in fine-tuning than the randomly initialized one. A closer look at the parameter changes of the pre-trained Transformers reveals that their parameters do not change that much and that the bad performance of the model pre-trained with image data could partially come from large gradients and gradient clipping. To study what information the Transformer pre-trained with language data utilizes, we fine-tune this model with no context provided, finding that the model learns efficiently even without context information. Subsequent follow-up analysis supports the hypothesis that pre-training with language data is likely to make the Transformer get context-like information and utilize it to solve the downstream task.