Loss landscape and symmetries in Neural Networks

Neural networks (NNs) have been very successful in a variety of tasks ranging from machine translation to image classification. Despite their success, the reasons for their performance are still not well-understood. This thesis explores two main themes: loss landscapes and symmetries present in data.Machine learning consists of training models on data by optimizing the model parameters. This optimization is done by minimizing a loss function. NNs, a family of machine learning models, are created by composing functions, called layers. Informally, they can be visualized as a set of interconnected neurons.Ten years ago, NNs became the most popular models of machine learning. With their success come many open questions. For example, neural networks and glassy systems both have many degrees of freedom and highly non-convex objective or energy functions, respectively. However, glassy systems get stuck in local minima near where they are initialized, whereas neural networks avoid this even when they 100s of times more parameters than the number of data use to train them? (i) What drives this difference in behavior? (ii) How is it then that NNs do not become too specialized to the training data (overfitting)?In the first part of this thesis, we show that in classification tasks, NNs undergo a jamming transition dependent on the number of parameters, $N$ . This answers (i): With a sufficiently high $N$ above a critical number $N^*$ , local minima are avoided. Then, we establish a "double-descent" behavior in the test error of classification tasks: It decreases twice as a function of $N$ , before $N^*$ but also after, until infinity, where it converges to its minimum. We answer (ii) by explaining the origins of this double-descent. Finally, we introduce a phase diagram that describes the landscape of the loss function and unifies the two limits in which a neural network can converge when sending $N$ to infinity.In the second part of this thesis, we explore the issue of the curse of dimensionality (CD): Sampling a $d$ -dimensional space requires an exponential number of points $P$ . However, NNs perform well even for $P \ll \exp(d)$ . Symmetries in the data play a role in this conundrum. For example, to process images we use convolutional NNs (CNNs) which have the property of being locally connected and equivariant with respect to translations, i.e., a translation in the input leads to a corresponding translation in the output. Although empirical experience suggests that locality and equivariance contribute to the success of CNNs, it is difficult to understand how. Indeed, equivariance reduces the dimensionality of the data only slightly. Stability toward diffeomorphisms however might be the key to CD. We studied how NNs are affected by images distorted by diffeomorphisms. Our results suggest that locality and equivariance allow, during learning, to develop stability towards diffeomorphisms \textit{relative} to other generic transformations.Following this intuition, we have created new architectures by extending CNNs properties to 3D rotations.Our work contributes to the current understanding of the behavior of neural networks empirically observed by machine learning practitioners. Moreover, the architectures developed for 3D rotation problems are currently being applied to a wide range of domains.

Machine Learning for Information Retrieval

David Grangier

In this thesis, we explore the use of machine learning techniques for information retrieval. More specifically, we focus on ad-hoc retrieval, which is concerned with searching large corpora to identify the documents relevant to user queries. This identification is performed through a ranking task. Given a user query, an ad-hoc retrieval system ranks the corpus documents, so that the documents relevant to the query ideally appear above the others. In a machine learning framework, we are interested in proposing learning algorithms that can benefit from limited training data in order to identify a ranker likely to achieve high retrieval performance over unseen documents and queries. This problem presents novel challenges compared to traditional learning tasks, such as regression or classification. First, our task is a ranking problem, which means that the loss for a given query cannot be measured as a sum of an individual loss suffered for each corpus document. Second, most retrieval queries present a highly unbalanced setup, with a set of relevant documents accounting only for a very small fraction of the corpus. Third, ad-hoc retrieval corresponds to a kind of "double" generalization problem, since the learned model should not only generalize to new documents but also to new queries. Finally, our task also presents challenging efficiency constraints, since ad-hoc retrieval is typically applied to large corpora. The main objective of this thesis is to investigate the discriminative learning of ad-hoc retrieval models. For that purpose, we propose different models based on kernel machines or neural networks adapted to different retrieval contexts. The proposed approaches rely on different online learning algorithms that allow efficient learning over large corpora. The first part of the thesis focuses on text retrieval. In this case, we adopt a classical approach to the retrieval ranking problem, and order the text documents according to their estimated similarity to the text query. The assessment of semantic similarity between text items plays a key role in that setup and we propose a learning approach to identify an effective measure of text similarity. This identification is not performed relying on a set of queries with their corresponding relevant document sets, since such data are especially expensive to label and hence rare. Instead, we propose to rely on hyperlink data, since hyperlinks convey semantic proximity information that is relevant to similarity learning. This setup is hence a transfer learning setup, where we benefit from the proximity information encoded by hyperlinks to improve the performance over the ad-hoc retrieval task. We then investigate another retrieval problem, i.e. the retrieval of images from text queries. Our approach introduces a learning procedure optimizing a criterion related to the ranking performance. This criterion adapts our previous learning objective for learning textual similarity to the image retrieval problem. This yields an image ranking model that addresses the retrieval problem directly. This approach contrasts with previous research that relies on an intermediate image annotation task. Moreover, our learning procedure builds upon recent work on the online learning of kernel-based classifiers. This yields an efficient, scalable algorithm, which can benefit from recent kernels developed for image comparison. In the last part of the thesis, we show that the objective function used in the previous retrieval problems can be applied to the task of keyword spotting, i.e. the detection of given keywords in speech utterances. For that purpose, we formalize this problem as a ranking task: given a keyword, the keyword spotter should order the utterances so that the utterances containing the keyword appear above the others. Interestingly, this formulation yields an objective directly maximizing the area under the receiver operating curve, the most common keyword spotter evaluation measure. This objective is then used to train a model adapted to this intrinsically sequential problem. This model is then learned with a procedure derived from the algorithm previously introduced for the image retrieval task. To conclude, this thesis introduces machine learning approaches for ad-hoc retrieval. We propose learning models for various multi-modal retrieval setups, i.e. the retrieval of text documents from text queries, the retrieval of images from text queries and the retrieval of speech recordings from written keywords. Our approaches rely on discriminative learning and enjoy efficient training procedures, which yields effective and scalable models. In all cases, links with prior approaches were investigated and experimental comparisons were conducted.

