Francois Rivest

Knowledge-based cascade-correlation: Using knowledge to speed learning

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.

Timescale Invariance in the Pacemaker-Accumulator Family of Timing Models

Pacemaker-accumulator (PA) systems have been the most popular kind of timing model in the half-century since their introduction by Treisman (1963). Many alternative timing models have been designed predicated on different assumptions, though the dominant PA model during this period — Gibbon and Church’s Scalar Expectancy Theory (SET) — invokes most of them. As in Treisman, SET’s implementation assumes a fixed-rate clock-pulse generator and encodes durations by storing average pulse counts; unlike Treisman’s model, SET’s decision process invokes Weber’s law of magnitude-comparison to account for timescale-invariant temporal precision in animal behavior. This is one way to deal with the ‘Poisson timing’ issue, in which relative temporal precision increases for longer durations, contrafactually, in a simplified version of Treisman’s model. First, we review the fact that this problem does not afflict Treisman’s model itself due to a key assumption not shared by SET. Second, we develop a contrasting PA model, an extension of Killeen and Fetterman’s Behavioral Theory of Timing that accumulates Poisson pulses up to a fixed criterion level, with pulse rates adapting to time different intervals. Like Treisman’s model, this time-adaptive, opponent Poisson, drift–diffusion model accounts for timescale invariance without first assuming Weber’s law. It also makes new predictions about response times and learning speed and connects interval timing to the popular drift–diffusion model of perceptual decision making. With at least three different routes to timescale invariance, the PA model family can provide a more compelling account of timed behavior than may be generally appreciated.

An adaptive drift-diffusion model of interval timing dynamics

Animals readily learn the timing between salient events. They can even adapt their timed responding to rapidly changing intervals, sometimes as quickly as a single trial. Recently, drift-diffusion models-widely used to model response times in decision making-have been extended with new learning rules that allow them to accommodate steady-state interval timing, including scalar timing and timescale invariance. These time-adaptive drift-diffusion models (TDDMs) work by accumulating evidence of elapsing time through their drift rate, thereby encoding the to-be-timed interval. One outstanding challenge for these models lies in the dynamics of interval timing-when the to-be-timed intervals are non-stationary. On these schedules, animals often fail to exhibit strict timescale invariance, as expected by the TDDMs and most other timing models. Here, we introduce a simple extension to these TDDMs, where the response threshold is a linear function of the observed event rate. This new model compares favorably against the basic TDDMs and the multiple-time-scale (MTS) habituation model when evaluated against three published datasets on timing dynamics in pigeons. Our results suggest that the threshold for triggering responding in interval timing changes as a function of recent intervals.

COULD KNOWLEDGE-BASED NEURAL LEARNING BE USEFUL IN DEVELOPMENTAL ROBOTICS? THE CASE OF KBCC

The new field of developmental robotics faces the formidable challenge of implementing effective learning mechanisms in complex, dynamic environments. We make a case that knowledge-based learning algorithms might help to meet this challenge. A constructive neural learning algorithm, knowledge-based cascade-correlation (KBCC), autonomously recruits previously-learned networks in addition to the single hidden units recruited by ordinary cascade-correlation. This enables learning by analogy when adequate prior knowledge is available, learning by induction from examples when there is no relevant prior knowledge, and various combinations of analogy and induction. A review of experiments with KBCC indicates that recruitment of relevant existing knowledge typically speeds learning and sometimes enables learning of otherwise impossible problems. Some additional domains of interest to developmental robotics are identified in which knowledge-based learning seems essential. The characteristics of KBCC in relation to other knowledge-based neural learners and analogical reasoning are summarized as is the neurological basis for learning from knowledge. Current limitations of this approach and directions for future work are discussed.

