Optimizing the performance of self-organizing feature maps like the Ko(cid:173) honen map involves the choice of the output space topology. We present a topographic product which measures the preservation of neighborhood relations as a criterion to optimize the output space topology of the map with regard to the global dimensionality DA as well as to the dimensi(cid:173) ons in the individual directions. We test the topographic product method not only on synthetic mapping examples, but also on speech data. In the latter application our method suggests an output space dimensionality of DA 3, in coincidence with recent recognition results on the same data set.

A self-organizing neural network for sequence classification called SARDNET is described and analyzed experimentally. SARDNET extends the Kohonen Feature Map architecture with activation re(cid:173) tention and decay in order to create unique distributed response patterns for different sequences. The network has proven successful on mapping ar(cid:173) bitrary sequences of binary and real numbers, as well as phonemic representations of English words. Potential applications include isolated spoken word recognition and cognitive science models of sequence processing.

We introduce an exploration bonus for deep reinforcement learning methods calculated using self-organising feature maps. Our method uses adaptive resonance theory (ART) providing online, unsupervised clustering to quantify the novelty of a state. This heuristic is used to add an intrinsic reward to the extrinsic reward signal for then to optimize the agent to maximize the sum of these two rewards. We find that this method was able to play the game Ordeal at a human level after a comparable number of training epochs to ICM arXiv:1705.05464. Agents augmented with RND arXiv:1810.12894 were unable to achieve the same level of performance in our space of hyperparameters.

A self-organizing neural network for sequence classification called SARDNET is described and analyzed experimentally. SARDNET extends the Kohonen Feature Map architecture with activation retention anddecay in order to create unique distributed response patterns for different sequences. SARDNET yields extremely dense yet descriptive representations of sequential input in very few training iterations.The network has proven successful on mapping arbitrary sequencesof binary and real numbers, as well as phonemic representations of English words. Potential applications include isolated spoken word recognition and cognitive science models of sequence processing. 1 INTRODUCTION While neural networks have proved a good tool for processing static patterns, classifying sequentialinformation has remained a challenging task. The problem involves recognizing patterns in a time series of vectors, which requires forming a good internal representationfor the sequences. Several researchers have proposed extending the self-organizing feature map (Kohonen 1989, 1990), a highly successful static pattern classification method, to sequential information (Kangas 1991; Samarabandu andJakubowicz 1990; Scholtes 1991). Below, three of the most recent of these networks are briefly described. The remainder of the paper focuses on a new architecture designed to overcome the shortcomings of these approaches.

A self-organizing neural network for sequence classification called SARDNET is described and analyzed experimentally. SARDNET extends the Kohonen Feature Map architecture with activation retention and decay in order to create unique distributed response patterns for different sequences.

A self-organizing neural network for sequence classification called SARDNET is described and analyzed experimentally. SARDNET extends the Kohonen Feature Map architecture with activation retention and decay in order to create unique distributed response patterns for different sequences.

Self-organizing feature maps like the Kohonen map (Kohonen, 1989, Ritter et al., 1990) not only provide a plausible explanation for the formation of maps in brains, e.g. in the visual system (Obermayer et al., 1990), but have also been applied to problems like vector quantization, or robot arm control (Martinetz et al., 1990). The underlying organizing principle is the preservation of neighborhood relations. For this principle to lead to a most useful map, the topological structure of the output space must roughly fit the structure of the input data. However, in technical 1141 1142 Bauer, Pawelzik, and Geisel applications this structure is often not a priory known. For this reason several attempts have been made to modify the Kohonen-algorithm such, that not only the weights, but also the output space topology itself is adapted during learning (Kangas et al., 1990, Martinetz et al., 1991). Our contribution is also concerned with optimal output space topologies, but we follow a different approach, which avoids a possibly complicated structure of the output space. First we describe a quantitative measure for the preservation of neighborhood relations in maps, the topographic product P. The topographic product had been invented under the name of" wavering product" in nonlinear dynamics in order to optimize the embeddings of chaotic attractors (Liebert et al., 1991).

Self-organizing feature maps like the Kohonen map (Kohonen, 1989, Ritter et al., 1990) not only provide a plausible explanation for the formation of maps in brains, e.g. in the visual system (Obermayer et al., 1990), but have also been applied to problems like vector quantization, or robot arm control (Martinetz et al., 1990). The underlying organizing principle is the preservation of neighborhood relations. For this principle to lead to a most useful map, the topological structure of the output space must roughly fit the structure of the input data. However, in technical 1141 1142 Bauer, Pawelzik, and Geisel applications this structure is often not a priory known. For this reason several attempts have been made to modify the Kohonen-algorithm such, that not only the weights, but also the output space topology itself is adapted during learning (Kangas et al., 1990, Martinetz et al., 1991). Our contribution is also concerned with optimal output space topologies, but we follow a different approach, which avoids a possibly complicated structure of the output space. First we describe a quantitative measure for the preservation of neighborhood relations in maps, the topographic product P. The topographic product had been invented under the name of" wavering product" in nonlinear dynamics in order to optimize the embeddings of chaotic attractors (Liebert et al., 1991).