École Polytechnique Fédérale de Lausanne2008

Machine Learning for Information Retrieval

David Grangier

In this thesis, we explore the use of machine learning techniques for information retrieval. More specifically, we focus on ad-hoc retrieval, which is concerned with searching large corpora to identify the documents relevant to user queries. Thisidentification is performed through a ranking task. Given a user query, an ad-hoc retrieval system ranks the corpus documents, so that the documents relevant to the query ideally appear above the others. In a machine learning framework, we are interested in proposing learning algorithms that can benefit from limited training data in order to identify a ranker likely to achieve high retrieval performance over unseen documents and queries. This problem presents novel challenges compared to traditional learning tasks, such as regression or classification. First, our task is a ranking problem, which means that the loss for a given query cannot be measured as a sum of an individual loss suffered for each corpus document. Second, most retrieval queries present a highly unbalanced setup, with a set of relevant documents accounting only for a very small fraction of the corpus. Third, ad-hoc retrieval corresponds to a kind of ``double'' generalization problem, since the learned model should not only generalize to new documents but also to new queries. Finally, our task also presents challenging efficiency constraints, since ad-hoc retrieval is typically applied to large corpora. % The main objective of this thesis is to investigate the discriminative learning of ad-hoc retrieval models. For that purpose, we propose different models based on kernel machines or neural networks adapted to different retrieval contexts. The proposed approaches rely on different online learning algorithms that allow efficient learning over large corpora. The first part of the thesis focus on text retrieval. In this case, we adopt a classical approach to the retrieval ranking problem, and order the text documents according to their estimated similarity to the text query. The assessment of semantic similarity between text items plays a key role in that setup and we propose a learning approach to identify an effective measure of text similarity. This identification is not performed relying on a set of queries with their corresponding relevant document sets, since such data are especially expensive to label and hence rare. Instead, we propose to rely on hyperlink data, since hyperlinks convey semantic proximity information that is relevant to similarity learning. This setup is hence a transfer learning setup, where we benefit from the proximity information encoded by hyperlinks to improve the performance over the ad-hoc retrieval task. We then investigate another retrieval problem, i.e. the retrieval of images from text queries. Our approach introduces a learning procedure optimizing a criterion related to the ranking performance. This criterion adapts our previous learning objective for learning textual similarity to the image retrieval problem. This yields an image ranking model that addresses the retrieval problem directly. This approach contrasts with previous research that rely on an intermediate image annotation task. Moreover, our learning procedure builds upon recent work on the online learning of kernel-based classifiers. This yields an efficient, scalable algorithm, which can benefit from recent kernels developed for image comparison. In the last part of the thesis, we show that the objective function used in the previous retrieval problems can be applied to the task of keyword spotting, i.e. the detection of given keywords in speech utterances. For that purpose, we formalize this problem as a ranking task: given a keyword, the keyword spotter should order the utterances so that the utterances containing the keyword appear above the others. Interestingly, this formulation yields an objective directly maximizing the area under the receiver operating curve, the most common keyword spotter evaluation measure. This objective is then used to train a model adapted to this intrinsically sequential problem. This model is then learned with a procedure derived from the algorithm previously introduced for the image retrieval task. To conclude, this thesis introduces machine learning approaches for ad-hoc retrieval. We propose learning models for various multi-modal retrieval setups, i.e. the retrieval of text documents from text queries, the retrieval of images from text queries and the retrieval of speech recordings from written keywords. Our approaches rely on discriminative learning and enjoy efficient training procedures, which yields effective and scalable models. In all cases, links with prior approaches were investigated and experimental comparisons were conducted.

