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Abstract

Distributed intelligent systems increasingly need to train across data silos without centralizing raw data. Federated learning keeps data local, but heterogeneous partitions can degrade accuracy and require repeated full-model exchange. Split learning reduces communication through cut-layer activations, but standard protocols do not generally recover pooled mini-batch gradients and may expose activations and gradients in plaintext. We present TL++, a two-mode traversal-learning framework that constructs virtual batches across nodes to recover centralized mini-batch gradient behavior under explicit synchronization assumptions. Base mode exchanges cut-layer activations and gradients instead of full models. Secure mode secret-shares each cut-layer activation and gradient between an orchestrator and a non-colluding helper, so neither server alone observes plaintext cut-layer tensors. This protection is limited to a semi-honest, non-colluding two-server setting; labels and output values used for loss remain visible to the orchestrator. In the lightweight secure path evaluated here, exactness requires the sharewise server path to be linear or affine; nonlinear server operations require nonlinear MPC or are approximate. We formalize TL++, analyze communication and computation costs, and evaluate it against federated- and split-learning baselines on CIFAR-10 and BioGPT/ PubMedQA using full fine-tuning and LoRA. On CIFAR-10, TL++ base cut 1 and exact secure cut 3 achieve 91 _._ 41 0 _._ 19% and 90 _._ 93 0 _._ 17% accuracy, outperforming the strongest measured non-TL++ baseline by more than 12 percentage points. TL++ base cut 1 also reduces per-step communication payload by 13 _._ 1 relative to full-model synchronization. PubMedQA results similarly favor TL++ under both tuning settings, though they remain descriptive without paired trajectories. Overall, TL++ approaches centralized-level utility while reducing communication and supporting scoped activation-level secret sharing.