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The transformer architecture is widely used in machine learning models and consists of two alternating sublayers: attention heads and MLPs. We prove that an MLP neuron can be implemented by a masked attention head with internal dimension 1…

Mathematical reasoning is an increasingly important indicator of large language model (LLM) capabilities, yet we lack understanding of how LLMs process even simple mathematical tasks. To address this, we reverse engineer how three mid-sized…

Modern approaches to enhancing Large Language Models' factual accuracy and knowledge utilization face a fundamental trade-off: non-parametric retrieval-augmented generation (RAG) provides flexible access to external knowledge but suffers…

Recently, large language models (LLMs) have advanced recommendation systems (RSs), and recent works have begun to explore how to integrate LLMs into industrial RSs. While most approaches deploy LLMs offline to generate and pre-cache…

We present a new mixed-integer programming (MIP) approach for offline multiple change-point detection by casting the problem as a globally optimal piecewise linear (PWL) fitting problem. Our main contribution is a family of strengthened MIP…

We analytically derive the geometrical structure of the weight space in multilayer neural networks (MLN), in terms of the volumes of couplings associated to the internal representations of the training set. Focusing on the parity and…

The construction of a multilayer perceptron (MLP) as a piecewise low-order polynomial approximator using a signal processing approach is presented in this work. The constructed MLP contains one input, one intermediate and one output layers.…

Non-negative Matrix Factorization (NMF) is an intensively used technique for obtaining parts-based, lower dimensional and non-negative representation. Researchers in biology, medicine, pharmacy and other fields often prefer NMF over other…

In this paper we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which…

Injectivity is the defining property of a mapping that ensures no information is lost and any input can be perfectly reconstructed from its output. By performing hard thresholding, the ReLU function naturally interferes with this property,…

We consider regression models involving multilayer perceptrons (MLP) with one hidden layer and a Gaussian noise. The estimation of the parameters of the MLP can be done by maximizing the likelihood of the model. In this framework, it is…

Traditional machine learning is generally treated as a black-box optimization problem and does not typically produce interpretable functions that connect inputs and outputs. However, the ability to discover such interpretable functions is…

In this paper, we propose a trainable multiplication layer (TML) for a neural network that can be used to calculate the multiplication between the input features. Taking an image as an input, the TML raises each pixel value to the power of…

Low-rank adapters enable fine-tuning of large models with only a small number of parameters, thus reducing storage costs and minimizing the risk of catastrophic forgetting. However, they often pose optimization challenges, with poor…

In the field of computer vision, recent works show that a pure MLP architecture mainly stacked by fully-connected layers can achieve competing performance with CNN and transformer. An input image of vision MLP is usually split into multiple…

Superposition -- when a neural network represents more ``features'' than it has dimensions -- seems to pose a serious challenge to mechanistically interpreting current AI systems. Existing theory work studies \emph{representational}…

By exploiting the correlation between the structure and the solution of Mixed-Integer Linear Programming (MILP), Machine Learning (ML) has become a promising method for solving large-scale MILP problems. Existing ML-based MILP solvers…

Fine-tuning a pre-trained language model (PLM) emerges as the predominant strategy in many natural language processing applications. However, this process is known to be expensive, especially on edge devices with low computing power. While…

Linear programming (LP) relaxations are widely employed in exact solution methods for multilinear programs (MLP). One example is the family of Recursive McCormick Linearization (RML) strategies, where bilinear products are substituted for…

Mixup generates augmented samples by linearly interpolating inputs and labels with a controllable ratio. However, since it operates in the latent embedding level, the resulting samples are not human-interpretable. In contrast, LLM-based…