Daily Papers

Chunked prefill has become a widely adopted serving strategy for long-context large language models, but efficient attention computation in this regime remains challenging. Existing sparse attention methods are primarily designed for one-shot prefill and do not translate efficiently to chunked prefill: block-sparse kernels lose efficiency when the query length is limited by the chunk size, while fine-grained pattern search becomes costly when repeated over the accumulated KV cache at every chunk. QUOKA, a recent method that directly targets chunked prefill, avoids sparse-kernel overhead but relies on query-subsampled, token-level KV selection, which can miss query-specific KV entries and introduce explicit KV-copy overhead. To address these limitations, we propose CompactAttention, a chunked-prefill attention mechanism based on Block-Union KV Selection. CompactAttention treats 2D block-sparse masks as KV-selection signals rather than direct sparse-kernel execution plans, and converts them into GQA-aware per-group KV block tables through Q-block union and intra-group union. This construction produces the minimal block tables that preserve all KV blocks selected by the input masks under paged execution constraints, enabling selected KV blocks to be accessed in place without explicit KV compaction. On LLaMA-3.1-8B-Instruct, CompactAttention maintains accuracy close to dense attention on the RULER benchmark while delivering up to 2.72times attention speedup at 128K context length under chunked prefill.

KV-cache memory is a major bottleneck in real-world LLM serving, where systems must simultaneously support latency-sensitive small-batch requests and high-throughput concurrent workloads. Although many KV-cache compression methods improve offline accuracy or compression ratio, they often violate practical serving constraints such as paged memory layouts, regular memory access, and fused attention execution, limiting their effectiveness in deployment. In this work, we identify the minimal set of 4-bit KV-cache quantization methods that remain viable under these constraints. Our central finding is that a simple design--token-wise INT4 quantization with block-diagonal Hadamard rotation--consistently achieves the best accuracy-efficiency trade-off. Across multiple models and benchmarks, this approach recovers nearly all of the accuracy lost by naive INT4, while more complex methods such as vector quantization and Hessian-aware quantization provide only marginal additional gains once serving compatibility is taken into account. To make this practical, we implement a fused rotation-quantization kernel that integrates directly into paged KV-cache layouts and introduces zero measurable end-to-end overhead, matching plain INT4 throughput across concurrency levels. Our results show that effective KV-cache compression is fundamentally a systems co-design problem: under real serving constraints, lightweight block-diagonal Hadamard rotation is a viable method that delivers near-lossless accuracy without sacrificing serving efficiency.

Long-context LLM inference is bottlenecked by the quadratic attention complexity and linear KV cache growth. Prior approaches mitigate this via post-hoc selection or eviction but overlook the root inefficiency: indiscriminate writing to memory. In this paper, we formalize KV cache management as a causal system of three primitives: KV Admission, Selection, and Eviction. We instantiate KV Admission via Write-Gated KV (WG-KV), a lightweight mechanism that learns to predict token utility before cache entry. By filtering out low-utility states early to maintain a compact global cache alongside a sliding local cache, WG-KV reduces memory usage by 46-68% and delivers 3.03-3.70x prefill and 1.85-2.56x decode speedups on Llama and Qwen models, while maintaining compatibility with FlashAttention and Paged-KV systems. These results demonstrate that learning what to write is a principled and practical recipe for efficient long-context inference. Code is available at https://github.com/EMCLab-Sinica/WG-KV.

Long-context LLMs demand accurate inference at low latency, yet decoding becomes primarily constrained by KV cache as context grows. Prior pruning methods are largely context-agnostic: their token selection ignores step-wise relevance and local semantics, which undermines quality. Moreover, their irregular accesses and selection overheads yield only limited wall-clock speedups. To address this, we propose CHESS, an algorithm-system co-design KV-cache management system. Algorithmically, CHESS introduces a context-aware, hierarchical selection policy that dynamically reconstructs a coherent context for the current decoding. System-wise, coarse granularity selection eliminates expensive data movement, fully realizing practical acceleration from theoretical sparsity. Extensive evaluations demonstrate that CHESS surpasses Full-KV quality using only 1\% of the KV cache, delivers low-latency stable inference with up to 4.56times higher throughput, and consistently outperforms other strong baselines. Code is available at https://anonymous.4open.science/r/CHESS-9958/{https://anonymous.4open.science/r/CHESS/}.

