Cognitive Dual-Pathway Reasoning (CDPR)

• Cognitive Dual-Pathway Reasoning (CDPR) is a family of cognitive and computational models that decompose inference into fast, intuitive and slow, reflective pathways.
• It underpins varied applications including large language models, multimodal intent recognition, and knowledge graph reasoning by leveraging either architectural separation or prompt-conditioned routing.
• Recent implementations such as PLE, CDR, and ACPO demonstrate improvements in accuracy, token efficiency, and computational cost through adaptive pathway selection and dual-mode processing.

Searching arXiv for papers on Cognitive Dual-Pathway Reasoning and closely related formulations. Cognitive Dual-Pathway Reasoning (CDPR) is a family of cognitive and computational formulations in which inference is organized around two distinct but coordinated modes: a fast, intuitive, direct pathway and a slower, deliberative, reflective pathway. In the literature, these pathways are variously described as Type 1 versus Type 2, System 1 versus System 2, generative versus evaluative processing, no-think versus think, retrieval versus reasoning, intuition versus deliberation, or direct-answer versus chain-of-thought. CDPR is therefore not a single architecture but a recurrent design principle spanning cognitive theory, LLMs, knowledge-graph reasoning, multimodal intent recognition, medical multimodal reasoning, and bounded neural models (Sowden et al., 2014, Deng et al., 2024, Du et al., 2019, Wang et al., 10 May 2026, Wang et al., 29 Apr 2026).

1. Conceptual lineage in dual-process theory

The conceptual basis of CDPR lies in dual-process accounts of cognition. In the creative-thinking literature reviewed by Sowden, Pringle, and Gabora, the first pathway is characterized as rapid, unconscious, automatic, associative, and high-capacity, with little or no working-memory load; the second is characterized as slow, effortful, conscious, analytic, rule-based, reflective, and working-memory limited. Within that framing, the first pathway is associated with idea generation or divergent processing, whereas the second pathway is associated with idea evaluation, convergence, refinement, selection, and rejection (Sowden et al., 2014).

The same review identifies two especially relevant models. Howard-Jones’s Dual-State Model distinguishes a generative, associative, defocused state from an evaluative, analytic, focused state, with shifts induced by training or environmental cues. Gabora’s Honing Theory describes iterative interplay between associative generation and analytic refinement, governed by a shift function along an associative–analytic continuum. A simplified dynamic expression presented in the review writes the system as a two-state process,

$$\frac{dG}{dt} = \alpha G - \beta S(G,E)G,\qquad \frac{dE}{dt} = \gamma E + \delta S(G,E)G,$$

with a possible sigmoid shift function

$S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$

This formalization does not claim a canonical CDPR equation; rather, it supplies a toy dynamical-system model for shifting between associative generation and analytic control (Sowden et al., 2014).

The same source also links the dual pathways to neuroimaging and chronometric markers. It summarizes evidence that the anterior insula and anterior cingulate cortex become active immediately before insight solutions, with the anterior cingulate cortex acting as a gate between the Default Mode Network and the Central Executive Network. It further reports that DMN regions and hippocampus/MTL are active during free-form idea generation, with average BOLD change of approximately $+0.8$–$1.2$ versus baseline, whereas CEN regions become strongly active during evaluation, with BOLD change of approximately $+1.5$–$2.0$. EEG markers are likewise differentiated: generation is associated with increases in lower-band alpha $8$–$10$ Hz over frontal sites, whereas evaluation is associated with increases in upper-band alpha $10$–$12$ Hz and beta $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$0–$S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$1 Hz over right prefrontal cortex. Chronometric proposals in that review center on identifying shift times $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$2, inter-shift intervals $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$3, and their correlations with originality and feasibility, thereby treating pathway transition itself as a measurable object (Sowden et al., 2014).

2. Principal computational forms

In contemporary machine-learning work, CDPR appears in several computational forms rather than one standardized implementation.

Form	Representative formulation	Core mechanism
Architectural separation	PLE (Wang et al., 29 Apr 2026)	Two semantically locked MLP experts, one for think and one for no-think
Prompt-conditioned dual mode	Dual Tuning (Zheng et al., 4 Feb 2026)	One model trained under CoT and Direct-Answer prompts
Self-training distillation	CFLLMs (Deng et al., 2024)	Distill successful System 2 outputs into future zero-CoT System 1 answers
Meta-cognitive routing	CDR (Du et al., 17 Aug 2025)	Compute a complexity score and route to $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$4 or $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$5
Iterative retrieval–reasoning loop	CogKR (Du et al., 2019)	Alternate fast evidence collection and structured reasoning over a cognitive graph
Branch-specialized multimodal fusion	MIR CDPR (Wang et al., 10 May 2026)	Intuition pathway builds consensus; reasoning pathway resolves inconsistency

These formulations differ chiefly in where the duality is imposed. Some separate parameters, as in architecture-level expert duplication or fully distinct pathways. Some keep the transformer body unchanged and impose duality through prompts, multi-pass inference, or auxiliary routing. Some externalize the two pathways into a control layer above inference. Others define duality functionally, for example as retrieval followed by structured reasoning on a dynamically built subgraph. A recurrent implication is that CDPR is best understood as a design pattern for partitioning cognitive labor rather than as a commitment to any single module type or training regime.

