Data Trajectory Alignment for LLM Domain Adaptation: A Two-Phase Synthesis Framework for Telecommunications Mathematics

TL;DR

Data Trajectory Alignment (DTA) introduces a two-phase, model-agnostic data-curation framework that reshapes how solutions are produced to match a target LLM’s inductive biases, addressing trajectory debt in telecom mathematics. Phase I synthesizes diverse high-coverage data via a teacher ensemble; Phase II rewrites teacher trajectories to align with the student and selects high-signal exemplars using agreement and reflection-based judgments. On Telemath, DTA achieves state-of-the-art pass@1 (72.45%) without thinking-mode inference, while delivering substantial edge-efficiency gains (e.g., ~42% energy per token reduction) over baselines. Ablation studies further show that trajectory alignment improves general mathematics tasks, reduces latent-space drift, and shifts token emphasis toward reasoning scaffolds rather than surface domain nouns, highlighting its utility as a practical domain adaptation strategy for low-resource verticals beyond telecom.

Abstract

General-purpose large language models (LLMs) are increasingly deployed in verticals such as telecommunications, where adaptation is hindered by scarce, low-information-density corpora and tight mobile/edge constraints. We propose Data Trajectory Alignment (DTA), a two-phase, model-agnostic data curation framework that treats solution processes - not only final answers - as first-class supervision. Phase I (Initializing) synthesizes diverse, high-coverage candidates using an ensemble of strong teachers. Phase II (DTA) rewrites teacher solutions to align intermediate steps and presentation style with the target student's inductive biases and then performs signal-aware exemplar selection via agreement checks and reflection-based judging. Instantiated on telecommunications mathematics (e.g., link budgets, SNR/AMC selection, and power-control feasibility), DTA yields state-of-the-art (SOTA) accuracy on TELEMATH without enabling explicit "thinking" modes: 72.45% pass@1, surpassing distilled-only training by +17.65 points and outperforming a strong baseline (Qwen3-32B with thinking enabled) by +2.94 points. Token-shift analyses indicate that DTA concentrates gains on logical-structural discourse markers rather than merely amplifying domain nouns, indicating improved reasoning scaffolding. Under edge-like inference settings, DTA improves efficiency by reducing reliance on multi-sample voting and disabling expensive reasoning heuristics, cutting energy per output token by ~42% versus Qwen3-32B (thinking mode enabled) and end-to-end latency by ~60% versus Qwen3-32B (thinking mode disabled). These results demonstrate that aligning how solutions are produced enables compact, high-yield supervision that is effective for both accuracy and efficiency, offering a practical recipe for domain adaptation in low-resource verticals beyond telecom.

Figures (6)

• Figure 1: The working flow of two-phase framework: initializing and DTA
• Figure 2: Word cloud of token shift in Telemath benchmark
• Figure 3: Pairwise LLM-judge comparisons between models on OlympiadBench.
• Figure 4: Training loss in the math ablation: $g2_{\text{gene}}$ (DTA-only) converges faster and to a lower minimum than $g1_{\text{gene}}$ (raw SFT).
• Figure 5: PCA shift of Qwen3-32B across training methods and benchmarks.