Efficient Key-Value (KV) cache management is essential for processing long text sequences in large language models (LLMs), where memory constraints often limit performance. Conventional KV eviction strategies, such as top-k selection based on attention scores, depend on static heuristics that fail to capture the evolving implicit dependencies among tokens during inference. To overcome this, we propose GraphKV, a graph-based framework that redefines token selection for KV cache compression. In GraphKV, tokens are modeled as nodes with importance scores, and edges represent their similarity relationships. Through a decay-signal-propagation mechanism, token importance is dynamically updated by propagating information across the graph, enabling adaptive retention of the most contextually significant tokens. GraphKV can be seamlessly utilized in existing KV cache eviction methods such as SnapKV and PyramidKV in a plug-and-play manner. Codes will be released on Github.

While large language models (LLMs) excel at handling long-context sequences, they require substantial prefill computation and key-value (KV) cache, which can heavily burden computational efficiency and memory usage in both prefill and decoding stages. Recent works that compress KV caches with prefill acceleration reduce this cost but inadvertently tie the prefill compute reduction to the decoding KV budget. This coupling arises from overlooking the layer-dependent variation of critical context, often leading to accuracy degradation. To address this issue, we introduce FastKV, a KV cache compression framework designed to reduce latency in both prefill and decoding by leveraging the stabilization of token importance in later layers. FastKV performs full-context computation until a Token-Selective Propagation (TSP) layer, which forwards only the most informative tokens to subsequent layers. From these propagated tokens, FastKV independently selects salient KV entries for caching, thereby decoupling KV budget from the prefill compute reduction based on the TSP decision. This independent control of the TSP rate and KV retention rate enables flexible optimization of efficiency and accuracy. Experimental results show that FastKV achieves speedups of up to 1.82times in prefill and 2.87times in decoding compared to the full-context baseline, while matching the accuracy of the baselines that only accelerate the decoding stage. Our code is available at https://github.com/dongwonjo/FastKV.

As large language models (LLMs) process increasing context windows, the memory usage of KV cache has become a critical bottleneck during inference. The mainstream KV compression methods, including KV pruning and KV quantization, primarily focus on either token or precision dimension and seldom explore the efficiency of their combination. In this paper, we comprehensively investigate the token-precision trade-off in KV cache compression. Experiments demonstrate that storing more tokens in the KV cache with lower precision, i.e., quantized pruning, can significantly enhance the long-context performance of LLMs. Furthermore, in-depth analysis regarding token-precision trade-off from a series of key aspects exhibit that, quantized pruning achieves substantial improvements in retrieval-related tasks and consistently performs well across varying input lengths. Moreover, quantized pruning demonstrates notable stability across different KV pruning methods, quantization strategies, and model scales. These findings provide valuable insights into the token-precision trade-off in KV cache compression. We plan to release our code in the near future.

Large language model (LLM) based agentic workflows have become a popular paradigm for coordinating multiple specialized agents to solve complex tasks. To improve serving efficiency, existing LLM systems employ prefix caching to reuse key-value (KV) tensors corresponding to agents' fixed prompts, thereby avoiding redundant computation across repeated invocations. However, current systems typically evict KV caches using a Least Recently Used (LRU) policy, which fails to anticipate future agent usage and often discards KV caches shortly before their reuse. This leads to frequent cache misses and substantial recomputation or swapping overhead. We present KVFlow, a workflow-aware KV cache management framework tailored for agentic workloads. KVFlow abstracts the agent execution schedule as an Agent Step Graph and assigns each agent a steps-to-execution value that estimates its temporal proximity to future activation. These values guide a fine-grained eviction policy at the KV node level, allowing KVFlow to preserve entries likely to be reused and efficiently manage shared prefixes in tree-structured caches. Moreover, KVFlow introduces a fully overlapped KV prefetching mechanism, which proactively loads required tensors from CPU to GPU in background threads for agents scheduled in the next step, thereby avoiding cache miss stalls during generation. Compared to SGLang with hierarchical radix cache, KVFlow achieves up to 1.83times speedup for single workflows with large prompts, and up to 2.19times speedup for scenarios with many concurrent workflows.

