A Landscape Theory of Association: Paths and Choices in Representation Space

Association enables a cue to activate related representations, supporting memory retrieval and flexible reasoning. Understanding this process requires explaining both how an association unfolds and why one destination is selected over alternatives. However, descriptions based solely on representational similarity or energy barriers do not jointly explain these two aspects. We develop a landscape model in which modes of a representation density define associative states and calibrated gradient diffusion connects their basins. Our model separates three quantities: fixed-duration path likelihood, governed by the full Onsager-Machlup action; the weak-noise scale of direct escape, determined by exit barriers; and next-state choice, obtained by normalizing competing exit rates. By doing so, the framework links the representation landscape to associative paths and destination choices, revealing how local curvature shapes probable routes and how competition among accessible destinations governs selection. Across three controlled landscapes, free-time escape-rate slopes recover both barrier predictions within 5.45 percent; in an equal-barrier design, an action-independent moving-tube PDE recovers the complete ordering of six prespecified paths predicted by the full Onsager-Machlup action, whereas the quadratic-only truncation selects a different winner. On a five-well landscape, 160,000 first-exit trajectories recover all four barrier-difference log-odds slopes within 4.5 percent; a fixed-center energy intervention raises the targeted exit probability by 21.8 percentage points on average and reverses the dominant destination. Together, these results quantitatively connect landscape geometry to associative paths, escape scales, and next-state choice.