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ManCAR: Manifold-Constrained Latent Reasoning with Adaptive Test-Time Computation for Sequential Recommendation

Kun Yang, Yuxuan Zhu, Yazhe Chen, Siyao Zheng, Bangyang Hong, Kangle Wu, Yabo Ni, Anxiang Zeng, Cong Fu, Hui Li

TL;DR

This work proposes ManCAR (Manifold-Constrained Adaptive Reasoning), a principled framework that grounds reasoning within the topology of a global interaction graph and provides a variational interpretation of ManCAR to theoretically validate its drift-prevention and adaptive test-time stopping mechanisms.

Abstract

Sequential recommendation increasingly employs latent multi-step reasoning to enhance test-time computation. Despite empirical gains, existing approaches largely drive intermediate reasoning states via target-dominant objectives without imposing explicit feasibility constraints. This results in latent drift, where reasoning trajectories deviate into implausible regions. We argue that effective recommendation reasoning should instead be viewed as navigation on a collaborative manifold rather than free-form latent refinement. To this end, we propose ManCAR (Manifold-Constrained Adaptive Reasoning), a principled framework that grounds reasoning within the topology of a global interaction graph. ManCAR constructs a local intent prior from the collaborative neighborhood of a user's recent actions, represented as a distribution over the item simplex. During training, the model progressively aligns its latent predictive distribution with this prior, forcing the reasoning trajectory to remain within the valid manifold. At test time, reasoning proceeds adaptively until the predictive distribution stabilizes, avoiding over-refinement. We provide a variational interpretation of ManCAR to theoretically validate its drift-prevention and adaptive test-time stopping mechanisms. Experiments on seven benchmarks demonstrate that ManCAR consistently outperforms state-of-the-art baselines, achieving up to a 46.88% relative improvement w.r.t. NDCG@10. Our code is available at https://github.com/FuCongResearchSquad/ManCAR.

ManCAR: Manifold-Constrained Latent Reasoning with Adaptive Test-Time Computation for Sequential Recommendation

TL;DR

This work proposes ManCAR (Manifold-Constrained Adaptive Reasoning), a principled framework that grounds reasoning within the topology of a global interaction graph and provides a variational interpretation of ManCAR to theoretically validate its drift-prevention and adaptive test-time stopping mechanisms.

Abstract

Sequential recommendation increasingly employs latent multi-step reasoning to enhance test-time computation. Despite empirical gains, existing approaches largely drive intermediate reasoning states via target-dominant objectives without imposing explicit feasibility constraints. This results in latent drift, where reasoning trajectories deviate into implausible regions. We argue that effective recommendation reasoning should instead be viewed as navigation on a collaborative manifold rather than free-form latent refinement. To this end, we propose ManCAR (Manifold-Constrained Adaptive Reasoning), a principled framework that grounds reasoning within the topology of a global interaction graph. ManCAR constructs a local intent prior from the collaborative neighborhood of a user's recent actions, represented as a distribution over the item simplex. During training, the model progressively aligns its latent predictive distribution with this prior, forcing the reasoning trajectory to remain within the valid manifold. At test time, reasoning proceeds adaptively until the predictive distribution stabilizes, avoiding over-refinement. We provide a variational interpretation of ManCAR to theoretically validate its drift-prevention and adaptive test-time stopping mechanisms. Experiments on seven benchmarks demonstrate that ManCAR consistently outperforms state-of-the-art baselines, achieving up to a 46.88% relative improvement w.r.t. NDCG@10. Our code is available at https://github.com/FuCongResearchSquad/ManCAR.
Paper Structure (33 sections, 3 theorems, 23 equations, 7 figures, 6 tables, 2 algorithms)

This paper contains 33 sections, 3 theorems, 23 equations, 7 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Our Proposed ManCAR
  3. Problem Setting and Notation
  4. Manifold-Constrained Latent Reasoning
  5. Variational Training Objective
  6. Local Graph Smoothness by KL Distillation
  7. Implementation of ManCAR Objective
  8. Training Scheduling and Adaptive Test-Time Reasoning
  9. Experiments
  10. Experimental Setup
  11. Datasets and Preprocess
  12. Evaluation Metrics.
  13. Baselines.
  14. Implementation.
  15. Overall Performance (Tab. \ref{['tab:performance_cross']}).
  16. ...and 18 more sections

Key Result

proposition 1

Let $\mathcal{C}$ be a finite candidate set and $\mathbf{e}_c \in \mathbb{R}^d$ denote the embedding of item $c \in \mathcal{C}$. Given a reasoning state $\mathbf{r} \in \mathbb{R}^d$, define the induced predictive distribution as: Let $Q$ be any fixed teacher distribution supported on $\mathcal{C}$. Then the KL distillation loss $\mathcal{L}(\mathbf{r}) = D_\mathrm{KL}\!\left(Q \,\|\, P(\cdot \m

Figures (7)

  • Figure 1: Illustration of constrained versus unconstrained latent reasoning. Graph-conditioned reasoning trajectories remain within a collaborative manifold defined by neighbor items, enabling stable and directed refinement toward the target. In contrast, unconstrained reasoning may drift outside feasible regions, leading to inefficient or unstable paths.
  • Figure 2: Overview of ManCAR. ManCAR performs multi-step latent reasoning constrained by a graph-induced candidate set. At each step, the reasoning state is regularized toward a scheduled teacher prior defined on collaboratively reachable items, ensuring manifold-consistent refinement. Adaptive test-time termination stops reasoning when the induced item distributions stabilize.
  • Figure 3: Performance ceiling analysis on Office and Toys.
  • Figure 4: Sensitivity analysis on Video and CDs. (a) and (b): NDCG@10 and Recall@10 w.r.t. #context items; (c) and (d): NDCG@10 and Recall@10 w.r.t. regularization loss weight $\lambda$; (e) and (f): NDCG@10 and Recall@10 w.r.t. temperature $\tau_{\mathrm{base}}$; (g) and (h): NDCG@10 and Recall@10 w.r.t. $\gamma_{\mathrm{base}}$.
  • Figure 5: NDCG@10 w.r.t. reason step $T^\prime$ on CDs and Office.
  • ...and 2 more figures

Theorems & Definitions (3)

  • proposition 1: Local Graph Smoothness Induced by KL Distillation
  • proposition 2: Continuation tracking under contraction and bounded teacher drift
  • proposition 3: Graph-Conditioned Variational Regularization Training Objective