In-context learning (ICL) is a cornerstone of large language model (LLM) functionality, yet its theoretical foundations remain elusive due to the complexity of transformer architectures. In particular, most existing work only theoretically explains how the attention mechanism facilitates ICL under certain data models. It remains unclear how the other building blocks of the transformer contribute to ICL. To address this question, we study how a two-attention-layer transformer is trained to perform ICL on n-gram Markov chain data, where each token in the Markov chain statistically depends on the previous n tokens. We analyze a sophisticated transformer model featuring relative positional embedding, multi-head softmax attention, and a feed-forward layer with normalization. We prove that the gradient flow with respect to a cross-entropy ICL loss converges to a limiting model that performs a generalized version of the "induction head" mechanism with a learned feature, resulting from the congruous contribution of all the building blocks. In the limiting model, the first attention layer acts as a copier, copying past tokens within a given window to each position, and the feed-forward network with normalization acts as a selector that generates a feature vector by only looking at informationally relevant parents from the window. Finally, the second attention layer is a classifier that compares these features with the feature at the output position, and uses the resulting similarity scores to generate the desired output. Our theory is further validated by simulation experiments.

We consider a commonly studied supervised classification of a synthetic dataset whose labels are generated by feeding a one-layer neural network with random i.i.d inputs. We study the generalization performances of standard classifiers in the high-dimensional regime where α = n/d is kept finite in the limit of a high dimension d and number of samples n.

We implemented the encoder (feature mapping f and g) by using multilayer perceptrons with ReLU activation and the decoder by using a symmetric architecture of encoder.

Implicit Neural Representations (INRs) encoding continuous multi-media data via multi-layer perceptrons has shown undebatable promise in various computer vision tasks. Despite many successful applications, editing and processing an INR remains intractable as signals are represented by latent parameters of a neural network. Existing works manipulate such continuous representations via processing on their discretized instance, which breaks down the compactness and continuous nature of INR. In this work, we present a pilot study on the question: how to directly modify an INR without explicit decoding? We answer this question by proposing an implicit neural signal processing network, dubbed INSP-Net, via differential operators on INR. Our key insight is that spatial gradients of neural networks can be computed analytically and are invariant to translation, while mathematically we show that any continuous convolution filter can be uniformly approximated by a linear combination of high-order differential operators. With these two knobs, INSP-Net instantiates the signal processing operator as a weighted composition of computational graphs corresponding to the high-order derivatives of INRs, where the weighting parameters can be data-driven learned. Based on our proposed INSP-Net, we further build the first Convolutional Neural Network (CNN) that implicitly runs on INRs, named INSP-ConvNet.

We show that passing input points through a simple Fourier feature mapping enables a multilayer perceptron (MLP) to learn high-frequency functions in lowdimensional problem domains. These results shed light on recent advances in computer vision and graphics that achieve state-of-the-art results by using MLPs to represent complex 3D objects and scenes. Using tools from the neural tangent kernel (NTK) literature, we show that a standard MLP has impractically slow convergence to high frequency signal components. To overcome this spectral bias, we use a Fourier feature mapping to transform the effective NTK into a stationary kernel with a tunable bandwidth. We suggest an approach for selecting problem-specific Fourier features that greatly improves the performance of MLPs for low-dimensional regression tasks relevant to the computer vision and graphics communities.

We thank the reviewers for their kind and thoughtful comments on our work. Below, we respond to reviewer-specific comments. Our claim that a standard multilayer perceptron "fails to learn high frequencies in theory" is based on the theoretical For example, in the abstract, modifying "a standard MLP fails to learn high frequencies both We directly extend the 1D experiment in Figure 4 to a two-dimensional setting in Section 1.4 of the supplement, and

We propose a video editing framework, NaRCan, which integrates a hybrid deformation field and diffusion prior to generate high-quality natural canonical images to represent the input video. Our approach utilizes homography to model global motion and employs multi-layer perceptrons (MLPs) to capture local residual deformations, enhancing the model's ability to handle complex video dynamics. By introducing a diffusion prior from the early stages of training, our model ensures that the generated images retain a high-quality natural appearance, making the produced canonical images suitable for various downstream tasks in video editing, a capability not achieved by current canonical-based methods. Furthermore, we incorporate low-rank adaptation (LoRA) fine-tuning and introduce a noise and diffusion prior update scheduling technique that accelerates the training process by 14 times. Extensive experimental results show that our method outperforms existing approaches in various video editing tasks and produces coherent and high-quality edited video sequences.

Vision Transformers (ViTs) are widely used in a variety of applications, while they usually have a fixed architecture that may not match the varying computational resources of different deployment environments. Thus, it is necessary to adapt ViT architectures to devices with diverse computational overheads to achieve an accuracy-efficient trade-off. This concept is consistent with the motivation behind Learngene. To achieve this, inspired by polynomial decomposition in calculus, where a function can be approximated by linearly combining several basic components, we propose to linearly decompose the ViT model into a set of components called learngenes during element-wise training. These learngenes can then be recomposed into differently scaled, pre-initialized models to satisfy different computational resource constraints. Such a decomposition-recomposition strategy provides an economical and flexible approach to generating different scales of ViT models for different deployment scenarios. Compared to model compression or training from scratch, which require to repeatedly train on large datasets for diverse-scale models, such strategy reduces computational costs since it only requires to train on large datasets once. Extensive experiments are used to validate the effectiveness of our method: ViTs can be decomposed and the decomposed learngenes can be recomposed into diverse-scale ViTs, which can achieve comparable or better performance compared to traditional model compression and pre-training methods. The code for our experiments is available in the supplemental material.