Alternative Time Representation in Dopamine Models

Dopaminergic neuron activity has been modeled during learning and appetitive behavior, most commonly using the temporal-difference (TD) algorithm. However, a proper representation of elapsed time and of the exact task is usually required for the model to work. Most models use timing elements such as delay-line representations of time that are not biologically realistic for intervals in the range of seconds. The interval-timing literature provides several alternatives. One of them is that timing could emerge from general network dynamics, instead of coming from a dedicated circuit. Here, we present a general rate-based learning model based on long short-term memory (LSTM) networks that learns a time representation when needed. Using a naïve network learning its environment in conjunction with TD, we reproduce dopamine activity in appetitive trace conditioning with a constant CS-US interval, including probe trials with unexpected delays. The proposed model learns a representation of the environment dynamics in an adaptive biologically plausible framework, without recourse to delay lines or other special-purpose circuits. Instead, the model predicts that the task-dependent representation of time is learned by experience, is encoded in ramp-like changes in single-neuron activity distributed across small neural networks, and reflects a temporal integration mechanism resulting from the inherent dynamics of recurrent loops within the network. The model also reproduces the known finding that trace conditioning is more difficult than delay conditioning and that the learned representation of the task can be highly dependent on the types of trials experienced during training. Finally, it suggests that the phasic dopaminergic signal could facilitate learning in the cortex.

A dual-phase technique for pruning constructive networks

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.

Application of knowledge-based cascade-correlation to vowel recognition

Neural network algorithms are usually limited in their ability to use prior knowledge automatically. A recent algorithm, a knowledge-based cascade-correlation (KBCC), extends the cascade-correlation by evaluating and recruiting previously learned networks in its architecture. In this paper, we describe KBCC and illustrate its performance on the problem of recognizing vowels.

Knowledge-based cascade-correlation

Neural network modeling typically ignores the role of knowledge in learning by starting from random weights. A new algorithm extends cascade-correlation by recruiting previously learned networks as well as single hidden units. Knowledge-based cascade-correlation (KBCC) finds, adapts, and uses its relevant knowledge to speed learning. In this paper, we describe KBCC and illustrate its performance on a small, but clear problem.

Conditioning and time representation in long short-term memory networks

Dopaminergic models based on the temporal-difference learning algorithm usually do not differentiate trace from delay conditioning. Instead, they use a fixed temporal representation of elapsed time since conditioned stimulus onset. Recently, a new model was proposed in which timing is learned within a long short-term memory (LSTM) artificial neural network representing the cerebral cortex (Rivest et al. in J Comput Neurosci 28(1):107–130, 2010). In this paper, that model’s ability to reproduce and explain relevant data, as well as its ability to make interesting new predictions, are evaluated. The model reveals a strikingly different temporal representation between trace and delay conditioning since trace conditioning requires working memory to remember the past conditioned stimulus while delay conditioning does not. On the other hand, the model predicts no important difference in DA responses between those two conditions when trained on one conditioning paradigm and tested on the other. The model predicts that in trace conditioning, animal timing starts with the conditioned stimulus offset as opposed to its onset. In classical conditioning, it predicts that if the conditioned stimulus does not disappear after the reward, the animal may expect a second reward. Finally, the last simulation reveals that the buildup of activity of some units in the networks can adapt to new delays by adjusting their rate of integration. Most importantly, the paper shows that it is possible, with the proposed architecture, to acquire discharge patterns similar to those observed in dopaminergic neurons and in the cerebral cortex on those tasks simply by minimizing a predictive cost function.

Complex problem solving with reinforcement learning

We previously measured human performance on a complex problem-solving task that involves finding which ball in a set is lighter or heavier than the others with a limited number of weightings. None of the participants found a correct solution within 30 minutes without help of demonstrations or instructions. In this paper, we model human performance on this task using a biologically plausible computational model based on reinforcement learning. We use a SARSA-based Softmax learning algorithm where the reward function is learned using cascade-correlation neural networks. First, we find that the task can be learned by reinforcement alone with substantial training. Second, we study the number of alternative actions available to Softmax and find that 5 works well for this problem which is compatible with estimates of human working memory size. Third, we find that simulations are less accurate than humans given equivalent amount of training We suggest that humans use means-ends analysis to self-generate rewards in non-terminal states. Implementing such self-generated rewards might improve model accuracy. Finally, we pretrain models to prefer simple actions, like humans. We partially capture a simplicity bias, and find that it had little impact on accuracy.