Zibo Diao | Searcharxiv

arXiv2026

Minimal Deadlock-Free Routing for Degree-Six Triangular-Lattice Meshes and Tori with Two Forbidden Turns

Degree-six triangular-lattice interconnection networks offer substantial minimal-path diversity, but their additional directions complicate deadlock-free routing under wormhole flow control. We study a finite hexagon-shaped mesh and its periodic torus quotient in a common six-direction coordinate system. For the finite mesh, we construct a minimal partially adaptive routing relation that uses one virtual channel and forbids only two directed turns. For the torus, we prove that every source-destination pair has a unique closest lattice lift, but that the same two-turn physical routing relation still has a cyclic one-VC resource CDG for every n >= 3. We eliminate this residual periodic dependency by combining two virtual channels with Hamiltonian coordinates and group-specific datelines. Each same-group segment crosses its dateline at most once, which permits a global rank on VC-labelled channel resources. We prove minimal all-pairs connectivity for both physical routing relations and acyclicity of the complete resource CDG for the proposed one-VC mesh and two-VC torus constructions. For a single static bidirectional link failure known before a routing epoch, we further rotate the turn rule toward the failed orientation and replace a failed hop by a same-group two-hop triangle bypass. This restricted extension preserves all-pairs connectivity and the original VC counts, with at most one additional hop relative to the healthy shortest-path distance.

cs.AR↗

arXiv2026

Lossless Anti-Distillation Sampling

Frontier commercial generative models face a growing threat from distillation, whereby a distiller harvests generated responses and trains a competing model of its own at drastically lower cost. Existing defenses either rely on modifying the models outputs, thereby sacrificing response quality for benign users, or on behavioral detection methods, which can be readily circumvented by distributing queries across multiple accounts. In this work, we propose Lossless Anti-Distillation Sampling (LADS), a novel sampling scheme specifically designed to counter multi-account distillation while maintaining a lossless experience for benign users. Concretely, LADS derives the randomness underlying each generation from a private seed determined by the semantic content of the query and the number of times the user has queried the model. By construction, every benign user receives a response independently sampled from the original model at each visit, and thus experiences no distortion. In contrast, for a distiller, different accounts share latent randomness whenever their queries fall in the same semantic bucket. As a result, the harvested data becomes correlated, potentially reducing sample diversity and degrading generalization. Using uniform convergence theory, we show that LADS provably degrades the convergence rate of the distillers generalization gap relative to standard i.i.d. sampling in both unconditional and conditional generation settings. Experiments on image generation, mathematical reasoning, and code generation confirm that LADS substantially degrades the performance of distilled students while preserving exact statistical fidelity for individual users.

cs.LG↗