3. Architecture-level separation and bounded dual-path models

A particularly explicit architecture-level realization is "Path-Lock Expert" (Wang et al., 29 Apr 2026). PLE replaces the single MLP in each decoder layer with two semantically locked experts, one dedicated to think and one to no-think, while embeddings, positional encoding, LayerNorms, self-attention sublayers, and the final language-model head remain shared. For layer $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$6, the forward pass is

$S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$7

$S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$8

where $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$9 is a single routing decision for the entire sequence. Routing is deterministic: $+0.8$0 if the final control token is /think, $+0.8$1 if it is /no_think, and $+0.8$2 otherwise. Because $+0.8$3 is fixed once per sequence and cached before generation, PLE preserves the dense model’s per-token FLOPs while giving each mode its own parameter slice in every MLP block. In supervised fine-tuning, only the active expert receives mode-specific updates, so $+0.8$4, while shared parameters still receive gradients. On a Qwen3-4B backbone, PLE reduced no-think reflective tokens on AIME24 from $+0.8$5 to $+0.8$6, improved no-think accuracy from $+0.8$7 to $+0.8$8, and maintained think-mode performance at approximately $+0.8$9. Across MATH500, AIME24, MMLU-STEM, and GPQA-Diamond, the paper reports a Pareto-optimal frontier: cleaner and more accurate no-think behavior while preserving think-mode capability (Wang et al., 29 Apr 2026).

A more deliberately bounded neural realization appears in "AI Mental Models" (Anthony, 23 Mar 2026). There, the intuition pathway is a single linear layer $1.2$0 with ReLU and a $1.2$1-way output head, whereas the deliberation pathway uses a separate encoder $1.2$2, five candidate states $1.2$3, a learned soft gate $1.2$4, and a mixed deliberation logit $1.2$5. The joint training loss is $1.2$6. Despite using approximately $1.2$7 trainable weights in total, the model achieves aggregate $1.2$8 for intuition and $1.2$9 for deliberation under $+1.5$0-fold cross-validation, with a significant deliberation advantage across folds $+1.5$1. The interpretability analyses further report a dominant workhorse state, an Oac-leaning specialist, and several weakly used or unused states whose exact indices vary across runs. In this bounded setting, CDPR is not implemented as long sequential chain-of-thought but as a learned division of labor between a coarse first-pass distribution and a more differentiated second-stage mixture (Anthony, 23 Mar 2026).

Taken together, these two lines of work establish two strong architectural readings of CDPR. One treats the pathways as mode-specific parameter slices within a large autoregressive model; the other treats them as explicitly distinct sub-networks with interpretable internal specialization.

4. Prompt-conditioned, self-training, and adaptive routing systems

A prompt-conditioned and self-training formulation is given by the CogniDual Framework for LLMs (Deng et al., 2024). For a batch of questions $+1.5$2, the framework elicits System 1 answers $+1.5$3 under “Answer directly, no rationale” and System 2 answers $+1.5$4 under “Please think step-by-step and then answer,” compares both to the ground truth via a semantic-matching judge, filters instances where System 2 is correct and System 1 is not, rewrites the successful System 2 outputs into concise answers, and then LoRA-fine-tunes on that distilled set using $+1.5$5. This operationalizes the claim that repeated self-training can reduce the gap $+1.5$6 until a plateau is reached. Empirically, on ReClor and LogiQA 2.0, the framework raises no-CoT accuracy from near zero to tens of points, while on GSM8K gains are modest because models tend to produce implicit CoT anyway; it also reduces inference latency by $+1.5$7–$+1.5$8 when no CoT is required (Deng et al., 2024).

A different formulation is "Cognitive Decision Routing" (Du et al., 17 Aug 2025), which defines CDPR as a triad $+1.5$9 with $2.0$0, a meta-cognitive layer $2.0$1 computing $2.0$2, and a routing rule $2.0$3 that selects the pathway based on threshold $2.0$4. The feature set comprises Correlation Strength $2.0$5, Domain Crossing $2.0$6, Stakeholder Multiplicity $2.0$7, and Uncertainty Level $2.0$8. The threshold is adapted online by

$2.0$9

with $8$0 on a sliding window of $8$1 queries. On $8$2 queries per condition, Uniform Fast obtains $8$3 accuracy and Uniform Slow $8$4, whereas CDR reaches $8$5 with a linear scorer and $8$6 with a neural scorer. Relative to Uniform Slow, the neural version yields $8$7 percentage points accuracy, $8$8 consistency, $8$9 token usage, $10$0 latency reduction, and estimated $10$1 API-cost savings, with especially large gains on professional judgment tasks (Du et al., 17 Aug 2025).

