Transformers typically cache an independent key-value (KV) representation for each token at every layer. Recent work reveals that a token's KV representations across neighboring layers are correlated and contain shared information. We hypothesize that this correlation implies incremental inter-layer changes, which can be effectively captured by low-dimensional deltas. Motivated by this, we propose KVPath, a new KV representation paradigm that connects KV representations across the network depth into a path. The path establishes a full-dimensional base KV at the first layer, while subsequent layers generate low-dimensional delta KVs to update the preceding KV, thereby constructing their own KV states. By caching the base KV once alongside these compact delta KVs, KVPath preserves distinct layer-specific representations without storing full KV states at every layer. We develop two variants of KVPath: KVPath-Residual, which updates vector values via residual addition, and KVPath-Rolling, which progressively updates feature dimensions in a rolling manner. Under matched parameter counts, KVPath reduces KV-cache storage by up to 68\% for Grouped-Query Attention (GQA) and 55\% for Multi-Head Latent Attention (MLA), while maintaining or even improving model performance.
Self-consistency (SC) is a widely used decoding strategy for improving chain-of-thought reasoning, but it requires sampling many complete reasoning trajectories with a preset budget. Its efficient variants reduce the cost mainly by stopping full-trajectory sampling early or distributing the number of samples across questions. In this paper, we propose StepBack, a step-level error-localized resampling method for efficient test-time reasoning. Given a small set of draft trajectories, StepBack localizes likely first error positions using lightweight signals and then resamples the detected error step and its suffix, followed by majority answer voting. Empirically, StepBack matches the accuracy of SC on average across seven mathematical reasoning and multi-hop QA benchmarks, while reducing token usage by up to 41.26%. In addition, by nature, StepBack can be combined with adaptive inference methods such as Adaptive Consistency, further improving their inference-time efficiency.