ADAPT: Hybrid Prompt Optimization for LLM Feature Visualization

Prompt-based adaptation offers several ways to specialize a frozen language model, ranging from natural-language prompt optimization to learned continuous prompts. These methods are usually compared through downstream performance, although similar outputs need not arise from similar internal computations. We study how discrete prompt optimization, prompt tuning, and prefix tuning alter the processing of dense and mixture-of-experts language models. Our analysis shows that the location of the adaptation predicts how task information is carried to the output: optimized text primarily changes response construction, input-level prompts write their influence into content representations, and layer-wise prefixes maintain direct control through attention. In MoE models, these differences further induce distinct expert-routing patterns. At the same time, common representation-level measurements respond strongly to generic context changes and do not reliably distinguish useful adaptations from matched placebos. We argue that understanding prompt adaptation requires separating representation drift from the part of that drift that is aligned with, and causally used by, the model's task computation. This perspective provides practical guidance for selecting, evaluating, and interpreting prompt adaptation methods.

Automated prompt optimization is crucial for eliciting reliable reasoning from large language models (LLMs), yet most API-only prompt optimizers iteratively edit monolithic prompts, coupling components and obscuring credit assignment, limiting controllability, and wasting tokens. We propose Adaptive Prompt Structure Factorization (aPSF), an API-only framework (prompt-in/text-out; no access to model internals) that uses an Architect model to discover task-specific prompt structures as semantic factors. aPSF then performs interventional, single-factor updates: interventional factor-level scoring estimates each factor's marginal contribution via validation-performance changes, and error-guided factor selection routes updates to the current dominant failure source for more sample-efficient optimization. Across multiple advanced reasoning benchmarks, aPSF outperforms strong baselines including principle-aware optimizers, improving accuracy by up to +2.16 percentage points on average, and reduces optimization cost by 45--87% tokens on MultiArith while reaching peak validation in 1 step.

Large language models (LLMs) achieve strong generation and reasoning performance, but the Transformer architecture incurs high inference cost. Existing acceleration methods often rely on task-specific fine-tuning or training from scratch, increasing adaptation cost and limiting cross-task usability. We present an Adaptive Depth Sparse Framework (AdaDSF) that converts off-the-shelf pre-trained LLMs into depth-sparse models without full retraining. Our key insight is that layers contribute unequally to representation transformation, characterized by the cosine similarity between layer input and output hidden states. Based on this, AdaDSF assigns layer-wise token retention ratios from similarity statistics, uses a lightweight router to select informative tokens at each layer, and introduces a feature-preserving alignment objective to match intermediate and final representations between sparse and dense models. On GPT-NeoX and Qwen2.5 over language modeling and commonsense reasoning, AdaDSF substantially reduces inference FLOPs while preserving performance close to dense counterparts. Under comparable sparsity, AdaDSF consistently yields smaller accuracy degradation than strong baselines including MoD, D-LLM, and DLO.