Rapid-Chase Theory

• Rapid-Chase Theory is a behavioral framework defining strictly sequential feedforward visual processing, where primes trigger initial motor responses.
• It establishes three formal criteria—Initiation, Takeover, and Independence—to differentiate feedforward from recurrent processing using measurable motor outputs.
• Empirical studies using pointing tasks and EEG confirm RCT predictions by demonstrating invariant early priming trajectories and SOA-ordered divergence.

Rapid-Chase Theory (RCT) is a behavioral framework formalizing the identification of strictly feedforward processing in visual response priming paradigms. RCT posits that sequentially presented visual prime and target stimuli evoke strictly sequential, non-overlapping feedforward sweeps through the visual-motor cascade. Each sweep can directly drive measurable, continuous motor output. The theory provides rigorous, testable criteria—Initiation, Takeover, and Independence—for when observed responses reflect feedforward rather than recurrent or interactive processing, bridging covert neural operations with overt behavioral trajectories (Schmidt, 2014).

1. Theoretical Foundations and Motivation

Classical models of visual processing emphasize a two-stage architecture: an initial, rapid, hierarchical feedforward sweep followed by slower, recurrent feedback loops. Neurophysiological and psychophysical evidence (e.g., Lamme & Roelfsema 2000; Bullier 2004; VanRullen & Thorpe 2002) differentiates a fast, unidirectional feedforward phase from a slower, recurrent, iterative stage that refines perceptual representations. However, directly measuring feedforward sweeps in the human cortex is infeasible with non-invasive methods. Consequently, Schmidt et al. (2006, 2011) introduced "bridging principles" that link unobservable feedforward neural signals to observable, continuous motor outputs via response priming paradigms.

In these paradigms, a briefly presented prime stimulus precedes a target by a variable stimulus-onset asynchrony (SOA). Primes congruent with the target's required response accelerate responding, while incongruent primes impede it. Priming effects may increase with SOA even as subjective prime visibility wanes—a hallmark of feedforward propagation. RCT asserts that each stimulus (prime, then target) initiates a complete, strictly sequential feedforward sweep that can sequentially and exclusively control early and late response phases, respectively (Schmidt, 2014).

2. Formal Behavioral Criteria of Feedforward Processing

RCT operationalizes feedforward processing using three qualitative and formally defined criteria: Initiation, Takeover, and Independence. The criteria use priming trajectories $f_i(t)$, where $i$ denotes the SOA condition. Key notational elements are as follows:

• $t$: Time, aligned to prime onset.
• $I_T$: Vector of prime properties (e.g., intensity, duration).
• $T$: Vector of target properties.
• $f_{\text{con},i}(t;I_T,T)$, $f_{\text{inc},i}(t;I_T,T)$: Time courses of a continuous response measure (e.g., finger position) for consistent and inconsistent trials at $SOA_i$.
• $$f_i(t;I_T,T) \equiv f_{\text{inc},i}(t;I_T,T) - f_{\text{con},i}(t;I_T,T)$$: Priming effect trajectory at $SOA_i$.
• $i$0: Common onset of $i$1 for all $i$2.
• $i$3: "Branching time" when $i$4 diverges from the common segment $i$5.

The formal criteria are:

Criterion	Qualitative Description	Mathematical Statement
Initiation	Prime, not target, determines response onset and initial direction.	$i$6
Takeover	Target influences the response before completion; curves grow with SOA after branching.	$i$7
Independence	Early kinematics depend only on prime; initial segment independent of target characteristics.	$i$8 (no dependence on $i$9)

Corollaries deduced from these criteria include:

1. $t$0 is constant across conditions (onset locked to the prime).
2. Branching times are ordered with SOA ($t$1).
3. The invariant segment $t$2 depends on $t$3 but not $t$4.
4. Trajectories $t$5 are identical up to $t$6.
5. Post-branching, the priming effect's magnitude increases monotonically with SOA.

Succinctly: for $t$7,

1. $t$8
2. $t$9

3. Measurement in Continuous Motor Output

Any continuously varying motor output can be analyzed using RCT formalism. Canonical measurements include:

Pointing Trajectories

• $I_T$0 and $I_T$1: 2D finger positions along the prime–target axis.
• Priming effect: $I_T$2.
• $I_T$3 is identified as the earliest time $I_T$4 exceeds a threshold; branching times $I_T$5 mark divergence between SOA conditions.

Isometric Keypress Force

• $I_T$6, $I_T$7: Keypress forces.
• $I_T$8.

Lateralized Readiness Potential (LRP) in EEG

• $I_T$9, $T$0: Event-related brain potentials from consistent/inconsistent trials.
• $T$1.
• Onset/branching times extracted via jackknife or derivative-based detection.

The dependent variable $T$2 is always referenced to SOA ($T$3). Strict sequentiality predicts an SOA-ordered invariance and monotonic growth post-branching for all measured outputs (Schmidt, 2014).

4. Paradigmatic Examples and Empirical Data

Schmidt & Schmidt (2009) exemplify RCT fulfillment using a pointing task with natural images. Typical trial structure: fixation, 33-ms prime, variable blank, target (until response), with SOAs of 33, 66, and 100 ms. Task: point to the “animal” among two images, with congruent primes matching target locations and incongruent primes swapped.

Results:

• All SOAs yield an identical priming trajectory $T$4 up to $T$5 ms.
• The earliest branching (divergence) occurs first for the shortest SOA, then in SOA order ($T$6...).
• After branching, each longer SOA curve continues to increase in magnitude, matching RCT predictions.

Replication using varied stimulus sets (toy animals, objects) confirmed these patterns. In contrast, a challenging size-judgment task disrupted invariance and failed to meet RCT criteria, supporting the specificity of the framework to rapid, feedforward categorization (Schmidt, 2014).

5. Implications for Neural Dynamics: Feedforward versus Recurrent Processing

Empirical conformance to all RCT criteria behaviorally demonstrates the presence of strictly sequential, non-overlapping feedforward sweeps: the prime controls initial response dynamics, followed—at a branching time dictated by SOA—by target-driven takeover. This is consistent with the direct-parameter-specification principle articulated by Neumann, wherein a single-pass, bottom-up sweep directly specifies evolving motor parameters.

Failure to meet RCT criteria, such as early dependence of the priming effect on target features, or response trajectories displaying "fan" (rather than strict "branching") patterns, indicates temporal overlap or interleaving of prime and target processing streams. This is interpreted as evidence for recurrent or interactive mechanisms enabling early target influence before completion of the prime-driven sweep. Taken together, RCT offers a rigorous assay for differentiating strictly feedforward from recurrent visual-motor computations in human behavior (Schmidt, 2014).

6. Theoretical and Methodological Significance

Rapid-Chase Theory articulates a set of formal, testable predictions linking the abstract, covert notion of feedforward cortical sweeps to fine-grained, overt motor trajectories. These predictions establish a behavioral surrogate for direct neural measures, thus enabling non-invasive assessment of processing architecture in real-time visuomotor behavior. Empirical compliance (or its absence) with RCT criteria affords differentiation between visual processing modes and informs on the temporal structure underlying sensorimotor transformations (Schmidt, 2014).