# Learning in AIR

Nodes marked by the user with positive or negative feedback act as sources of a signal that then propagates backwards along the weighted links. A local learning rule then modifies the weight on links directly or indirectly involved in the query process. Several learning rules were investigated; the experiments reported here used a learning rule that correlated the activity of the PRE-SYNAPTIC $node_i$ with the feedback signal experienced by the POST-SYNAPTIC $node_j$: w_{ij} & \propto & Corr(n_{i}& Corr(n_{i}\ active, n_{j}\ relevant) \\ & = & \frac{\mu_{a_{i} \cdot r_{j}} - \mu_{a_{i}} \cdot \mu{r_{j}}}{\sigma_{a_{i}} \cdot \sigma_{r_{j}}} \\ & = & \frac{\Sigma (a_{i} \cdot r_{j}) - \frac{\Sigma a_{i} \Sigma r_{j}}{N}}{\sqrt{\Sigma a_{i}^{2} - \frac{(\Sigma a_{i})^{2}}{N}} \sqrt{\Sigma r_{j}^{2} - \frac{(\Sigma r_{j})^{2}}{N}}} \end{eqnarray*}

AIR makes a most-direct correspondence between the connectionist notion of {activity} and the IR notion of $\Pr(\mathname{Rel})$ (cf. Section §5.5 ): The activity level of nodes at the end of the propagation phase is considered to be a prediction of the probability that this node will be judged relevant to the query presented by the user. This interpretation constrained the AIR system design in several ways (e.g., activity is a real number bounded between zero and one, query nodes are activated fully). AIR also allows negative activity, which is interpreted as the probability that a node is {\em not} relevant. The next step of the argument is to consider a link weight $w_{AB}$ to be the conditional probability that $Node_{B}$ is relevant given that $Node_{A}$ is relevant. Next, this definition must be extended inductively to include indirect, transitive paths that AIR uses extensively for its retrievals.

The system's interactions with users are then considered experiments. Given a query, AIR predicts which nodes will be considered relevant and the user confirms or disconfirms this prediction. These results update the system's weights (conditional probabilities) so as reflect the system's updated estimates. Thus, AIR's representation results from the combination of two completely different sources of evidence: the word frequency statistics underlying its initial indexing; and the opinions of its users.

A straight-forward mechanism exists for incrementally introducing new documents into AIR's database. Links are established from the new document to all of its initial keywords and to its authors; new keyword and author nodes are created as necessary. The weights on these links are distributed evenly so that they sum to a constant. Because the sum of the (outgoing) weights for all nodes is to remain constant, any associative weight to the new document must come from existing link weights. a new parameter ({*CONSERVATIVE*}) is introduced to control the weight given these new links at the expense of existing ones. If the network is untrained by users, this parameter can be set to zero so as to make the effect of an incremental addition exactly the same as if the new document had been part of the initial collection. In a trained network, setting {\tt *CONSERVATIVE*} near unity insures that the system's experience incorporated in existing link weights is not sacrificed to make the new connections. Also, note that the computation required to place the new document is strictly local: only the links directly adjacent to the new documents immediate neighbors need be changed. The major observation about the inclusion of new documents, however, is that there is an immediate place'' for new documents in AIR's existing representation.

A second source of new information to the AIR system comes from users' queries. If a query contains a term unknown to AIR, this term is held in abeyance and AIR executes the query based on the remaining terms. Then, after the user has designated which of AIR's responses are relevant to this query, a new node corresponding to the new query term is created and becomes subjected to exactly the same learning rule used for all other nodes.

While easily incorporating new documents and new query terms are valuable properties for any IR system, from the perspective of machine learning these are both examples of simple rote learning, and necessarily dependant on the specifics of the IR task domain. The main focus of the AIR system is the use of general purpose connectionist learning techniques that, once the initial document network is constructed, are quite independent from the IR task.

FOA © R. K. Belew - 00-09-21