Near-term quantum workloads are shaped by coupled compilation and execution choices: qubit layout, routing, basis translation, gate suppression, measurement mitigation, shot budget, and artifact reproducibility. This paper analyzes QBalance, a Python workflow library for dataset-level selection among quantum compilation, noise-suppression, and error-mitigation strategies built on the Qiskit ecosystem. The contribution is formulated as a finite multi-objective strategy-selection problem over circuits, backends, and transformation policies. The manuscript derives the implemented weighted objective, non-dominated selection rule, survival-product error proxy, Bayesian linear candidate-ordering surrogate, and distributional diagnostics. It also positions the system relative to established work on Qiskit pass-manager compilation, SABRE-style routing, randomized compiling, dynamical decoupling, zero-noise extrapolation, matrix-free measurement mitigation, circuit cutting, and Thompson sampling. The analysis shows that QBalance provides a reproducible orchestration and artifact model for quantum workflow studies. It also establishes precise limitations: the current bandit mechanism orders candidates but does not reduce the number of candidate evaluations, the custom layout heuristic is greedy and only partially topology-aware, the implemented ZNE helper is parity-centered, and the cutting integration is a hook rather than a full reconstruction pipeline.

With the advancements in long-context inference capabilities of large language models (LLMs), the KV cache has become one of the foundational components. However, its substantial GPU memory consumption makes KV cache compression a key technique for enabling efficient LLM inference in industrial scenarios. While recent studies have focused on optimizing the memory occupied by the KV cache, they overlook two critical factors: preserving semantic coherence and considering task-specific characteristic during compression. To address these limitations, we propose a novel task-adaptive KV cache window selection method, WindowKV. WindowKV dynamically selects local semantic windows consisting of consecutive tokens, according to task-specific characteristics, ensuring the retained KV cache captures continuous, essential context. Additionally, we introduce an intra-group layer KV cache indices sharing strategy to reduce computational overhead, achieving a balance between performance and efficiency. We rigorously evaluate WindowKV on the LongBench benchmark, and the results demonstrate that it maintains a performance comparable to full KV cache retention while using only 12% of the original KV cache, significantly reducing memory requirements. Furthermore, our method also achieves state-of-the-art results in the Needle-in-a-Haystack evaluation, highlighting its effectiveness and robustness.

KV-Cache compression methods generally sample a KV-Cache of effectual tokens or quantize it into lower bits. However, these methods cannot exploit the redundancy of the hidden dimension of KV tensors. This paper investigates a unique hidden dimension approach called Palu, a novel KV-Cache compression framework that utilizes low-rank projection. Palu decomposes the linear layers into low-rank matrices, caches the smaller intermediate states, and reconstructs the full keys and values on the fly. To improve accuracy, compression rate, and efficiency, Palu further encompasses (1) a medium-grained low-rank decomposition scheme, (2) an efficient rank search algorithm, (3) a low-rank-aware quantization algorithm, and (4) matrix fusion with optimized GPU kernels. Our extensive experiments with popular LLMs show that Palu can compress KV-Cache by more than 91.25% while maintaining a significantly better accuracy (up to 1.19 lower perplexity) than state-of-the-art KV-Cache quantization methods at a similar or even higher memory usage. When compressing KV-Cache for 50%, Palu delivers up to 1.61x end-to-end speedup for the attention module. Our code is publicly available at https://github.com/shadowpa0327/Palu.

Recent work on KV cache quantization, culminating in TurboQuant, has approached the Shannon entropy limit for per-vector compression of transformer key-value caches. We observe that this limit applies to a strictly weaker problem than the one that actually matters: compressing the KV cache as a sequence. The tokens stored in a KV cache are not arbitrary floating-point data -- they are samples from the exact formal language the model was trained on, and the model is by construction a near-optimal predictor of that language. We introduce sequential KV compression, a two-layer architecture that exploits this structure. The first layer, probabilistic prefix deduplication, identifies semantically equivalent shared prefixes across sessions using the trie metric d_T(s, s') = -log_2 P_M(s ^ s') from Probabilistic Language Tries (PLTs). The second layer, predictive delta coding, stores only the residual of each new KV vector from the model's own prediction of it, achieving a per-token entropy bound of H(KV_{i+1} | KV_{<=i}) <= H(token_{i+1} | token_{<=i}). We prove that at typical language model perplexity -- approximately 10-20 for fluent English text -- this bound is 3.3-4.3 bits on average per token position, compared to TurboQuant's 3 bits per vector component (with typical attention heads having 64-128 components). The theoretical compression ratio over TurboQuant is approximately 914,000x at the Shannon limit. Even at 1000x above the entropy floor -- a deliberately pessimistic worst-case overhead, two orders of magnitude above the 2-5x typical of practical source coders -- the ratio remains approximately 914x over TurboQuant, with compression improving rather than degrading as context length grows. The two layers are orthogonal and compose with existing per-vector quantization methods including TurboQuant.

