Minimal-Intervention KV Retention: A Design-Space Study and a Diversity-Penalty Survivor

KV-cache compression at small budgets is a crowded design space spanning cache representation, head-wise routing, compression cadence, decoding behavior, and within-budget scoring. We study seven mechanisms across these five families under matched mean cache on long-form mathematical reasoning (MATH-500~\cite{hendrycks2021math}) with two distilled-reasoning models (Qwen-7B and Llama-8B variants of DeepSeek-R1-Distill~\cite{deepseek2025r1}) at budgets $b \in \{64, 128\}$. All seven were rejected. We then propose $α$, a one-function modification to the TriAttention~\cite{mao2026triattention} retention scorer that replaces argmax-top-$k$ with greedy facility-location-inspired selection under a V-space redundancy penalty controlled by a single weight $λ$. A pre-registered protocol tunes $λ$ on a frozen development split and confirms on a disjoint held-out split; with $λ= 0.5$, $α$ clears Bonferroni on two of the four (model, budget) cells (Qwen $b{=}128$ and Llama $b{=}64$), no cell is significantly negative, and the pre-registered Branch~A triggers. The finding is asymmetric: a minimal scoring modification beat heavier structural redesigns in this regime, and the combined matched-memory, sympy-graded, held-out confirmation protocol is the evidence standard that made the asymmetry visible.

MoE-nD: Per-Layer Mixture-of-Experts Routing for Multi-Axis KV Cache Compression

KV cache memory is the dominant bottleneck for long-context LLM inference. Existing compression methods each act on a single axis of the four-dimensional KV tensor -- token eviction (sequence), quantization (precision), low-rank projection (head dimension), or cross-layer sharing -- but apply the same recipe to every layer. We show that this homogeneity leaves accuracy on the table: different layers respond very differently to each compression operation, and the optimal per-layer mix of eviction and quantization is far from uniform. We propose MoE-nD, a mixture-of-experts framework that routes each layer to its own (eviction-ratio, K-bits, V-bits) tuple under a global memory budget. An offline-calibrated greedy solver chooses the routing that minimizes predicted quality loss; at inference time, per-layer heterogeneous eviction and quantization are applied jointly through a single attention patch. On a 4-task subset of LongBench-v1 (16k inputs, n=50 per task, adapted reasoning-model protocol; see section Experiments), MoE-nD's hetero variant matches our uncompressed 1.9~GB baseline at 14x compression (136~MB) while every other compressed baseline we tested (1d, 2d_uniform, 2d) at comparable or smaller memory stays under 8/100. The gains hold on AIME reasoning benchmarks (+6 to +27 pts over the strongest per-layer-quantization baseline across eight configurations). Two null results -- MATH-500 and LongBench's TREC -- share a principled cause (short inputs, solver picks keep=1.0 on most layers), cleanly characterizing when per-layer eviction routing has headroom to help.

A Survey of Lottery Ticket Hypothesis

The Lottery Ticket Hypothesis (LTH) states that a dense neural network model contains a highly sparse subnetwork (i.e., winning tickets) that can achieve even better performance than the original model when trained in isolation. While LTH has been proved both empirically and theoretically in many works, there still are some open issues, such as efficiency and scalability, to be addressed. Also, the lack of open-source frameworks and consensual experimental setting poses a challenge to future research on LTH. We, for the first time, examine previous research and studies on LTH from different perspectives. We also discuss issues in existing works and list potential directions for further exploration. This survey aims to provide an in-depth look at the state of LTH and develop a duly maintained platform to conduct experiments and compare with the most updated baselines.