ThomCat: A Bayesian Blackboard Model of Hierarchical Temporal Perception

We present a Bayesian blackboard system for tempo- ral perception, applied to a minidomain task in musical scene analysis. It is similar to the classic Copycat archi- tecture (Hofstadter 1995) but is derived from rigourous modern Bayesian network theory (Bishop 2006), with heuristics added for speed. It borrows ideas of prim- ing, pruning and attention and fuses them with modern inference algorithms, and provides a general theory of hierarchical constructive perception, illustrated and im - plemented in a minidomain. p(SONG → V ERSE,CHORUS,V ERSE) = 1 p(V ERSE → A,A,B) = 0.75 p(V ERSE → B,B,A,A) = 0.25 p(CHORUS → K,L,K,L) = 1;p(A → c) = 1 p(B → c,g) = 1;p(K → f,am) = 1;p(L → f,g) = 1 The most notable is the global key which acts to prefer co- herent sets of chords and notes throughout the whole mu- sical scene. Similarly, melodic themes are often repeated throughout a performance, with a bias to preferring rewrite rules that have previously been applied. This is typically the case in jazz, rock and many non-Western art musics: a composition is a fluid entity consisting of recognizable chunks and conventions which are combined in real time by the player. At the structural level, performers may decide on the fly to insert extra verses and choruses if the perfor- mance is going well and the audience is wanting more; or to cut out sections if it is going badly. At the low level of chords, rhythm players are likely to improvise around the standard chords, with different changes having probabilities. An almost-known grammar means that the performance is generated from a grammar which is mostly similar to the grammar known by the perceiver, but may include additional and differing rules and differing probabilities. The perce iver must thus allow for the fallibility of its own knowledge of the grammar and be prepared to learn new rules on the fly. The context-sensitive nature of the global factors, and the required allowance for one's own failure preclude the use of the fast dynamic programming algorithms used in sim- plified language processing tasks such as the Inside-Outsid e algorithm, and more general scene analysis techniques are needed. Indeed this was a reason for selection of the mi- crodomain as representative of general scene analysis. We consider musical scenes comprised of observations of low-level chords, assuming one chord per bar, and that chords are the terminals of the almost-known grammar, and influenced by global key. This minidomain task is enough to capture and illustrate the general context-sensitive an d 'almost-known' requirements of general scene analysis. In particular we do not consider perception of melodies or in- dividual notes in the present work. Our architecture, Thom- Cat, is largely inspired by the Copycat blackboard system (Mitchell 1993a), which itself was explicitly based upon (and cites) Ising models, Gibbs sampling and simulated an- nealing (Hofstadter 1987). This statistical mechanics bas is is generally under-appreciated due to Copycat's use of non- standard terminology and heuristics. ThomCat is an explic- itly Bayesian version of the Copycat architecture applied to the music minidomain. Creation and destruction of hypothe- ses by agents is translated into a simple rule which restrict s