Efficiently serving large language models (LLMs) requires batching many requests together to reduce the cost per request. Yet, the key-value (KV) cache, which stores attention keys and values to avoid re-computations, significantly increases memory demands and becomes the new bottleneck in speed and memory usage. This memory demand increases with larger batch sizes and longer context lengths. Additionally, the inference speed is limited by the size of KV cache, as the GPU's SRAM must load the entire KV cache from the main GPU memory for each token generated, causing the computational core to be idle during this process. A straightforward and effective solution to reduce KV cache size is quantization, which decreases the total bytes taken by KV cache. However, there is a lack of in-depth studies that explore the element distribution of KV cache to understand the hardness and limitation of KV cache quantization. To fill the gap, we conducted a comprehensive study on the element distribution in KV cache of popular LLMs. Our findings indicate that the key cache should be quantized per-channel, i.e., group elements along the channel dimension and quantize them together. In contrast, the value cache should be quantized per-token. From this analysis, we developed a tuning-free 2bit KV cache quantization algorithm, named KIVI. With the hardware-friendly implementation, KIVI can enable Llama (Llama-2), Falcon, and Mistral models to maintain almost the same quality while using 2.6times less peak memory usage (including the model weight). This reduction in memory usage enables up to 4times larger batch size, bringing 2.35times sim 3.47times throughput on real LLM inference workload. The source code is available at https://github.com/jy-yuan/KIVI.

The increasing size of the Key-Value (KV) cache during the Large Language Models long-context inference is the main obstacle for its balance between the deployment cost and task accuracy. To reduce the KV cache size in such scenarios, most previous efforts leveraged on the attention weight to evict non-critical cache tokens. But there is a trade-off in those methods, they usually require major modifiation of the inference infrastructure and significant computation overhead. Base on the fact that the Large Lanuage models are autoregresssive models, we propose {\it LagKV}, a KV allocation strategy only relying on straight forward comparison among KV themself. It is a totally attention free method which offers easy integration to the main stream inference platform and comparable performance comparing to other complicated KV compression methods. Results on LongBench and PasskeyRetrieval show that, our approach achieves nearly zero loss when the ratio is 2times and approx 90% of the original model performance for 8times. Especially in the 64-digit passkey retrieval task, our mehod outperforms the attention weight based method H_2O over 60% with same compression ratios. Our code is available at https://github.com/AI-Lab-China-Merchants-Bank/LagKV.

Key-Value (KV) cache has become a bottleneck of LLMs for long-context generation. Despite the numerous efforts in this area, the optimization for the decoding phase is generally ignored. However, we believe such optimization is crucial, especially for long-output generation tasks based on the following two observations: (i) Excessive compression during the prefill phase, which requires specific full context impairs the comprehension of the reasoning task; (ii) Deviation of heavy hitters occurs in the reasoning tasks with long outputs. Therefore, SCOPE, a simple yet efficient framework that separately performs KV cache optimization during the prefill and decoding phases, is introduced. Specifically, the KV cache during the prefill phase is preserved to maintain the essential information, while a novel strategy based on sliding is proposed to select essential heavy hitters for the decoding phase. Memory usage and memory transfer are further optimized using adaptive and discontinuous strategies. Extensive experiments on LongGenBench show the effectiveness and generalization of SCOPE and its compatibility as a plug-in to other prefill-only KV compression methods.

Key-Value (KV) cache plays a crucial role in accelerating inference in large language models (LLMs) by storing intermediate attention states and avoiding redundant computation during autoregressive generation. However, its memory footprint scales linearly with sequence length, often leading to severe memory bottlenecks on resource-constrained hardware. Prior work has explored offloading KV cache to the CPU while retaining only a subset on the GPU, but these approaches often rely on imprecise token selection and suffer performance degradation in long-generation tasks such as chain-of-thought reasoning. In this paper, we propose a novel KV cache management strategy, IceCache, which integrates semantic token clustering with PagedAttention. By organizing semantically related tokens into contiguous memory regions managed by a hierarchical, dynamically updatable data structure, our method enables more efficient token selection and better utilization of memory bandwidth during CPU-GPU transfers. Experimental results on LongBench show that, with a 256-token budget, IceCache maintains 99% of the original accuracy achieved by the full KV cache model. Moreover, compared to other offloading-based methods, IceCache attains competitive or even superior latency and accuracy while using only 25% of the KV cache token budget, demonstrating its effectiveness in long-sequence scenarios. The code is available on our project website at https://yuzhenmao.github.io/IceCache/.

