39068570
Learning, Logic, and Topology in a Common Framework
Many connections have been established between learning and logic, or learning and topology, or logic and topology. Still, the connections are not at the heart of these fields. Each of them is fairly independent of the others when attention is restricted to basic notions and main results. We show that connections can actually be made at a fundamental level, and result in a parametrized logic that needs topological notions for its early developments, and notions from learning theory for interpretation and applicability.One of the key properties of first-order logic is that the classical notion of logical consequence is compact. We generalize the notion of logical consequence, and we generalize compactness to s-weak compactness where s is an ordinal. The effect is to stratify the set of generalized logical consequences of a theory into levels, and levels into layers. Deduction corresponds to the lower layer of the first level above the underlying theory, learning with less than s mind changes to layer s of the first level, and learning in the limit to the first layer of the second level. Refinements of Borel-like hierarchies provide the topological tools needed to develop the framework.
2402100
Input-Dependence in Function-Learning
In the standard literature on inductive inference, a learner sees as input the course of values of the function to be learned. In the present work, it is investigated how reasonable this choice is and how sensitive the model is with respect to variations like the overgraph or undergraph of the function. Several implications and separations are shown and for the basic notions, a complete picture is obtained. Furthermore, relations to oracles, additional information and teams are explored.
7592429
On the Convergence of Incremental Knowledge Base Construction
Ripple Down Rules is a practical methodology to build knowledge-based systems, which has proved successful in a wide range of commercial applications. However, little work has been done on its theoretical foundations. In this paper, we formalise the key features of the method. We present the process of building a correct knowledge base as a discovery scenario involving a user, an expert, and a system. The user provides data for classification. The expert helps the system to build its knowledge base incrementally, using the output of the latter in response to the last datum provided by the user. In case the system’s output is not satisfactory, the expert guides the system to improve its future performance while not affecting its ability to properly classify past data. We examine under which conditions the sequence of knowledge bases constructed by the system eventually converges to a knowledge base that faithfully represents the target classification function. Our results are in accordance with the observed behaviour of real-life systems.
38643151
Learning from Each Other
Since its inception, the field of machine learning has seen the advent of several learning paradigms, designed to frame the issues central to the learning activity, provide effective learning methods, and investigate the power and limitations inherent to the process of successful learning. In this article, we propose a formalization that underlies the key concepts of many such paradigms and discuss their relevance to scientific discovery, with the aim of assessing what scientists can expect from machines designed to assist them in their quest for the discovery of valid laws. We illustrate the formalization on several variations of a card game, and highlight the differences that paradigms impose on learners, as well as the assumptions they make on the nature of the learning process. We then use the formalization to describe a multi-agent interaction protocol, that has been inspired by these paradigms and that has been validated recently on some groups of agents. Finally, we propose extensions to this protocol.
39139980
On Sufficient Conditions for Learnability of Logic Programs from Positive Data
Shinohara, Arimura, and Krishna Rao have shown learnability in the limit of minimal models of classes of logic programs from positive only data. In most cases, these results involve logic programs in which the "size" of the head yields a bound on the size of the body literals. However, when local variables are present, such a bound on body literal size cannot directly be ensured. The above authors achieve such a restriction using technical notions like mode and linear inequalities. The present paper develops a conceptually clean framework where the behavior of local variables is controlled by nonlocal ones. It is shown that for certain classes of logic programs, learnablity from positive data is equivalent to limiting identification of bounds for the number of clauses and the number of local variables. This reduces the learning problem finding two integers. This cleaner framework generalizes all the known results and establishes learnability of new classes.
37212285
Quantification over names and modalities
34573352
A Vision System on Chip for Industrial Control
This paper describes the building of an original vision system on chip. Our smart sensor performs motion detection and pattern recognition with only one single line of pixels. The maximum cross-correlation number is processed by the processors network. A peculiar methodology was defined to tackle the sensor’s processing part design. Relying on our architectural synthesis tool GAUT, it leads to an optimal matching between the application specifications, the sensor’s architecture and the processor’s. The elementary processor’s architecture is detailed. Its CMOS VLSI implementation is sketched, as well as the sensor’s analog part and the light to byte conversion. The circuit’s final structure and floorplan are outlined. Its performances are exhibited.
