Implicit Neural Representations (INRs), as a versatile representation paradigm, have achieved success in various computer vision tasks. Due to the spectral bias of the vanilla multi-layer perceptrons (MLPs), existing methods focus on designing MLPs with sophisticated architectures or repurposing training techniques for highly accurate INRs. In this paper, we delve into the linear dynamics model of MLPs and theoretically identify the empirical Neural Tangent Kernel (eNTK) matrix as a reliable link between spectral bias and training dynamics. Based on eNTK matrix, we propose a practical inductive gradient adjustment method, which could purposefully improve the spectral bias via inductive generalization of eNTK-based gradient transformation matrix. We evaluate our method on different INRs tasks with various INR architectures and compare to existing training techniques. The superior representation performance clearly validates the advantage of our proposed method. Armed with our gradient adjustment method, better INRs with more enhanced texture details and sharpened edges can be learned from data by tailored improvements on spectral bias.

Transformers exhibit In-Context Learning (ICL), where these models solve new tasks by using examples in the prompt without additional training. In our work, we identify and analyze two key components of ICL: (1) context-scaling, where model performance improves as the number of in-context examples increases and (2) task-scaling, where model performance improves as the number of pre-training tasks increases. While transformers are capable of both context-scaling and task-scaling, we empirically show that standard Multi-Layer Perceptrons (MLPs) with vectorized input are only capable of task-scaling. To understand how transformers are capable of context-scaling, we first propose a significantly simplified transformer architecture without key, query, value weights. We show that it performs ICL comparably to the original GPT-2 model in various statistical learning tasks including linear regression, teacher-student settings. Furthermore, a single block of our simplified transformer can be viewed as data dependent feature map followed by an MLP. This feature map on its own is a powerful predictor that is capable of context-scaling but is not capable of task-scaling. We show empirically that concatenating the output of this feature map with vectorized data as an input to MLPs enables both context-scaling and task-scaling. This finding provides a simple setting to study context and task-scaling for ICL.

This study employs explainable artificial intelligence (XAI) techniques to analyze the behavior of asphalt concrete with varying aggregate gradations, focusing on resilience modulus (MR) and dynamic stability (DS) as measured by wheel track tests. The research utilizes a deep learning model with a multi-layer perceptron architecture to predict MR and DS based on aggregate gradation parameters derived from Bailey's Method, including coarse aggregate ratio (CA), fine aggregate coarse ratio (FAc), and other mix design variables. The model's performance was validated using k-fold cross-validation, demonstrating superior accuracy compared to alternative machine learning approaches. SHAP (SHapley Additive exPlanations) values were applied to interpret the model's predictions, providing insights into the relative importance and impact of different gradation characteristics on asphalt concrete performance. Key findings include the identification of critical aggregate size thresholds, particularly the 0.6 mm sieve size, which significantly influences both MR and DS. The study revealed size-dependent performance of aggregates, with coarse aggregates primarily affecting rutting resistance and medium-fine aggregates influencing stiffness. The research also highlighted the importance of aggregate lithology in determining rutting resistance. To facilitate practical application, web-based interfaces were developed for predicting MR and DS, incorporating explainable features to enhance transparency and interpretation of results. This research contributes a data-driven approach to understanding the complex relationships between aggregate gradation and asphalt concrete performance, potentially informing more efficient and performance-oriented mix design processes in the future.

The Visual Simultaneous Localization and Mapping (V-SLAM) system has seen significant development in recent years, demonstrating high precision in environments with limited dynamic objects. However, their performance significantly deteriorates when deployed in settings with a higher presence of movable objects, such as environments with pedestrians, cars, and buses, which are common in outdoor scenes. To address this issue, we propose a Multilayer Perceptron (MLP)-based real-time stereo SLAM system that leverages complete geometry information to avoid information loss. Moreover, there is currently no publicly available dataset for directly evaluating the effectiveness of dynamic and static feature classification methods, and to bridge this gap, we have created a publicly available dataset containing over 50,000 feature points. Experimental results demonstrate that our MLP-based dynamic and static feature point discriminator has achieved superior performance compared to other methods on this dataset. Furthermore, the MLP-based real-time stereo SLAM system has shown the highest average precision and fastest speed on the outdoor KITTI tracking datasets compared to other dynamic SLAM systems.The open-source code and datasets are available at https://github.com/TaozheLi/MLP-SLAM.

