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Deep neural networks, as a powerful system to represent high dimensional complex functions, play a key role in deep learning. Convergence of deep neural networks is a fundamental issue in building the mathematical foundation for deep…
Neural networks are one of the first major milestones in developing artificial intelligence systems. The utilisation of integrated photonics in neural networks offers a promising alternative approach to microelectronic and hybrid…
In this paper, we give a causal solution to the problem of spline interpolation using H-infinity optimal approximation. Generally speaking, spline interpolation requires filtering the whole sampled data, the past and the future, to…
In this paper, we study the following nonlinear matrix decomposition (NMD) problem: given a sparse nonnegative matrix $X$, find a low-rank matrix $\Theta$ such that $X \approx f(\Theta)$, where $f$ is an element-wise nonlinear function. We…
Layer normalization (LN) is an essential component of modern neural networks. While many alternative techniques have been proposed, none of them have succeeded in replacing LN so far. The latest suggestion in this line of research is a…
Due to the limitations of Moore's Law and the increasing demand of computing, optical neural network (ONNs) are gradually coming to the stage as an alternative to electrical neural networks. The control of nonlinear activation functions in…
The choice of activation functions in deep networks has a significant effect on the training dynamics and task performance. Currently, the most successful and widely-used activation function is the Rectified Linear Unit (ReLU). Although…
Exploiting activation sparsity is a promising approach to significantly accelerating the inference process of large language models (LLMs) without compromising performance. However, activation sparsity is determined by activation functions,…
Deep reinforcement learning agents progressively lose representational capacity during training: neurons become dormant, removing active capacity from the network, and effective rank collapses, leaving surviving neurons redundant. Existing…
Rapid design space exploration in early design stage is critical to algorithm-architecture co-design for accelerators. In this work, a pre-RTL cycle-accurate accelerator simulator based on SystemC transaction-level modeling (TLM),…
A new effective solution to the problem of Hermite $G^1$ interpolation with a clothoid curve is here proposed, that is a clothoid that interpolates two given points in a plane with assigned unit tangent vectors. The interpolation problem is…
NeRF-based SLAM has recently achieved promising results in tracking and reconstruction. However, existing methods face challenges in providing sufficient scene representation, capturing structural information, and maintaining global…
Human Activity Recognition (HAR) with wearable sensors is essential for applications in healthcare, fitness, and human-computer interaction. Bio-impedance sensing offers unique advantages for fine-grained motion capture but remains…
We present Neural Splines, a technique for 3D surface reconstruction that is based on random feature kernels arising from infinitely-wide shallow ReLU networks. Our method achieves state-of-the-art results, outperforming recent neural…
Multiplication layers are a key component in various influential neural network modules, including self-attention and hypernetwork layers. In this paper, we investigate the approximation capabilities of deep neural networks with…
Infrared imaging is indispensable for its ability to penetrate obscurants and visualize thermal signatures, yet its practical use is hindered by the intrinsic limitations of conventional detectors. Nonlinear upconversion, which converts…
While there have been many developments in computational probes of both strongly-correlated molecular systems and machine-learning accelerated molecular dynamics, there remains a significant gap in capabilities in simulating accurate…
We study neural networks with trainable low-degree rational activation functions and show that they are more expressive and parameter-efficient than modern piecewise-linear and smooth activations such as ELU, LeakyReLU, LogSigmoid, PReLU,…
Ternary quantization has emerged as a powerful technique for reducing both computational and memory footprint of large language models (LLM), enabling efficient real-time inference deployment without significantly compromising model…
The mathematical complexity and high dimensionality of neural networks slow both training and deployment, demanding heavy computational resources. This has driven the search for alternative architectures built from novel components,…