62212474
A design flow dedicated to multi-mode architectures for DSP applications
This paper addresses the design of multi-mode architectures for digital signal processing applications. We present a dedicated design flow and its associated high-level synthesis tool, named GAUT. Given a unified description of a set of time-wise mutually exclusive tasks and their associated throughput constraints, a single RTL hardware architecture optimized in area is generated. In order to reduce the register, steering logic (multiplexers) and controller (decoding logic) complexities, we propose a joint-scheduling algorithm which maximizes the similarities between control steps and specific binding approaches for both functional units and storage elements which maximize the similarities between the datapaths. We show through a set of test cases that our approach offers significant area saving relative to the state-of-the-art.
15437667
A multi-level design flow for incorporating IP cores: case study of 1D wavelet IP integration
The design of high performance multimedia systems in a short time force us to use IP blocks in many designs. However, their correct integration in a design implies more complex verification problems. In this paper, we present a C++/SystemC based simulation flow at multiple levels of abstraction. Our approach is to use SystemC to describe both the application and a set of algorithmic IP cores to be incorporated throughout the design flow. Our methodology supports design refinement through four main abstraction levels, offers verification techniques at each level and allows the use of EDA co-verification tools. The use of C++/SystemC to model all parts of the system provides great flexibility and enables faster simulation compared to existing methodologies. An illustrative case study for wavelet based compression system design shows that our methodology supports efficient algorithmic specification, where IP models can be easily incorporated, modified and simulated in order to quickly evaluate alternative system implementation.
34309839
Design of a flexible 2-D discrete wavelet transform IP core for JPEG2000 image coding in embedded imaging systems
The increasingly demanding requirements of multimedia applications have led to the definition of complex image and video coding standards such as JPEG2000 and MPEG4. Implementation of image or video encoders or decoders on mobile device requires high integration densities together with ability for "real-time" (on-the-fly) data processing. Today, the electronic system design community is mainly concerned with defining efficient System-on-a-Chip (SoC) design methodologies in order to benefit from the high integration capabilities of current application-specific integrated circuit and field-programmable gate array technologies on the one hand, and manage the increasing algorithmic complexity of applications on the other hand. Intellectual property (IP) reuse is considered as the key to speed up the system design and verification flow and make it more reliable.In this context, we have introduced a novel methodology for VLSI implementation of computation-intensive algorithms targeting digital signal processing applications. Our methodology combines IP reuse and high-level synthesis (HLS) and introduces the notion of "Behavioral IP". This approach aims at leveraging IP re-usability through functional and architectural flexibility based on: (1) modeling a component's behavior at a high abstraction level and (2) benefiting from HLS tools for architectural exploration and hardware generation.In this paper, we illustrate our methodology in the case of a 2-D discrete wavelet transform IP core for JPEG2000 image compression. We describe the successive views of the component throughout the design flow, from the application level down to the architectural level. We also provide synthesis results showing the variety of dedicated architectures that can be generated depending on user-defined functional-level, system-level and architectural-level requirements. We compare the performance and re-usability of the set of obtained architectures versus hand-crafted RTL specifications.
5876918
A Methodology for Efficient Space-Time Adapter Design Space Exploration: A Case Study of an Ultra Wide Band Interleaver
This paper presents a solution to efficiently explore the design space of communication adapters. In most digital signal processing (DSP) applications, the overall architecture of the system is significantly affected by communication architecture, so the designers need specifically optimized adapters. By explicitly modeling these communications within an effective graph-theoretic model and analysis framework, we automatically generate an optimized architecture, named Space-Time AdapteR (STAR). Our design flow inputs a C description of input/output data scheduling, and user requirements (throughput, latency, parallelism...), and formalizes communication constraints through a resource constraints graph (RCG). The RCG properties enable an efficient architecture space exploration in order to synthesize a STAR component. The proposed approach has been tested to design an industrial data mixing block example: an ultra-wideband interleaver.