Theory-driven learning : using intra-example relationships to constrain learning

We describe an incremental learning algorithm, called theory-driven learning, that creates rules to predict the effect of actions. Theory-driven learning exploits knowledge of regularities among rules to constrain the learning problem. We demonstrate that this knowledge enables the learning system to rapidly converge on accurate predictive rules and to tolerate more complex training data. An algorithm for incrementally learning these regularities is described and we provide evidence that the resulting regularities are sufficiently general to facilitate learning in new domains

Stochastic subspace correction in Hilbert space

We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is solved. we show that convergence rates for the expectation of the squared error can be guaranteed under weaker conditions than previously established in [Constr. Approx. 44:1 (2016), 121-139]. A connection to the theory of learning algorithms in reproducing kernel Hilbert spaces is revealed.Comment: 15 page

Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps

A new neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors. The architecture, called Fuzzy ARTMAP, achieves a synthesis of fuzzy logic and Adaptive Resonance Theory (ART) neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and ART category choice, resonance, and learning. Fuzzy ARTMAP also realizes a new Minimax Learning Rule that conjointly minimizes predictive error and maximizes code compression, or generalization. This is achieved by a match tracking process that increases the ART vigilance parameter by the minimum amount needed to correct a predictive error. As a result, the system automatically learns a minimal number of recognition categories, or "hidden units", to met accuracy criteria. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy logic play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Improved prediction is achieved by training the system several times using different orderings of the input set. This voting strategy can also be used to assign probability estimates to competing predictions given small, noisy, or incomplete training sets. Four classes of simulations illustrate Fuzzy ARTMAP performance as compared to benchmark back propagation and genetic algorithm systems. These simulations include (i) finding points inside vs. outside a circle; (ii) learning to tell two spirals apart; (iii) incremental approximation of a piecewise continuous function; and (iv) a letter recognition database. The Fuzzy ARTMAP system is also compared to Salzberg's NGE system and to Simpson's FMMC system.British Petroleum (89-A-1204); Defense Advanced Research Projects Agency (90-0083); National Science Foundation (IRI 90-00530); Office of Naval Research (N00014-91-J-4100); Air Force Office of Scientific Research (90-0175

The Extreme Value Machine

It is often desirable to be able to recognize when inputs to a recognition function learned in a supervised manner correspond to classes unseen at training time. With this ability, new class labels could be assigned to these inputs by a human operator, allowing them to be incorporated into the recognition function --- ideally under an efficient incremental update mechanism. While good algorithms that assume inputs from a fixed set of classes exist, e.g., artificial neural networks and kernel machines, it is not immediately obvious how to extend them to perform incremental learning in the presence of unknown query classes. Existing algorithms take little to no distributional information into account when learning recognition functions and lack a strong theoretical foundation. We address this gap by formulating a novel, theoretically sound classifier --- the Extreme Value Machine (EVM). The EVM has a well-grounded interpretation derived from statistical Extreme Value Theory (EVT), and is the first classifier to be able to perform nonlinear kernel-free variable bandwidth incremental learning. Compared to other classifiers in the same deep network derived feature space, the EVM is accurate and efficient on an established benchmark partition of the ImageNet dataset.Comment: Pre-print of a manuscript accepted to the IEEE Transactions on Pattern Analysis and Machine Intelligence (T-PAMI) journa

3-D Object Recognition by the ART-EMAP Evidence Accumulation Network

ART-EMAP synthesizes adaptive resonance theory (AHT) and spatial and temporal evidence integration for dynamic predictive mapping (EMAP). The network extends the capabilities of fuzzy ARTMAP in four incremental stages. Stage I introduces distributed pattern representation at a view category field. Stage 2 adds a decision criterion to the mapping between view and object categories, delaying identification of ambiguous objects when faced with a low confidence prediction. Stage 3 augments the system with a field where evidence accumulates in medium-term memory (MTM). Stage 4 adds an unsupervised learning process to fine-tune performance after the limited initial period of supervised network training. Simulations of the four ART-EMAP stages demonstrate performance on a difficult 3-D object recognition problem.Advanced Research Projects Agency (ONR N00014-92-J-4015); National Science Foundation (IRI-90-00530); Office of Naval Research (N00014-91-J-1309); Air Force Office of Scientific Research (90-0083

Challenging Neural Dialogue Models with Natural Data: Memory Networks Fail on Incremental Phenomena

Natural, spontaneous dialogue proceeds incrementally on a word-by-word basis; and it contains many sorts of disfluency such as mid-utterance/sentence hesitations, interruptions, and self-corrections. But training data for machine learning approaches to dialogue processing is often either cleaned-up or wholly synthetic in order to avoid such phenomena. The question then arises of how well systems trained on such clean data generalise to real spontaneous dialogue, or indeed whether they are trainable at all on naturally occurring dialogue data. To answer this question, we created a new corpus called bAbI+ by systematically adding natural spontaneous incremental dialogue phenomena such as restarts and self-corrections to the Facebook AI Research's bAbI dialogues dataset. We then explore the performance of a state-of-the-art retrieval model, MemN2N, on this more natural dataset. Results show that the semantic accuracy of the MemN2N model drops drastically; and that although it is in principle able to learn to process the constructions in bAbI+, it needs an impractical amount of training data to do so. Finally, we go on to show that an incremental, semantic parser -- DyLan -- shows 100% semantic accuracy on both bAbI and bAbI+, highlighting the generalisation properties of linguistically informed dialogue models.Comment: 9 pages, 3 figures, 2 tables. Accepted as a full paper for SemDial 201