Large reasoning models (LRMs) achieve state-of-the-art performance on challenging benchmarks by generating long chains of intermediate steps, but their inference cost is dominated by decoding, where each new token must attend to the entire growing sequence. One approach to reduce this latency is to evict entries from the key-value (KV) cache, thereby reducing the active context used in attention computation. However, such sparse attention methods suffer from severe accuracy degradation on reasoning tasks due to cumulative selection errors and the evolving importance of tokens over long derivations. We present DELTA, a training-free sparse attention mechanism that improves computational efficiency without sacrificing model accuracy. DELTA partitions transformer layers into three groups: initial layers that use full attention, a small set of Δ-layers that identify salient tokens via aggregated head-level attention scores, and subsequent sparse-attention layers that attend only to the selected subset. This design preserves the full KV cache in GPU memory for accuracy, while avoiding expensive full-attention computation over many layers. On reasoning benchmarks such as AIME and GPQA-Diamond, DELTA matches or surpasses full attention in accuracy, while reducing the number of attended tokens by up to 4.25× and delivering 1.54× end-to-end speedup. Our results show that selective reuse of intermediate attention maps offers a robust path toward efficient long-context reasoning. The code is available at https://github.com/hoenza/DELTA.

Inference for Large Language Models (LLMs) is computationally demanding. To reduce the cost of auto-regressive decoding, Key-Value (KV) cache is used to store intermediate activations, which significantly lowers the computational overhead for token generation. However, the memory required for the KV cache grows rapidly, often exceeding the capacity of GPU memory. A cost-effective alternative is to offload KV cache to CPU memory, which alleviates GPU memory pressure, but shifts the bottleneck to the limited bandwidth of the PCIe connection between the CPU and GPU. Existing methods attempt to address these issues by overlapping GPU computation with I/O or employing CPU-GPU heterogeneous execution, but they are hindered by excessive data movement and dependence on CPU capabilities. Fully overlapping PCIe communication latency gets challenging as the size of the KV cache grows and/or the GPU compute capabilities increase. In this paper, we introduce KVPR, an efficient I/O-aware LLM inference method where the CPU first transfers a partial set of activations, from which the GPU can start recomputing the KV cache values. While the GPU recomputes the partial KV cache, the remaining portion of the KV cache is transferred concurrently from the CPU. This approach overlaps GPU recomputation with KV cache transfer to minimize idle GPU time and maximize inference performance. KVPR is fully automated by integrating a profiler module that utilizes input characteristics and system hardware information, a scheduler module to optimize the distribution of computation and communication workloads, and a runtime module to efficiently execute the derived execution plan. Experimental results show that KVPR achieves up to 35.8% lower latency and 46.2% higher throughput during decoding compared to state-of-the-art approaches. The code is available at https://github.com/chaoyij/KVPR.