Cognitive Deficit of Deep Learning in Numerosity

Subitizing, or the sense of small natural numbers, is an innate cognitive function of humans and primates; it responds to visual stimuli prior to the development of any symbolic skills, language or arithmetic. Given successes of deep learning (DL) in tasks of visual intelligence and given the primitivity of number sense, a tantalizing question is whether DL can comprehend numbers and perform subitizing. But somewhat disappointingly, extensive experiments of the type of cognitive psychology demonstrate that the examples-driven black box DL cannot see through superficial variations in visual representations and distill the abstract notion of natural number, a task that children perform with high accuracy and confidence. The failure is apparently due to the learning method not the CNN computational machinery itself. A recurrent neural network capable of subitizing does exist, which we construct by encoding a mechanism of mathematical morphology into the CNN convolutional kernels. Also, we investigate, using subitizing as a test bed, the ways to aid the black box DL by cognitive priors derived from human insight. Our findings are mixed and interesting, pointing to both cognitive deficit of pure DL, and some measured successes of boosting DL by predetermined cognitive implements. This case study of DL in cognitive computing is meaningful for visual numerosity represents a minimum level of human intelligence.Comment: Accepted for presentation at the AAAI-1

Building Efficient Query Engines in a High-Level Language

Abstraction without regret refers to the vision of using high-level programming languages for systems development without experiencing a negative impact on performance. A database system designed according to this vision offers both increased productivity and high performance, instead of sacrificing the former for the latter as is the case with existing, monolithic implementations that are hard to maintain and extend. In this article, we realize this vision in the domain of analytical query processing. We present LegoBase, a query engine written in the high-level language Scala. The key technique to regain efficiency is to apply generative programming: LegoBase performs source-to-source compilation and optimizes the entire query engine by converting the high-level Scala code to specialized, low-level C code. We show how generative programming allows to easily implement a wide spectrum of optimizations, such as introducing data partitioning or switching from a row to a column data layout, which are difficult to achieve with existing low-level query compilers that handle only queries. We demonstrate that sufficiently powerful abstractions are essential for dealing with the complexity of the optimization effort, shielding developers from compiler internals and decoupling individual optimizations from each other. We evaluate our approach with the TPC-H benchmark and show that: (a) With all optimizations enabled, LegoBase significantly outperforms a commercial database and an existing query compiler. (b) Programmers need to provide just a few hundred lines of high-level code for implementing the optimizations, instead of complicated low-level code that is required by existing query compilation approaches. (c) The compilation overhead is low compared to the overall execution time, thus making our approach usable in practice for compiling query engines

Learning by Seeing by Doing: Arithmetic Word Problems

Learning by doing in pursuit of real-world goals has received much attention from education researchers but has been unevenly supported by mathematics education software at the elementary level, particularly as it involves arithmetic word problems. In this article, we give examples of doing-oriented tools that might promote children\u27s ability to see significant abstract structures in mathematical situations. The reflection necessary for such seeing is motivated by activities and contexts that emphasize affective and social aspects. Natural language, as a representation already familiar to children, is key in these activities, both as a means of mathematical expression and as a link between situations and various abstract representations. These tools support children\u27s ownership of a mathematical problem and its expression; remote sharing of problems and data; software interpretation of children\u27s own word problems; play with dynamically linked representations with attention to children\u27s prior connections; and systematic problem variation based on empirically determined level of difficulty

A survey of behavioral-level partitioning systems

Many approaches have been developed to partition a system's behavioral description before a structural implementation is synthesized. We highlight the foundations and motivations for behavioral partitioning. We survey behavioral partitioning approaches, discussing abstraction levels, goals, major steps, and key assumptions in each

Debugging Scandal: The Next Generation

In 1997, the general lack of debugging tools was termed "the debugging scandal". Today, as new languages are emerging to support software evolution, once more debugging support is lagging. The powerful abstractions offered by new languages are compiled away and transformed into complex synthetic structures. Current debugging tools only allow inspection in terms of this complex synthetic structure; they do not support observation of program executions in terms of the original development abstractions. In this position paper, we outline this problem and present two emerging lines of research that ease the burden for debugger implementers and enable developers to debug in terms of development abstractions. For both approaches we identify language-independent debugger components and those that must be implemented for every new language. One approach restores the abstractions by a tool external to the program. The other maintains the abstractions by using a dedicated execution environment, supporting the relevant abstractions. Both approaches have the potential of improving debugging support for new languages. We discuss the advantages and disadvantages of both approaches, outline a combination thereof and also discuss open challenges