These are my recent Pinboard.in links:
- “Autoencoders are unsupervised machine learning circuits whose learning goal is to minimize a distortion measure between inputs and outputs. Linear autoencoders can be defined over any field and only real-valued linear autoencoder have been studied so far. Here we study complex-valued linear autoencoders where the components of the training vectors and adjustable matrices are defined over the complex field with the $L_2$ norm. We provide simpler and more general proofs that unify the real-valued and complex-valued cases, showing that in both cases the landscape of the error function is invariant under certain groups of transformations. The landscape has no local minima, a family of global minima associated with Principal Component Analysis, and many families of saddle points associated with orthogonal projections onto sub-space spanned by sub-optimal subsets of eigenvectors of the covariance matrix. The theory yields several iterative, convergent, learning algorithms, a clear understanding of the generalization properties of the trained autoencoders, and can equally be applied to the hetero-associative case when external targets are provided. Partial results on deep architecture as well as the differential geometry of autoencoders are also presented. The general framework described here is useful to classify autoencoders and identify general common properties that ought to be investigated for each class, illuminating some of the connections between information theory, unsupervised learning, clustering, Hebbian learning, and auto encoders.”
neural-networks machine-learning classification encoding algorithms nudge-targets [1108.5685] Predicting flow reversals in chaotic natural convection using data assimilation
“A simplified model of natural convection, similar to the Lorenz (1963) system, is compared to computational fluid dynamics simulations in order to test data assimilation methods and better understand the dynamics of convection. The thermosyphon is represented by a long time flow simulation, which serves as a reference “truth”. Forecasts are then made using the Lorenz-like model and synchronized to noisy and limited observations of the truth using data assimilation. The resulting analysis is observed to infer dynamics absent from the model when using short assimilation windows. Furthermore, chaotic flow reversal occurrence and residency times in each rotational state are forecast using analysis data. Flow reversals have been successfully forecast in the related Lorenz system, as part of a perfect model experiment, but never in the presence of significant model error or unobserved variables. Finally, we provide new details concerning the fluid dynamical processes present in the thermosyphon during these flow reversals.”
chaos dynamical-systems experiment prediction numerical-methods algorithms nudge-targets- “Motivated by the problems of computing sample covariance matrices, and of transforming a collection of vectors to a basis where they are sparse, we present a simple algorithm that computes an approximation of the product of two n-by-n real matrices A and B.…”
approximation algorithms nudge-targets [1110.5296] Computing a Longest Common Palindromic Subsequence
“The {em longest common subsequence (LCS)} problem is a classic and well-studied problem in computer science. Palindrome is a word which reads the same forward as it does backward. The {em longest common palindromic subsequence (LCPS)} problem is an interesting variant of the classic LCS problem which finds the longest common subsequence between two given strings such that the computed subsequence is also a palindrome. In this paper, we study the LCPS problem and give efficient algorithms to solve this problem. To the best of our knowledge, this is the first attempt to study and solve this interesting problem.”
combinatorics strings algorithms nudge-targets