IDIAP2008

Learning embeddings: efficient algorithms and applications

Cijo Jose

Learning to embed data into a space where similar points are together and dissimilar points are far apart is a challenging machine learning problem. In this dissertation we study two learning scenarios that arise in the context of learning embeddings and one scenario in efficiently estimating an empirical expectation. We present novel algorithmic solutions and demonstrate their applications on a wide range of data-sets. The first scenario deals with learning from small data with large number of classes. This setting is common in computer vision problems such as person re-identification and face verification. To address this problem we present a new algorithm called Weighted Approximate Rank Component Analysis (WARCA), which is scalable, robust, non-linear and is independent of the number of classes. We empirically demonstrate the performance of our algorithm on 9 standard person re-identification data-sets where we obtain state of the art performance in terms of accuracy as well as computational speed. The second scenario we consider is learning embeddings from sequences. When it comes to learning from sequences, recurrent neural networks have proved to be an effective algorithm. However there are many problems with existing recurrent neural networks which makes them data hungry (high sample complexity) and difficult to train. We present a new recurrent neural network called Kronecker Recurrent Units (KRU), which addresses the issues of existing recurrent neural networks through Kronecker matrices. We show its performance on 7 applications, ranging from problems in computer vision, language modeling, music modeling and speech recognition. Most of the machine learning algorithms are formulated as minimizing an empirical expectation over a finite collection of samples. In this thesis we also investigate the problem of efficiently estimating a weighted average over large data-sets. We present a new data-structure called Importance Sampling Tree (IST), which permits fast estimation of weighted average without looking at all the samples. We show successfully the evaluation of our data-structure in the training of neural networks in order to efficiently find informative samples.

EPFL2018

Machine Learning for Information Retrieval

David Grangier

École Polytechnique Fédérale de Lausanne2008

Learning embeddings: efficient algorithms and applications

Cijo Jose

EPFL2018

Machine Learning for Information Retrieval

David Grangier

In this thesis, we explore the use of machine learning techniques for information retrieval. More specifically, we focus on ad-hoc retrieval, which is concerned with searching large corpora to identify the documents relevant to user queries. Thisidentification is performed through a ranking task. Given a user query, an ad-hoc retrieval system ranks the corpus documents, so that the documents relevant to the query ideally appear above the others. In a machine learning framework, we are interested in proposing learning algorithms that can benefit from limited training data in order to identify a ranker likely to achieve high retrieval performance over unseen documents and queries. This problem presents novel challenges compared to traditional learning tasks, such as regression or classification. First, our task is a ranking problem, which means that the loss for a given query cannot be measured as a sum of an individual loss suffered for each corpus document. Second, most retrieval queries present a highly unbalanced setup, with a set of relevant documents accounting only for a very small fraction of the corpus. Third, ad-hoc retrieval corresponds to a kind of ``double'' generalization problem, since the learned model should not only generalize to new documents but also to new queries. Finally, our task also presents challenging efficiency constraints, since ad-hoc retrieval is typically applied to large corpora. % The main objective of this thesis is to investigate the discriminative learning of ad-hoc retrieval models. For that purpose, we propose different models based on kernel machines or neural networks adapted to different retrieval contexts. The proposed approaches rely on different online learning algorithms that allow efficient learning over large corpora. The first part of the thesis focus on text retrieval. In this case, we adopt a classical approach to the retrieval ranking problem, and order the text documents according to their estimated similarity to the text query. The assessment of semantic similarity between text items plays a key role in that setup and we propose a learning approach to identify an effective measure of text similarity. This identification is not performed relying on a set of queries with their corresponding relevant document sets, since such data are especially expensive to label and hence rare. Instead, we propose to rely on hyperlink data, since hyperlinks convey semantic proximity information that is relevant to similarity learning. This setup is hence a transfer learning setup, where we benefit from the proximity information encoded by hyperlinks to improve the performance over the ad-hoc retrieval task. We then investigate another retrieval problem, i.e. the retrieval of images from text queries. Our approach introduces a learning procedure optimizing a criterion related to the ranking performance. This criterion adapts our previous learning objective for learning textual similarity to the image retrieval problem. This yields an image ranking model that addresses the retrieval problem directly. This approach contrasts with previous research that rely on an intermediate image annotation task. Moreover, our learning procedure builds upon recent work on the online learning of kernel-based classifiers. This yields an efficient, scalable algorithm, which can benefit from recent kernels developed for image comparison. In the last part of the thesis, we show that the objective function used in the previous retrieval problems can be applied to the task of keyword spotting, i.e. the detection of given keywords in speech utterances. For that purpose, we formalize this problem as a ranking task: given a keyword, the keyword spotter should order the utterances so that the utterances containing the keyword appear above the others. Interestingly, this formulation yields an objective directly maximizing the area under the receiver operating curve, the most common keyword spotter evaluation measure. This objective is then used to train a model adapted to this intrinsically sequential problem. This model is then learned with a procedure derived from the algorithm previously introduced for the image retrieval task. To conclude, this thesis introduces machine learning approaches for ad-hoc retrieval. We propose learning models for various multi-modal retrieval setups, i.e. the retrieval of text documents from text queries, the retrieval of images from text queries and the retrieval of speech recordings from written keywords. Our approaches rely on discriminative learning and enjoy efficient training procedures, which yields effective and scalable models. In all cases, links with prior approaches were investigated and experimental comparisons were conducted.

IDIAP2008