An algorithm for learning from hints

To take advantage of prior knowledge (hints) about the function one wants to learn, we introduce a method that generalizes learning from examples to learning from hints. A canonical representation of hints is defined and illustrated. All hints are represented to the learning process by examples, and examples of the function are treated on equal footing with the rest of the hints. During learning, examples from different hints are selected for processing according to a given schedule. We present two types of schedules; fixed schedules that specify the relative emphasis of each hint, and adaptive schedules that are based on how well each hint has been learned so far. Our learning method is compatible with any descent technique

Maximal codeword lengths in Huffman codes

The following question about Huffman coding, which is an important technique for compressing data from a discrete source, is considered. If p is the smallest source probability, how long, in terms of p, can the longest Huffman codeword be? It is shown that if p is in the range 0 less than p less than or equal to 1/2, and if K is the unique index such that 1/F(sub K+3) less than p less than or equal to 1/F(sub K+2), where F(sub K) denotes the Kth Fibonacci number, then the longest Huffman codeword for a source whose least probability is p is at most K, and no better bound is possible. Asymptotically, this implies the surprising fact that for small values of p, a Huffman code's longest codeword can be as much as 44 percent larger than that of the corresponding Shannon code

Isothermal Cylindrical Couette Flow Of Oldroyd 8-Constant Model Fluid Up To Second-order

The steady flow of an incompressible Oldroyd 8-constant fluid in the annular region between two concentric cylinders, or so-called cylindrical Couette flow, is investigated. The inner cylinder rotates with an angular velocity about its own axis, z-axis, while the outer cylinder is kept at rest. The viscoelasticity of the fluid is assumed to dominate the inertia such that the latter can be neglected in the momentum equation. An analytical solution is obtained through the expansion of the dynamical variables in power series of the dimensionless retardation time. The primary velocity term denotes the Newtonian rotation about the z-axis. The first-order is a vanishing term. The second-order results in a secondary flow represented by the stream-function. This second-order term is the viscoelastic contribution to the primary viscous flow. The second-order approximation depends on the four viscometric parameters of the fluid

Maximum Resilience of Artificial Neural Networks

The deployment of Artificial Neural Networks (ANNs) in safety-critical applications poses a number of new verification and certification challenges. In particular, for ANN-enabled self-driving vehicles it is important to establish properties about the resilience of ANNs to noisy or even maliciously manipulated sensory input. We are addressing these challenges by defining resilience properties of ANN-based classifiers as the maximal amount of input or sensor perturbation which is still tolerated. This problem of computing maximal perturbation bounds for ANNs is then reduced to solving mixed integer optimization problems (MIP). A number of MIP encoding heuristics are developed for drastically reducing MIP-solver runtimes, and using parallelization of MIP-solvers results in an almost linear speed-up in the number (up to a certain limit) of computing cores in our experiments. We demonstrate the effectiveness and scalability of our approach by means of computing maximal resilience bounds for a number of ANN benchmark sets ranging from typical image recognition scenarios to the autonomous maneuvering of robots.Comment: Timestamp research work conducted in the project. version 2: fix some typos, rephrase the definition, and add some more existing wor

Tunnel Probabilistic Structural Analysis Using the FORM

In this paper tunnel probabilistic structural analysis (TuPSA) was performed using the first order reliability method (FORM). In TuPSA, a tunnel performance function is defined according to the boundary between the structural stability and instability. Then the performance function is transformed from original space into the standard normal variable space to obtain the design point, reliability index, and also the probability of tunnel failure. In this method, it is possible to consider the design factors as the dependent or independent random parameters with arbitrary probability distributions. A software code is developed to perform the tunnel probabilistic structural analysis (TuPSA) using the FORM. For validation and verification of TuPSA, a typical tunnel example with random joints orientations as well as mechanical properties has been studied. The results of TuPSA were compared with those obtained from Monte-Carlo simulation. The results show, in spite of deterministic analysis which indicates that the rock blocks are stable, that TuPSA resulted in key-blocks failure with certain probabilities. Comparison between probabilistic and deterministic analyses results indicates that probabilistic results, including the design point and probability of failure, are more rational than deterministic factor of safety

Maximal codeword lengths in Huffman codes

computers &amp

Diversity and Specialization in Collaborative Swarm Systems

This paper addresses qualitative and quantitative diversity and specialization issues in the frame- work of self-organizing, distributed, artificial systems. Both diversity and specialization are obtained via distributed learning from initially homogeneous swarms. While measuring diversity essentially quantifies differences among the individuals, assessing the degree of specialization implies to correlate the swarm’s heterogeneity with its overall performance. Starting from a stick-pulling experiment in collective robotics, a task that requires the collaboration of two robots, we abstract and generalize in simulation the task constraints to k robots collaborating sequentially or in parallel. We investi- gate quantitatively the influence of task constraints and type of reinforcement signals on diversity and specialization in these collaborative experiments. Results show that, though diversity is not explicitly rewarded in our learning algorithm and there is no explicit communication among agents, the swarm becomes specialized after learning. The degree of specialization is affected strongly by environmental conditions and task constraints, and reveals characteristics related to performance and learning in a more consistent and clearer way than diversity does