Due to their weak inductive bias, Multi-Layer Perceptrons (MLPs) have subpar performance at low-compute levels compared to standard architectures such as convolution-based networks (CNN). Recent work, however, has shown that the performance gap drastically reduces as the amount of compute is increased without changing the amount of inductive bias. In this work, we study the converse: in the low-compute regime, how does the incremental increase of inductive bias affect performance? To quantify inductive bias, we propose a "soft MLP" approach, which we coin Interpolated MLP (I-MLP). We control the amount of inductive bias in the standard MLP by introducing a novel algorithm based on interpolation between fixed weights from a prior model with high inductive bias. We showcase our method using various prior models, including CNNs and the MLP-Mixer architecture. This interpolation scheme allows fractional control of inductive bias, which may be attractive when full inductive bias is not desired (e.g. in the mid-compute regime). We find experimentally that for Vision Tasks in the low-compute regime, there is a continuous and two-sided logarithmic relationship between inductive bias and performance when using CNN and MLP-Mixer prior models.

Positional encoding is a crucial component to allow attention-based deep model architectures such as Transformer to address sequences or images where the position of information matters. In this paper, we propose a novel positional encoding method based on learnable Fourier features. Instead of hard-coding each position as a token or a vector, we represent each position, which can be multi-dimensional, as a trainable encoding based on learnable Fourier feature mapping, modulated with a multi-layer perceptron. The representation is particularly advantageous for a spatial multi-dimensional position, e.g., pixel positions on an image, where L_2 distances or more complex positional relationships need to be captured. Our experiments based on several public benchmark tasks show that our learnable Fourier feature representation for multi-dimensional positional encoding outperforms existing methods by both improving the accuracy and allowing faster convergence.

Modern prediction problems arising in multilabel learning and learning to rank pose unique challenges to the classical theory of supervised learning. These problems have large prediction and label spaces of a combinatorial nature and involve sophisticated loss functions. We offer a general framework to derive mistake driven online algorithms and associated loss bounds. The key ingredients in our framework are a general loss function, a general vector space representation of predictions, and a notion of margin with respect to a general norm. Our general algorithm, Predtron, yields the perceptron algorithm and its variants when instantiated on classic problems such as binary classification, multiclass classification, ordinal regression, and multilabel classification.

Recently, there has been a surge of interest in representation learning in hyperbolic spaces, driven by their ability to represent hierarchical data with significantly fewer dimensions than standard Euclidean spaces. However, the viability and benefits of hyperbolic spaces for downstream machine learning tasks have received less attention. Specifically, we consider the problem of learning a large-margin classifier for data possessing a hierarchical structure. Our first contribution is a hyperbolic perceptron algorithm, which provably converges to a separating hyperplane. We then provide an algorithm to efficiently learn a large-margin hyperplane, relying on the careful injection of adversarial examples. Finally, we prove that for hierarchical data that embeds well into hyperbolic space, the low embedding dimension ensures superior guarantees when learning the classifier directly in hyperbolic space.

Steerable convolutional neural networks (CNNs) provide a general framework for building neural networks equivariant to translations and transformations of an origin-preserving group G, such as reflections and rotations. They rely on standard convolutions with G -steerable kernels obtained by analytically solving the group-specific equivariance constraint imposed onto the kernel space. As the solution is tailored to a particular group G, implementing a kernel basis does not generalize to other symmetry transformations, complicating the development of general group equivariant models. We propose using implicit neural representation via multi-layer perceptrons (MLPs) to parameterize G -steerable kernels. The resulting framework offers a simple and flexible way to implement Steerable CNNs and generalizes to any group G for which a G -equivariant MLP can be built.

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.