NestedKV: Nested Memory Routing for Long-Context KV Cache Compression

Long-context language models are limited by the memory footprint of the key-value (KV) cache. Existing training-free KV compression methods usually rank tokens by one importance signal -- attention, recency, layer-wise allocation, or key distinctiveness -- which becomes brittle when useful context is globally distinctive, locally episodic, or immediately relevant. We introduce NestedKV, a key-only KV cache compression method inspired by the Continuum Memory System in Nested Learning. NestedKV maintains global, block-level, and sliding-window key anchors, scores tokens by multi-time-scale cosine anomaly, and combines the resulting rankings with a training-free outer learner using head-adaptive mixing and surprise-gated token routing. The score is paired with adaptive per-head budgets and requires no training or LLM modification. Across RULER (4k--32k), LooGLE, LongBench, LongBench-E, InfiniteBench, and MMLU-Pro on Qwen3 and Llama-3.2 models, NestedKV is strongest when the retained cache is small. On Qwen3-4B, it improves over KeyDiff by up to 19.10 points on RULER and 19.29 on LongBench at $r=0.75$; at $r=0.95$, it retains 37.32 on LongBench versus 17.55 for KeyDiff.

SONIC: Segmented Optimized Nexus for Information Compression in Key-Value Caching

The linear growth of Key-Value (KV) cache remains a bottleneck for multi-turn LLM deployment. Existing KV cache compression methods often fail to account for the structural properties of multi-turn dialogues, relying on heuristic eviction that risks losing critical context. We propose \textbf{SONIC}, a learning-based framework that compresses historical segments into compact and semantically rich \textbf{Nexus} tokens. By integrating dynamic budget training, SONIC allows flexible adaptation to varying memory constraints without retraining. Experiments show that at compression ratios of 80\% and 50\%, SONIC consistently outperforms baselines such as H2O and StreamingLLM on four diverse multi-turn benchmarks. Specifically, on the widely used MTBench101 benchmark, SONIC achieves an average score improvement of 35.55\% over state-of-the-art baselines, validating its effectiveness in sustaining coherent multi-turn dialogues. Furthermore, SONIC enhances deployment efficiency, accelerating the overall inference process by 50.1\% compared to full-context generation.

Deconstructing Pre-training: Knowledge Attribution Analysis in MoE and Dense Models

Mixture-of-Experts (MoE) architectures decouple model capacity from per-token computation, enabling scaling beyond the computational limits imposed by dense scaling laws. Yet how MoE architectures shape knowledge acquisition during pre-training, and how this process differs from dense architectures, remains unknown. To address this issue, we introduce Gated-LPI (Log-Probability Increase), a neuron-level attribution metric that decomposes log-probability increase across neurons. We present a time-resolved comparison of knowledge acquisition dynamics in MoE and dense architectures, tracking checkpoints over 1.2M training steps (~ 5.0T tokens) and 600K training steps (~ 2.5T tokens), respectively. Our experiments uncover three patterns: (1) Low-entropy backbone. The top approximately 1% of MoE neurons capture over 45% of positive updates, forming a high-utility core, which is absent in the dense baseline. (2) Early consolidation. The MoE model locks into a stable importance profile within < 100K steps, whereas the dense model remains volatile throughout training. (3) Functional robustness. Masking the ten most important MoE attention heads reduces relational HIT@10 by < 10%, compared with > 50% for the dense model, showing that sparsity fosters distributed -- rather than brittle -- knowledge storage. These patterns collectively demonstrate that sparsity fosters an intrinsically stable and distributed computational backbone from early in training, helping bridge the gap between sparse architectures and training-time interpretability.

SSR: Speculative Parallel Scaling Reasoning in Test-time

Large language models (LLMs) have achieved impressive results on multi-step mathematical reasoning, yet at the cost of high computational overhead. This challenge is particularly acute for test-time scaling methods such as parallel decoding, which increase answer diversity but scale poorly in efficiency. To address this efficiency-accuracy trade-off, we propose SSR (Speculative Parallel Scaling Reasoning), a training-free framework that leverages a key insight: by introducing speculative decoding at the step level, we can accelerate reasoning without sacrificing correctness. SSR integrates two components: a Selective Parallel Module (SPM) that identifies a small set of promising reasoning strategies via model-internal scoring, and Step-level Speculative Decoding (SSD), which enables efficient draft-target collaboration for fine-grained reasoning acceleration. Experiments on three mathematical benchmarks-AIME 2024, MATH-500, and LiveMathBench - demonstrate that SSR achieves strong gains over baselines. For instance, on LiveMathBench, SSR improves pass@1 accuracy by 13.84% while reducing computation to 80.5% of the baseline FLOPs. On MATH-500, SSR reduces compute to only 30% with no loss in accuracy.