Optimizing the Key-Value (KV) cache of the Large Language Model (LLM) has been considered critical to saving the cost of inference. Most of the existing KV-cache compression algorithms attempted to sparsify the sequence of tokens by taking advantage of the different importance of tokens. In this work, we found that by identifying the importance of attention layers, we could optimize the KV-cache jointly from two dimensions. Based on our observations regarding layer-wise importance in inference, we propose SqueezeAttention to precisely optimize the allocation of KV-cache budget among layers on-the-fly and then incorporate three representative token sparsification algorithms to compress the KV-cache for each layer with its very own budget. By optimizing the KV-cache from both sequence's and layer's dimensions, SqueezeAttention achieves around 30% to 70% of the memory reductions and up to 2.2 times of throughput improvements in a wide range of LLMs and benchmarks. The code is available at https://github.com/hetailang/SqueezeAttention.

LLM-based workflows compose specialized agents to execute complex tasks, and these agents usually share substantial context, allowing KV-Cache reuse to save computation. Existing approaches either manage KV-Cache at agent level and fail to exploit the reuse opportunities within workflows, or manage cache at the workflow level but assume that each workflow calls a static sequence of agents. However, practical workflows are typically dynamic, where the sequence of invoked agents and thus induced cache reuse opportunities depend on the context of each task. To serve such dynamic workflows efficiently, we build a system dubbed PBKV (Prediction-Based KV-Cache Management). For each workflow, PBKV predicts the agent invocations in several future steps by fusing the guidance from historical workflows and context of the target workflow. Based on the predictions, PBKV estimates the reuse potential of cache entries and keeps the high-potential entries in GPU memory. To be robust to prediction errors, PBKV utilizes the predictions conservatively during both cache eviction and prefetching. Experiments on three workflow benchmarks show that PBKV achieves up to 1.85times speedup over LRU on dynamic workflows, and up to 1.26times speedup over the SOTA baseline KVFlow on the static workflow.

We compare two strategies for compressing the KV cache in transformer inference: rank reduction (discard dimensions) and quantization (keep all dimensions, reduce precision). At matched storage budgets across five models (124M-14B, MHA and GQA), we find that quantization consistently outperforms rank reduction by 4-364 PPL depending on model and compression level. The gap persists even when rank reduction is combined with quantization in hybrid baselines, and it grows with GQA aggressiveness. On LAMBADA, INT4 matches FP16 accuracy (+0.23 PPL on Mistral 7B, +0.58 on GPT-2) while rank-32 at identical storage collapses to 0.4%. We trace this gap to a structural asymmetry: under softmax attention routing, removing a dimension can flip which token is attended (a discrete failure), while quantization noise is bounded and typically preserves score ordering. We formalize this via a perturbation result showing projection damage exceeds quantization damage by 3 x 2^(2b) per direction under the softmax Fisher metric. A basis ablation confirms the finding is basis-independent (spread <0.4 PPL), establishing that the advantage comes from preserving dimensions, not from a better coordinate system. Joint K+V INT4 quantization achieves 75% total KV reduction at only +0.18 PPL on Mistral 7B.

Private large language model (LLM) inference based on secure multi-party computation (MPC) offers cryptographically-secure protection for both user prompt and proprietary model weights. However, it suffers from large latency overhead especially for long input sequences. While key-value (KV) cache eviction algorithms have been proposed to reduce the computation and memory cost for plaintext inference, they are not designed for MPC and cannot benefit private inference easily. In this paper, we propose an accurate and MPC-friendly KV cache eviction framework, dubbed MPCache. MPCache is built on the observation that historical tokens in a long sequence may have different effects on the downstream decoding. Hence, MPCache combines a look-once static eviction algorithm to discard unimportant tokens and a query-aware dynamic selection algorithm to further select a small subset of tokens for attention computation. As existing dynamic selection algorithms incur too much latency, we propose a series of optimizations to drastically reduce the KV cache selection overhead, including MPC-friendly similarity approximation, hierarchical KV cache clustering, and cross-layer index sharing strategy. With extensive experiments, we demonstrate that MPCache consistently outperforms prior-art KV cache eviction baselines across different LLM generation tasks and achieves 1.8~2.01x and 3.39~8.37x decoding latency and communication reduction on different sequence lengths, respectively.

