The St. Petersburg paradox is a centuries-old puzzle concerning a lottery with infinite expected payoff on which people are only willing to pay a small amount to play. Despite many attempts and several proposals, no generally-accepted resolution is yet at hand. In a recent paper, we show that this paradox can be understood in terms of the mind optimally using its limited computational resources (Nobandegani et al. 2019). Specifically, we show that the St. Petersburg paradox can be accounted for by a variant of normative expected-utility valuation which acknowledges cognitive limitations: sample-based expected utility (Nobandegani et al. 2018). SbEU provides a unified, algorithmic explanation of major experimental findings on this paradox. We conclude by discussing the implications of our work for algorithmically understanding human cognition and for developing human-like artificial intelligence.

In long-term potentiation (LTP), one of the most studied types of neural plasticity, synaptic strength is persistently increased in response to stimulation. Although a number of different proteins have been implicated in the sub-cellular molecular processes underlying induction and maintenance of LTP, the precise mechanisms remain unknown. A particular challenge is to demonstrate that a proposed molecular mechanism can provide the level of stability needed to maintain memories for months or longer, in spite of the fact that many of the participating molecules have much shorter life spans. Here we present a computational model that combines simulations of several biochemical reactions that have been suggested in the LTP literature and show that the resulting system does exhibit the required stability. At the core of the model are two interlinked feedback loops of molecular reactions, one involving the atypical protein kinase PKMζ and its messenger RNA, the other involving PKMζ and GluA2-containing AMPA receptors. We demonstrate that robust bistability-stable equilibria both in the synapse's potentiated and unpotentiated states-can arise from a set of simple molecular reactions. The model is able to account for a wide range of empirical results, including induction and maintenance of late-phase LTP, cellular memory reconsolidation and the effects of different pharmaceutical interventions.

Cascade-correlation (cascor) networks grow by recruiting hidden units to adjust their computational power to the task being learned. The standard cascor algorithm recruits each hidden unit on a new layer, creating deep networks. In contrast, the flat cascor variant adds all recruited hidden units on a single hidden layer. Student–teacher network approximation tasks were used to investigate the ability of flat and standard cascor networks to learn the input–output mapping of other, randomly initialized flat and standard cascor networks. For low-complexity approximation tasks, there was no significant performance difference between flat and standard student networks. Contrary to the common belief that standard cascor does not generalize well due to cascading weights creating deep networks, we found that both standard and flat cascor generalized well on problems of varying complexity. On high-complexity tasks, flat cascor networks had fewer connection weights and learned with less computational cost than standard networks did.

A new type of neural network is introduced, where symbolic rules are combined using a constructive algorithm. Initially, symbolic rules are converted into networks. Rule-based cascade-correlation (RBCC) then grows its architecture by a competitive process where these rule-based networks strive at capturing as much of the error as possible. A pruning technique for RBCC is also introduced, and the performance of the algorithm is assessed both on a simple artificial problem and on a real-world task of DNA splice-junction determination. Results of the real-world problem demonstrate the advantages of RBCC over other related algorithms in terms of processing time and accuracy.

An algorithm for performing simultaneous growing and pruning of cascade-correlation (CC) neural networks is introduced and tested. The algorithm adds hidden units as in standard CC, and removes unimportant connections by using optimal brain damage (OBD) in both the input and output phases of CC. To this purpose, OBD was adapted to prune weights according to two separate objective functions that are used in CC to train the network, respectively. Application of the new algorithm to two databases of the PROBEN1 benchmarks reveals that this new dual-phase pruning technique is effective in significantly reducing the size of CC networks, while providing a speed-up in learning times and improvements in generalization over novel test sets.

Research with neural networks typically ignores the role of knowledge in learning by initializing the network with random connection weights. We examine a new extension of a well-known generative algorithm, cascade-correlation. Ordinary cascade-correlation constructs its own network topology by recruiting new hidden units as needed to reduce network error. The extended algorithm, knowledge-based cascade-correlation (KBCC), recruits previously learned sub-networks as well as single hidden units. This paper describes KBCC and assesses its performance on a series of small, but clear problems involving discrimination between two classes. The target class is distributed as a simple geometric figure. Relevant source knowledge consists ofvarious linear transformations ofthe target distribution. KBCC is observed to find, adapt and use its relevant knowledge to speed learning significantly.

This paper presents a modular connectionist network model of the development of seriation (sorting) in children. The model uses the cascade-correlation generative connectionist algorithm. These cascade-correlation networks do better than existing rule-based models at developing through soft stage transitions, sorting more correctly with larger stimulus size increments and showing variation in seriation performance within stages. However, the full generative power of cascade-correlation was not found to be a necessary component for successfully modelling the development of seriation abilities. Analysis of network weights indicates that improvements in seriation are due to continuous small changes instead of the radical restructuring suggested by Piaget. The model suggests that seriation skills are present early in development and increase in precision during later development. The required learning environment has a bias towards smaller and nearly ordered arrays. The variability characteristic of children's performance arises from sorting subsets of the total array. The model predicts better sorting moves with more array disorder, and a dissociation between which element should be moved and where it should be moved.

Understanding knowledge representations in neural nets has been a difficult problem. Principal components analysis (PCA) of contributions (products of sending activations and connection weights) has yielded valuable insights into knowledge representations, but much of this work has focused on the correlation matrix of contributions. The present work shows that analyzing the variance-covariance matrix of contributions yields more valid insights by taking account of weights.