"The Thinking Boundary" (Zheng et al., 4 Feb 2026) formulates the decision problem more diagnostically than procedurally. It trains one multimodal model under both CoT and Direct-Answer prompts and evaluates task suitability through $10$2, $10$3, $10$4, $10$5, and a token-efficiency measure $10$6. A task is inside the Thinking Boundary precisely when both $10$7 and $10$8. In the reported experiments, no VSI-Bench or CV-Bench spatial subtask falls inside the Thinking Boundary; key mathematical subtasks such as Geometry, Logical, and Statistical do enter it; and MMMU is heterogeneous, with some subjects favoring CoT and others favoring DA. Reinforcement learning magnifies $10$9 on math tasks but does not change which tasks lie inside the boundary (Zheng et al., 4 Feb 2026).

A related attribution framework appears in "Decoupling Knowledge and Reasoning in LLMs" (Yang et al., 24 Jul 2025). There, fast thinking produces $10$0, slow thinking revises it into $10$1, and the central quantity is reasoning adjustment capability $10$2, with $10$3 decomposing correction versus overthinking. Across $10$4 LLMs and three datasets, the paper reports that mathematics, physics, and chemistry consistently rank highest in $10$5, whereas knowledge-intensive domains such as Political Science, History, and Law often show negative $10$6. Small models frequently have $10$7, because the overthinking rate $10$8 exceeds the correction rate $10$9. The same study uses centered kernel alignment to show high fast/slow similarity in lower layers and sharp divergence in upper layers, implying that knowledge retrieval primarily resides in early transformer layers while reasoning adjustments primarily engage deeper layers (Yang et al., 24 Jul 2025).

A reinforcement-learning variant is "Adaptive Cognition Policy Optimization" (Cheng et al., 22 May 2025). ACPO adds explicit reasoning-mode tokens, namely <fast_think>, </fast_think>, <slow_think>, and </slow_think>, and optimizes a composite reward built from answer correctness, an online token-length budget, and a system-pattern reward. The token-length budget is

$12$0

where $12$1 is the empirical group success rate. On AIME 2024 with a $12$2B model, ACPO reduces tokens from approximately $12$3K to approximately $12$4K while increasing accuracy from $12$5 to $12$6. On MATH 500 with a $12$7B model, it reduces tokens from $12$8 to $12$9 with only a $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$00 accuracy drop. On GSM8K, it raises accuracy from $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$01 to $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$02 while slightly lowering length from $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$03 to $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$04. The reported fast/slow token ratio declines from about $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$05 fast on easy problems to about $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$06 fast on difficult ones, matching the intended difficulty-adaptive split (Cheng et al., 22 May 2025).

5. Structured reasoning beyond text-only LLMs

In knowledge-graph reasoning, CDPR is instantiated by CogKR (Du et al., 2019). The model addresses one-shot relational learning by combining a summary module, which builds a relation vector $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$07 from a single support pair, with a reasoning module that constructs a small cognitive graph $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$08. System 1 is fast retrieval: it expands an unexplored entity by sampling actions from a learned policy over outgoing edges and a no-op. System 2 is structured reasoning: it updates node states by message passing over the current cognitive graph,

$S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$09

The alternation continues until no node remains unexplored or $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$10 reaches a preset limit $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$11. On NELL-One, CogKR reports $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$12 versus $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$13 for MultiHopKG and $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$14 for GMatching; on Wiki-One, it reports $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$15 versus $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$16 for GMatching. The paper further notes constant $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$17 inference time per query, independent of $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$18, and emphasizes that the cognitive graph aggregates evidence from multiple reasoning paths rather than a single path (Du et al., 2019).

In multimodal intent recognition, CDPR is used to manage consistency and conflict across text, video, and audio (Wang et al., 10 May 2026). The model first disentangles each modality into shared features $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$19 and private features $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$20 using separate MLPs, regularized by a similarity loss based on Central Moment Discrepancy and a difference loss enforcing orthogonality. The intuition pathway builds cross-modal consensus through raw fusion and pairwise products of shared features, yielding $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$21. The reasoning pathway operates on private features, computes a semantic conflict energy $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$22, calibrates it with Jensen–Shannon divergence and modality entropies to form $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$23, derives per-modality reliability weights, and outputs $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$24. A global gate $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$25 then fuses the branches:

$S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$26

On MIntRec, the method reports ACC $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$27 versus previous best $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$28, F1 $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$29 versus $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$30, and WF1 $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$31 versus $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$32. On MIntRec2.0, it reports ACC $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$33 versus $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$34, F1 $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$35 versus $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$36, and WF1 $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$37 versus $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$38. Under text noise with Gaussian $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$39, CDPR reaches F1 $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$40 versus the best baseline at approximately $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$41. The model also uses $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$42M parameters, about $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$43 fewer than MVCL-DAF’s $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$44M, while achieving $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$45 samples/s inference and $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$46 GB GPU memory on MIntRec2.0 (Wang et al., 10 May 2026).

