James L. McClelland SS 100, May 31, 2011 Learning in Neural Networks, with Implications for Representation and Learning of Language James L. McClelland SS 100, May 31, 2011

A Pattern Associator Network Corresponding output (e.g., smell of a rose) Matrix of connections Summed input p(a=1) Pattern representing a given input (e.g. sight of a rose)

Learning Rule for the Pattern Associator network For each output unit: Determine activity of the unit based on its input and activation function. If the unit is active when target is not: Reduce each weight coming into the unit from each active input unit. If the unit is not active when the target is active: Increase the weight coming into the unit from each active input unit. Each connection weight adjustment is very small Learning is gradual and cumulative If a set of weights exists that can correctly assign the desired output for each input, the network will gradually home in on it. However, in many cases, no solution is actually possible with only one layer of modifiable weights.

Overcoming the Limitations of Associator Networks Without ‘hidden units’, many input-output mappings cannot be captured. However, with just one layer of units between input and output, it is possible to capture any deterministic input-output mapping. What was missing was a method for training connections on both sides of hidden units. In 1986, such a method was developed by David Rumelhart and others. The network uses units whose activation is a continuous, non-linear function of their input. The network is trained to produce the corresponding output (target) pattern for each input pattern. This is done by adjusting each weight in the network to reduce the sum of squared differences between the network’s output activation and the corresponding target output: Si (ti-ai)2 With this algorithm, neural networks can represent and learn any computable function. How to ensure networks generalize ‘correctly’ to unseen examples is a hard problem, in part because defining what is the correct generalization is unclear. Summed input activation

Standard Approach to the Past Tense (and other Aspects of Language) We form the past tense by using a (simple) rule. ‘add ‘ed’: played, cooked, raided If an item is an exception, the rule is blocked. So we say ‘took’ instead of ‘taked’ If you’ve never seen an item before, you use the rule If an item is an exception, but you forget the exceptional past tense, you apply the rule Predictions: Regular inflection of ‘nonce forms’ This man is tupping. Yesterday he … This girl is blinging. Yesterday she … Over-regularization errors: Goed, taked, bringed

The Learning-Based, Neural Networks Approach Language (like perception, etc) arises from the interactions of neurons, each of which operates according to a common set of simple principles of processing, representation and learning. Units and rules are useful to approximately describe what emerges from these interactions but have no mechanistic or explanatory role in language processing, language change, or language learning.

An Learning-Based, Connectionist Approach to the Past Tense Knowledge is in connections Experience causes connections to change Sensitivity to regularities emerges Regular past tense Sub-regularities Knowledge of exceptions co-exists with knowledge of regular forms in the same connections.

The RM Model Learns from verb [root, past tense] pairs [Like, liked]; [love, loved]; [carry, carried]; [take, took] Present and past are represented as patterns of activation over units that stand for phonological features.

Over-regularization errors in the RM network Most frequent past tenses in English: Felt Had Made Got Gave Took Came Went Looked Needed Here’s where 400 more words were introduced Trained with top ten words only.

Additional characteristics The model exploits gangs of related exceptions. dig-dug cling-clung swing-swung The ‘regular pattern’ infuses exceptions as well as regulars: say-said, do-did have-had keep-kept, sleep-slept Burn-burnt Teach-taught

Elman’s Simple Recurrent Network Task is to predict the next element of a sequence on the output, given the current element on the input units. Each element is represented by a pattern of activation. Each box represents a set of units. Each dotted arrow represents all-to-all connections. The solid arrow indicates that the previous pattern on the hidden units is copied back to provide context for the next prediction. Learning occurs through connection weight adjustment using an extended version of the error correcting learning rule.

Hidden Unit Patterns for Elman Net Trained on Word Sequences

Key Features of the Both Models No lexical entries and no rules No problem of rule induction or grammar selection Note: While this approach has been highly contravertial, and has not become dominant in AI or Linguistics, it underlies a large body of work in psycholinguistics and neuropsychology, and remains under active exploration in many laboratories.

Questions from Sections What is the bridge between the two perspectives? Why should someone who is interested in symbolic systems have to know about both fields? Aren't they fundamentally opposites of each other? If not, where aren't they? How has neuroscience (and findings from studying the brain) shaped and assisted research traditionally conducted under the psychology umbrella? Has computational linguistics really solved 'the biggest part of the problem of AI'?