In this paper we explore how machine learning techniques can be applied to the discovery of efficient mathematical identities. We introduce an attribute grammar framework for representing symbolic expressions. Given a grammar of math operators, we build trees that combine them in different ways, looking for compositions that are analytically equivalent to a target expression but of lower computational complexity. However, as the space of trees grows exponentially with the complexity of the target expression, brute force search is impractical for all but the simplest of expressions. Consequently, we introduce two novel learning approaches that are able to learn from simpler expressions to guide the tree search. The first of these is a simple n -gram model, the other being a recursive neural-network. We show how these approaches enable us to derive complex identities, beyond reach of brute-force search, or human derivation.

In this paper we explore how machine learning techniques can be applied to the discovery of efficient mathematical identities. We introduce an attribute grammar framework for representing symbolic expressions. Given a grammar of math operators, we build trees that combine them in different ways, looking for compositions that are analytically equivalent to a target expression but of lower computational complexity. However, as the space of trees grows exponentially with the complexity of the target expression, brute force search is impractical for all but the simplest of expressions. Consequently, we introduce two novel learning approaches that are able to learn from simpler expressions to guide the tree search. The first of these is a simple n-gram model, the other being a recursive neural-network. We show how these approaches enable us to derive complex identities, beyond reach of brute-force search, or human derivation.

We present RXTX, a new algorithm for computing the product of matrix by its transpose $XX^{t}$ for $X\in \mathbb{R}^{n\times m}$. RXTX uses $5\%$ fewer multiplications and $5\%$ fewer operations (additions and multiplications) than State-of-the-Art algorithms. Note that the accelerations not only holds asymptotically for large matrices with $n \rightarrow \infty$, but also for small matrices including $n = 4$. The algorithm was discovered by combining Machine Learning-based search methods with Combinatorial Optimization.

Facial expression manipulation aims to change human facial expressions without affecting face recognition. In order to transform the facial expressions to target expressions, previous methods relied on expression labels to guide the manipulation process. However, these methods failed to preserve the details of facial features, which causes the weakening or the loss of identity information in the output image. In our work, we propose WEM-GAN, in short for wavelet-based expression manipulation GAN, which puts more efforts on preserving the details of the original image in the editing process. Firstly, we take advantage of the wavelet transform technique and combine it with our generator with a U-net autoencoder backbone, in order to improve the generator's ability to preserve more details of facial features. Secondly, we also implement the high-frequency component discriminator, and use high-frequency domain adversarial loss to further constrain the optimization of our model, providing the generated face image with more abundant details. Additionally, in order to narrow the gap between generated facial expressions and target expressions, we use residual connections between encoder and decoder, while also using relative action units (AUs) several times. Extensive qualitative and quantitative experiments have demonstrated that our model performs better in preserving identity features, editing capability, and image generation quality on the AffectNet dataset. It also shows superior performance in metrics such as Average Content Distance (ACD) and Expression Distance (ED).

There are two recent trends in transportation and the broader science/engineering fields, which make the headlines almost every day. The first one is the emergence of connected/automated vehicles (CAVs) that i) may introduce new, complex traffic dynamics and interactions in the current and future traffic streams, and ii) generate increasingly available and massive datasets from both vehicles and the infrastructure. The second trend is the rapid development and application of deep learning techniques that seem to revolutionize almost every aspect of technology, science, engineering, and the entire society. While there have been numerous studies and applications of deep learning in transportation, in the paper, we are interested in the question of whether deep learning can help discover traffic dynamics (car-following models in particular) from data directly with no or little human involvement. An affirmative answer to this question will not only help discover/develop traffic dynamics models in this era but also have important implications for other science/engineering fields where dynamical systems and their governing equations are widely used and studied. Car-following depicts the driving behavior of how a vehicle (driver) follows and interacts with the vehicle in front of it. It is one of the basic traffic models in revealing traffic dynamics characteristics at the microscopic traffic flow level Brackstone and McDonald [1999]. Car-following studies can be traced back to the 1950s and 1960s when Pipes [1953], Chandler et al. [1958], Kometani and Sasaki [1958], Gazis et al. [1959, 1961], and Helly [1959] initiated an era of modeling car-following and traffic dynamics.

