In September 2018, I published a blog about my forthcoming book on The Mathematical Foundations of Data Science. The central question we address is: How can we bridge the gap between mathematics needed for Artificial Intelligence (Deep Learning and Machine learning) with that taught in high schools (up to ages 17/18)? In this post, we present a chapter from this book called "A Taxonomy of Machine Learning Models." The book is now available for an early bird discount released as chapters. If you are interested in getting early discounted copies, please contact ajit.jaokar at feynlabs.ai.

In this post we will see how to vectorize across multiple training examples. The outcome will be similar to what we saw in Logistic Regression. These equations tell us how, when given an input feature vector \(x \), we can generate predictions. If we have \(m \) training examples we need to repeat this proces \(m \) times. The notation \( a {[2](i)} \) means that we are talking about activation in the second layer that comes from \(i {th} \) training example.

Hamiltonian learning is an important procedure in quantum system identification, calibration, and successful operation of quantum computers. Through queries to the quantum system, this procedure seeks to obtain the parameters of a given Hamiltonian model and description of noise sources. Standard techniques for Hamiltonian learning require careful design of queries and $O(\epsilon^{-2})$ queries in achieving learning error $\epsilon$ due to the standard quantum limit. With the goal of efficiently and accurately estimating the Hamiltonian parameters within learning error $\epsilon$ through minimal queries, we introduce an active learner that is given an initial set of training examples and the ability to interactively query the quantum system to generate new training data. We formally specify and experimentally assess the performance of this Hamiltonian active learning (HAL) algorithm for learning the six parameters of a two-qubit cross-resonance Hamiltonian on four different superconducting IBM Quantum devices. Compared with standard techniques for the same problem and a specified learning error, HAL achieves up to a $99.8\%$ reduction in queries required, and a $99.1\%$ reduction over the comparable non-adaptive learning algorithm. Moreover, with access to prior information on a subset of Hamiltonian parameters and given the ability to select queries with linearly (or exponentially) longer system interaction times during learning, HAL can exceed the standard quantum limit and achieve Heisenberg (or super-Heisenberg) limited convergence rates during learning.

Posted by Shekoofeh Azizi, AI Resident, Google Research In recent years, there has been increasing interest in applying deep learning to ...

Multi-Modal Self-Supervised Learning from videos has been shown to improve model's performance on various downstream tasks. However, such Self-Supervised pre-training requires large batch sizes and a large amount of computation resources due to the noise present in the uncurated data. This is partly due to the fact that the prevalent training scheme is trained on coarse-grained setting, in which vectors representing the whole video clips or natural language sentences are used for computing similarity. Such scheme makes training noisy as part of the video clips can be totally not correlated with the other-modality input such as text description. In this paper, we propose a fine-grained multi-modal self-supervised training scheme that computes the similarity between embeddings at finer-scale (such as individual feature map embeddings and embeddings of phrases), and uses attention mechanisms to reduce noisy pairs' weighting in the loss function. We show that with the proposed pre-training scheme, we can train smaller models, with smaller batch-size and much less computational resources to achieve downstream tasks performances comparable to State-Of-The-Art, for tasks including action recognition and text-image retrievals.

Computer scientists from Lancaster University have developed new AI technology that takes autonomous cars a step closer to our roads. Funded by global car manufacturer Ford, the three-year research project provides a step-change in AI car technology by enabling autonomous cars to recognise new and unexpected situations. Around the world, many different automotive brands, computing companies, and research teams, are developing autonomous car technologies and many of these are using a machine learning technique called'Deep Learning'. Deep Learning works by recognising patterns after the computer system has been shown a large number of different training examples. However, a fundamental drawback with Deep Learning algorithms is that they are unable to recognise scenarios that differ significantly from training examples and, unlike humans, they are incapable of exploring, improving and improvising.

How can an end-user provide feedback if a deployed structured prediction model generates incorrect output? Our goal is to allow users to correct errors directly through interaction, without retraining, by giving feedback on the model's output. We create a dynamic memory architecture with a growing memory of feedbacks about errors in the output. Given a new, unseen input, our model can use feedback from a similar, past erroneous state. On a script generation task, we show empirically that the model learns to apply feedback effectively (up to 30 points improvement), while avoiding similar past mistakes after deployment (up to 10 points improvement on an unseen set). This is a first step towards strengthening deployed models, potentially broadening their utility.

Sparsity priors are commonly used in denoising and image reconstruction. For analysis-type priors, a dictionary defines a representation of signals that is likely to be sparse. In most situations, this dictionary is not known, and is to be recovered from pairs of ground-truth signals and measurements, by minimizing the reconstruction error. This defines a hierarchical optimization problem, which can be cast as a bi-level optimization. Yet, this problem is unsolvable, as reconstructions and their derivative wrt the dictionary have no closed-form expression. However, reconstructions can be iteratively computed using the Forward-Backward splitting (FB) algorithm. In this paper, we approximate reconstructions by the output of the aforementioned FB algorithm. Then, we leverage automatic differentiation to evaluate the gradient of this output wrt the dictionary, which we learn with projected gradient descent. Experiments show that our algorithm successfully learns the 1D Total Variation (TV) dictionary from piecewise constant signals. For the same case study, we propose to constrain our search to dictionaries of 0-centered columns, which removes undesired local minima and improves numerical stability.

Our work reveals a structured shortcoming of the existing mainstream self-supervised learning methods. Whereas self-supervised learning frameworks usually take the prevailing perfect instance level invariance hypothesis for granted, we carefully investigate the pitfalls behind. Particularly, we argue that the existing augmentation pipeline for generating multiple positive views naturally introduces out-of-distribution (OOD) samples that undermine the learning of the downstream tasks. Generating diverse positive augmentations on the input does not always pay off in benefiting downstream tasks. To overcome this inherent deficiency, we introduce a lightweight latent variable model UOTA, targeting the view sampling issue for self-supervised learning. UOTA adaptively searches for the most important sampling region to produce views, and provides viable choice for outlier-robust self-supervised learning approaches. Our method directly generalizes to many mainstream self-supervised learning approaches, regardless of the loss's nature contrastive or not. We empirically show UOTA's advantage over the state-of-the-art self-supervised paradigms with evident margin, which well justifies the existence of the OOD sample issue embedded in the existing approaches. Especially, we theoretically prove that the merits of the proposal boil down to guaranteed estimator variance and bias reduction. Code is available: at https://github.com/ssl-codelab/uota.

In this paper, we tackle the inductive semi-supervised learning problem that aims to obtain label predictions for out-of-sample data. The proposed approach, called Optimal Transport Induction (OTI), extends efficiently an optimal transport based transductive algorithm (OTP) to inductive tasks for both binary and multi-class settings. A series of experiments are conducted on several datasets in order to compare the proposed approach with state-of-the-art methods. Experiments demonstrate the effectiveness of our approach. We make our code publicly available.