Many computational factors limit broader deployment of large language models. In this paper, we focus on a memory bottleneck imposed by the key-value (KV) cache, a computational shortcut that requires storing previous KV pairs during decoding. While existing KV cache methods approach this problem by pruning or evicting large swaths of relatively less important KV pairs to dramatically reduce the memory footprint of the cache, they can have limited success in tasks that require recollecting a majority of previous tokens. To alleviate this issue, we propose LESS, a simple integration of a (nearly free) constant sized cache with eviction-based cache methods, such that all tokens can be queried at later decoding steps. Its ability to retain information throughout time shows merit on a variety of tasks where we demonstrate LESS can help reduce the performance gap from caching everything, sometimes even matching it, all while being efficient.

Autoregressive next token prediction language models offer powerful capabilities but face significant challenges in practical deployment due to the high computational and memory costs of inference, particularly during the decoding stage. We introduce Set Block Decoding (SBD), a simple and flexible paradigm that accelerates generation by integrating standard next token prediction (NTP) and masked token prediction (MATP) within a single architecture. SBD allows the model to sample multiple, not necessarily consecutive, future tokens in parallel, a key distinction from previous acceleration methods. This flexibility allows the use of advanced solvers from the discrete diffusion literature, offering significant speedups without sacrificing accuracy. SBD requires no architectural changes or extra training hyperparameters, maintains compatibility with exact KV-caching, and can be implemented by fine-tuning existing next token prediction models. By fine-tuning Llama-3.1 8B and Qwen-3 8B, we demonstrate that SBD enables a 3-5x reduction in the number of forward passes required for generation while achieving same performance as equivalent NTP training.

Serving numerous users and requests concurrently requires good fairness in Large Language Models (LLMs) serving system. This ensures that, at the same cost, the system can meet the Service Level Objectives (SLOs) of more users , such as time to first token (TTFT) and time between tokens (TBT), rather than allowing a few users to experience performance far exceeding the SLOs. To achieve better fairness, the preemption-based scheduling policy dynamically adjusts the priority of each request to maintain balance during runtime. However, existing systems tend to overly prioritize throughput, overlooking the overhead caused by preemption-induced context switching, which is crucial for maintaining fairness through priority adjustments. In this work, we identify three main challenges that result in this overhead. 1) Inadequate I/O utilization. 2) GPU idleness. 3) Unnecessary I/O transmission during multi-turn conversations. Our key insight is that the block-based KV cache memory policy in existing systems, while achieving near-zero memory waste, leads to discontinuity and insufficient granularity in the KV cache memory. To respond, we introduce FastSwitch, a fairness-aware serving system that not only aligns with existing KV cache memory allocation policy but also mitigates context switching overhead. Our evaluation shows that FastSwitch outperforms the state-of-the-art LLM serving system vLLM with speedups of 1.4-11.2x across different tail TTFT and TBT.

Key-value (KV) caching has emerged as a crucial optimization technique for accelerating inference in large language models (LLMs). By allowing the attention operation to scale linearly rather than quadratically with the total sequence length, KV caching significantly enhances generation throughput. However, due to large context lengths in the modern LLMs, the memory footprint of the KV is a huge bottleneck for model deployment directly impacting the model's batch size, hindering its ability to deliver high-throughput. Existing research addresses this challenge using several techniques, such as discarding low-attention tokens, quantization, and matrix approximation which typically lead to a negative impact on the model accuracy. In this paper, We propose KVCrush technology which can be combined with many KV compression technologies to improve the model accuracy at a much smaller memory. KVCrush provides an alternate representation scheme for key-value states, along with a low-overhead token pruning algorithm that accounts for the token distribution in the KV cache, which in turn allows for a a smaller footprint while maintaining the accuracy of the model. Based on our results, KVCrush reduces LongBench KV Cache size by 4x with less than 1% accuracy drop and achieves state-of-the-art average accuracy with minimal overhead, incurring less than 0.5% total inference latency. KVCrush not only outperforms the accuracy of state-of-the-art importance-based token retention schemes but is also compatible with typical practical LLM deployments using KV cache paging schemes such as vLLM and mixed precision quantization.