A medical multimodal version appears in FundusExpert (Liu et al., 23 Jul 2025), where the two pathways are positioning and diagnosis rather than generic fast and slow reasoning. The positioning pathway performs segmentation with nnU-Net, converts masks to box proposals through DBSCAN, and extracts region embeddings; the diagnosis pathway fuses global image features with region features, predicts disease labels, and generates reports. Integration is achieved through a clinical cognitive chain that explicitly sequences “Region Localization,” “Feature Analysis,” “Diagnostic Reasoning,” and “Evidence Verification.” On clinical QA benchmarks, FundusExpert reports $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$47 on Fundus-MMBench and $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$48 on GMAI-MMBench, compared with MedRegA’s $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$49 and $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$50, respectively. In zero-shot region localization, it reports IoU $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$51 for optic cup, $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$52 for optic disc, $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$53 for hard exudates, $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$54 for cotton-wool spots, and $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$55 for microaneurysms, all above the reported MedRegA baselines. In report generation, its clinical consistency is $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$56 versus GPT-4o’s $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$57. The paper also reports a data-scaling law $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$58 with $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$59 and $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$60, arguing that cognitive-alignment annotations improve data-utilization efficiency (Liu et al., 23 Jul 2025).

6. Empirical regularities, limitations, and open problems

Several regularities recur across CDPR studies. First, reasoning is not uniformly beneficial. "The Thinking Boundary" explicitly rejects a reasoning-for-all paradigm by showing that no VSI-Bench or CV-Bench spatial subtask falls inside the boundary, while only selected mathematical and multidisciplinary tasks do (Zheng et al., 4 Feb 2026). The knowledge–reasoning decoupling study reaches a related conclusion in text-only LLMs: reasoning adjustment benefits mathematics, physics, and chemistry, but can impair knowledge-intensive domains such as Political Science, History, and Law, especially in small models with high overthinking rates (Yang et al., 24 Jul 2025). This suggests that pathway selection is task-conditional rather than universally monotone in deliberation depth.

Second, CDPR research repeatedly identifies control failure in shared models. PLE argues that leakage persists under training-only fixes because think and no-think modes remain encoded in the same feed-forward parameters, leading to gradient conflict and token-count asymmetry; its expert duplication is presented as a block-diagonalization of the Hessian between $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$61 and $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$62, thereby eliminating cross-mode conflicts at the second-order level (Wang et al., 29 Apr 2026). A plausible implication is that some failures attributed to prompting or data curation are in fact consequences of parameter sharing.

Third, the literature disagrees on how explicit the two pathways must be. Some frameworks insist on architectural separation, as in PLE or the bounded intuition–deliberation model. Others rely on prompts, self-distillation, or external routing without changing the transformer body, as in Dual Tuning, CFLLMs, and CDR. The CDR paper states a Computational Equivalence Principle according to which System 1 versus System 2 corresponds to complexity of operations rather than to separate network modules (Du et al., 17 Aug 2025). The diversity of implementations therefore reflects a live methodological question rather than settled consensus.

Open problems are stated explicitly across the papers. PLE identifies dynamic or learned gating, more than two experts, input-feature-conditioned routers, combination with RL-based reward shaping, and transfer to multimodal or instruction-finetuned foundations (Wang et al., 29 Apr 2026). CDR proposes dynamic intra-query pathway switching, personalized routing thresholds, and continual meta-learning of $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$63 and $S(G,E)=\frac{1}{1+e^{-\theta(G-E)}}.$64 (Du et al., 17 Aug 2025). ACPO highlights the need for unsupervised or open-ended settings in which answer correctness is not directly verifiable, along with entropy-based difficulty estimation and explicit value networks (Cheng et al., 22 May 2025). In multimodal settings, the MIR study indicates that conflict handling, anti-laziness supervision, and robust representation disentanglement remain central for maintaining performance under inconsistent signals (Wang et al., 10 May 2026).

Across these strands, CDPR has evolved from a cognitive-theoretic distinction into a general engineering principle for decomposing inference into direct and deliberative components, measuring when each should dominate, and controlling their interaction. The central unresolved issue is not whether dual pathways exist as a useful abstraction, but where the separation should be enforced: in prompts, in routing logic, in training objectives, in explicit modules, or in the architecture itself.