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Modular exponentiation is crucial to number theory and cryptography, yet remains largely unexplored from a mechanistic interpretability standpoint. We train a 4-layer encoder-decoder Transformer model to perform this operation and…

Machine Learning · Computer Science 2025-10-24 David Demitri Africa , Sara M. Kapoor , Theo Simon Sorg , Challenger Mishra

A key question in reinforcement learning is how an intelligent agent can generalize knowledge across different inputs. By generalizing across different inputs, information learned for one input can be immediately reused for improving…

Machine Learning · Computer Science 2020-10-06 Lucas Lehnert , Michael L. Littman

Feed-forward networks are widely used in cross-modal applications to bridge modalities by mapping distributed vectors of one modality to the other, or to a shared space. The predicted vectors are then used to perform e.g., retrieval or…

Machine Learning · Statistics 2018-06-05 Guillem Collell , Marie-Francine Moens

This work is focused on improving the character recognition capability of feed-forward back-propagation neural network by using one, two and three hidden layers and the modified additional momentum term. 182 English letters were collected…

Neural and Evolutionary Computing · Computer Science 2011-03-01 Amit Choudhary , Rahul Rishi

Deep neural networks are inherently opaque and challenging to interpret. Unlike hand-crafted feature-based models, we struggle to comprehend the concepts learned and how they interact within these models. This understanding is crucial not…

Computation and Language · Computer Science 2023-07-12 Shammur Absar Chowdhury , Nadir Durrani , Ahmed Ali

We present flattened convolutional neural networks that are designed for fast feedforward execution. The redundancy of the parameters, especially weights of the convolutional filters in convolutional neural networks has been extensively…

Neural and Evolutionary Computing · Computer Science 2015-11-23 Jonghoon Jin , Aysegul Dundar , Eugenio Culurciello

Pre-trained large language models (LLMs) exhibit impressive mathematical reasoning capabilities, yet how they compute basic arithmetic, such as addition, remains unclear. This paper shows that pre-trained LLMs add numbers using Fourier…

Machine Learning · Computer Science 2024-06-06 Tianyi Zhou , Deqing Fu , Vatsal Sharan , Robin Jia

Large language models exhibit sophisticated capabilities, yet understanding how they work internally remains a central challenge. A fundamental obstacle is that training selects for behavior, not circuitry, so many weight configurations can…

Machine Learning · Computer Science 2026-02-27 Joshua S. Schiffman

It is widely believed that deep neural networks contain layer specialization, wherein neural networks extract hierarchical features representing edges and patterns in shallow layers and complete objects in deeper layers. Unlike common…

Machine Learning · Computer Science 2022-03-04 Avi Schwarzschild , Arjun Gupta , Amin Ghiasi , Micah Goldblum , Tom Goldstein

Tabular foundational models are pre-trained models designed for a wide range of tabular data tasks. They have shown strong performance across domains, yet their internal representations and learned concepts remain poorly understood. This…

Machine Learning · Computer Science 2026-01-14 Aviral Gupta , Armaan Sethi , Dhruv Kumar

At typical context lengths, the feed-forward MLP block accounts for a large share of a transformer's compute budget, motivating sparse alternatives to dense MLP blocks. We study sparse, tree-structured feed-forward layers as drop-in…

Computation and Language · Computer Science 2026-04-13 Reza Sedghi , Robin Schiewer , Anand Subramoney , David Kappel

Memory is fundamental to intelligence, enabling learning, reasoning, and adaptability across biological and artificial systems. While Transformer architectures excel at sequence modeling, they face critical limitations in long-range context…

Machine Learning · Computer Science 2025-08-19 Parsa Omidi , Xingshuai Huang , Axel Laborieux , Bahareh Nikpour , Tianyu Shi , Armaghan Eshaghi

The Transformer model has achieved state-of-the-art performance in many sequence modeling tasks. However, how to leverage model capacity with large or variable depths is still an open challenge. We present a probabilistic framework to…

Computation and Language · Computer Science 2020-10-19 Xian Li , Asa Cooper Stickland , Yuqing Tang , Xiang Kong

Pre-training is crucial for learning deep neural networks. Most of existing pre-training methods train simple models (e.g., restricted Boltzmann machines) and then stack them layer by layer to form the deep structure. This layer-wise…

Machine Learning · Computer Science 2015-06-09 Zhiyuan Tang , Dong Wang , Yiqiao Pan , Zhiyong Zhang

Learning to solve complex sequences of tasks--while both leveraging transfer and avoiding catastrophic forgetting--remains a key obstacle to achieving human-level intelligence. The progressive networks approach represents a step forward in…

Hierarchical neural networks are exponentially more efficient than their corresponding "shallow" counterpart with the same expressive power, but involve huge number of parameters and require tedious amounts of training. Our main idea is to…

Machine Learning · Computer Science 2018-07-19 Bálint Daróczy , Rita Aleksziev , András Benczúr

Next-token prediction serves as the dominant component in current neural language models. During the training phase, the model employs teacher forcing, which predicts tokens based on all preceding ground truth tokens. However, this approach…

Computation and Language · Computer Science 2024-10-28 Yongjing Yin , Junran Ding , Kai Song , Yue Zhang

Embedding layers in transformer-based NLP models typically account for the largest share of model parameters, scaling with vocabulary size but not yielding performance gains proportional to scale. We propose an alternative approach in which…

Computation and Language · Computer Science 2025-05-06 Henry Ndubuaku , Mouad Talhi

Understanding the inner workings of Transformers is crucial for achieving more accurate and efficient predictions. In this work, we analyze the computation performed by Transformers in the layers after the top-1 prediction has become fixed,…

Computation and Language · Computer Science 2024-10-29 Daria Lioubashevski , Tomer Schlank , Gabriel Stanovsky , Ariel Goldstein

Transformer is the state-of-the-art model in recent machine translation evaluations. Two strands of research are promising to improve models of this kind: the first uses wide networks (a.k.a. Transformer-Big) and has been the de facto…

Computation and Language · Computer Science 2019-06-06 Qiang Wang , Bei Li , Tong Xiao , Jingbo Zhu , Changliang Li , Derek F. Wong , Lidia S. Chao
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