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when trees fall... | The New XOR Problem

In 1969, Marvin Minsky and Seymour Papert published Perceptrons: An Introduction to Computational Geometry. In it, they showed that a single-layer perceptron cannot compute the XOR function. The main argument relies on linear separability: Perceptrons are linear classifiers, which essentially means drawing a line to separate input that would result in 1 versus 0. You can do it in the OR and AND case, but not XOR.
Of course, we’re way past that now, neural networks with one hidden layer can solve that problem. ....

Michael Hahn , Marvin Minsky , Seymour Papert , Cassian Andor , Neural Networks , Data Structures , Computational Complexity , Theoretical Limitations , Neural Sequence Models , Constant Depth Threshold Circuits , Chomsky Hierarchy , Recognize Formal Languages , Theoretical Limitation , Universal Turing , Universal Transformer ,

The Transformer Family Version 2.0

Many new Transformer architecture improvements have been proposed since my last post on “The Transformer Family” about three years ago. Here I did a big refactoring and enrichment of that 2020 post — restructure the hierarchy of sections and improve many sections with more recent papers. Version 2.0 is a superset of the old version, about twice the length.
Notations Symbol Meaning $d$ The model size / hidden state dimension / positional encoding size. ....

Mostafa Dehghani , Olah Carter , Emilio Parisotto , Sainbayar Sukhbaatar , Alex Graves , Longformer Beltagy , Niki Parmar , Ashish Vaswani , Nikita Kitaev , Zihang Dai , Linformer Wang , Rahimi Recht , Aidann Gomez , Adaptive Computation Time For Recurrent Neural Networks , A Survey , Recurrent Neural Networks , Rotary Position Embedding , Memorizing Transformer , Aware Transformer , Linear Biases , Universal Transformer , Adaptive Attention , Adaptive Computation Time , Depth Adaptive Transformer , Confident Adaptive Language Model , Efficient Transformers ,