In this paper we explore how machine learning techniques can be applied to the discovery of efficient mathematical identities. We introduce an attribute grammar framework for representing symbolic expressions. Given a grammar of math operators, we build trees that combine them in different ways, looking for compositions that are analytically equivalent to a target expression but of lower computational complexity. However, as the space of trees grows exponentially with the complexity of the target expression, brute force search is impractical for all but the simplest of expressions. Consequently, we introduce two novel learning approaches that are able to learn from simpler expressions to guide the tree search. The first of these is a simple n-gram model, the other being a recursive neuralnetwork. We show how these approaches enable us to derive complex identities, beyond reach of brute-force search, or human derivation.

Multiword expressions (MWEs) are composed of multiple words and exhibit variable degrees of compositionality. As such, their meanings are notoriously difficult to model, and it is unclear to what extent this issue affects transformer architectures. Addressing this gap, we provide the first in-depth survey of MWE processing with transformer models. We overall find that they capture MWE semantics inconsistently, as shown by reliance on surface patterns and memorized information. MWE meaning is also strongly localized, predominantly in early layers of the architecture. Representations benefit from specific linguistic properties, such as lower semantic idiosyncrasy and ambiguity of target expressions. Our findings overall question the ability of transformer models to robustly capture fine-grained semantics. Furthermore, we highlight the need for more directly comparable evaluation setups.

This paper explores the task of identifying the overall sentiment expressed towards volitional entities (persons and organizations) in a document -- what we refer to as Entity-Level Sentiment Analysis (ELSA). While identifying sentiment conveyed towards an entity is well researched for shorter texts like tweets, we find little to no research on this specific task for longer texts with multiple mentions and opinions towards the same entity. This lack of research would be understandable if ELSA can be derived from existing tasks and models. To assess this, we annotate a set of professional reviews for their overall sentiment towards each volitional entity in the text. We sample from data already annotated for document-level, sentence-level, and target-level sentiment in a multi-domain review corpus, and our results indicate that there is no single proxy task that provides this overall sentiment we seek for the entities at a satisfactory level of performance. We present a suite of experiments aiming to assess the contribution towards ELSA provided by document-, sentence-, and target-level sentiment analysis, and provide a discussion of their shortcomings. We show that sentiment in our dataset is expressed not only with an entity mention as target, but also towards targets with a sentiment-relevant relation to a volitional entity. In our data, these relations extend beyond anaphoric coreference resolution, and our findings call for further research of the topic. Finally, we also present a survey of previous relevant work.

The image synthesis technique is relatively well established which can generate facial images that are indistinguishable even by human beings. However, all of these approaches uses gradients to condition the output, resulting in the outputting the same image with the same input. Also, they can only generate images with basic expression or mimic an expression instead of generating compound expression. In real life, however, human expressions are of great diversity and complexity. In this paper, we propose an evolutionary algorithm (EA) assisted GAN, named EvoGAN, to generate various compound expressions with any accurate target compound expression. EvoGAN uses an EA to search target results in the data distribution learned by GAN. Specifically, we use the Facial Action Coding System (FACS) as the encoding of an EA and use a pre-trained GAN to generate human facial images, and then use a pre-trained classifier to recognize the expression composition of the synthesized images as the fitness function to guide the search of the EA. Combined random searching algorithm, various images with the target expression can be easily sythesized. Quantitative and Qualitative results are presented on several compound expressions, and the experimental results demonstrate the feasibility and the potential of EvoGAN.

In this paper we explore how machine learning techniques can be applied to the discovery of efficient mathematical identities. We introduce an attribute grammar framework for representing symbolic expressions. Given a grammar of math operators, we build trees that combine them in different ways, looking for compositions that are analytically equivalent to a target expression but of lower computational complexity. However, as the space of trees grows exponentially with the complexity of the target expression, brute force search is impractical for all but the simplest of expressions. Consequently, we introduce two novel learning approaches that are able to learn from simpler expressions to guide the tree search. The first of these is a simple n-gram model, the other being a recursive neural-network.