Large Language Models (LLMs) have been widely adopted to process long-context tasks. However, the large memory overhead of the key-value (KV) cache poses significant challenges in long-context scenarios. Existing training-free KV cache compression methods typically focus on quantization and token pruning, which have compression limits, and excessive sparsity can lead to severe performance degradation. Other methods design new architectures with less KV overhead but require significant training overhead. To address the above two drawbacks, we further explore the redundancy in the channel dimension and apply an architecture-level design with minor training costs. Therefore, we introduce CSKV, a training-efficient Channel Shrinking technique for KV cache compression: (1) We first analyze the singular value distribution of the KV cache, revealing significant redundancy and compression potential along the channel dimension. Based on this observation, we propose using low-rank decomposition for key and value layers and storing the low-dimension features. (2) To preserve model performance, we introduce a bi-branch KV cache, including a window-based full-precision KV cache and a low-precision compressed KV cache. (3) To reduce the training costs, we minimize the layer-wise reconstruction loss for the compressed KV cache instead of retraining the entire LLMs. Extensive experiments show that CSKV can reduce the memory overhead of the KV cache by 80% while maintaining the model's long-context capability. Moreover, we show that our method can be seamlessly combined with quantization to further reduce the memory overhead, achieving a compression ratio of up to 95%.

The demand for inference on extremely large scale LLMs has seen enormous growth in the recent months. It made evident the colossal shortage of dedicated hardware capable of efficient and fast processing of the involved compute and memory movement. The problem is aggravated by the exploding raise in the lengths of the sequences being processed, since those require efficient on-chip storage of the KV-cache of size proportional to the sequence length. To make the required compute feasible and fit the involved data into available memory, numerous quantization techniques have been proposed that allow accurate quantization for both weights and activations. One of the main recent breakthroughs in this direction was introduction of the family of Block Floating Point (BFP) formats characterized by a block of mantissas with a shared scale factor. These enable memory- power-, and compute- efficient hardware support of the tensor operations and provide extremely good quantization accuracy. The main issues preventing widespread application of block formats is caused by the presence of outliers in weights and activations since those affect the accuracy of the other values in the same block. In this paper, we focus on the most critical problem of limited KV-cache storage. We propose a novel approach enabling usage of low precision BFP formats without compromising the resulting model accuracy. We exploit the common channel-wise patterns exhibited by the outliers to rearrange them in such a way, that their quantization quality is significantly improved. The methodology yields 2x savings in the memory footprint without significant degradation of the model's accuracy. Importantly, the rearrangement of channels happens at the compile time and thus has no impact on the inference latency.

KV cache stores key and value states from previous tokens to avoid re-computation, yet it demands substantial storage space, especially for long sequences. Adaptive KV cache compression seeks to discern the saliency of tokens, preserving vital information while aggressively compressing those of less importance. However, previous methods of this approach exhibit significant performance degradation at high compression ratios due to inaccuracies in identifying salient tokens. In this paper, we present ZipCache, an accurate and efficient KV cache quantization method for LLMs. First, we construct a strong baseline for quantizing KV cache. Through the proposed channel-separable tokenwise quantization scheme, the memory overhead of quantization parameters are substantially reduced compared to fine-grained groupwise quantization. To enhance the compression ratio, we propose normalized attention score as an effective metric for identifying salient tokens by considering the lower triangle characteristics of the attention matrix. Moreover, we develop an efficient approximation method that decouples the saliency metric from full attention scores, enabling compatibility with fast attention implementations like FlashAttention. Extensive experiments demonstrate that ZipCache achieves superior compression ratios, fast generation speed and minimal performance losses compared with previous KV cache compression methods. For instance, when evaluating Mistral-7B model on GSM8k dataset, ZipCache is capable of compressing the KV cache by 4.98times, with only a 0.38% drop in accuracy. In terms of efficiency, ZipCache also showcases a 37.3% reduction in prefill-phase latency, a 56.9% reduction in decoding-phase latency, and a 19.8% reduction in GPU memory usage when evaluating LLaMA3-8B model with a input length of 4096.

Efficient KV cache management in LLMs is crucial for long-context tasks like RAG and summarization. Existing KV cache compression methods enforce a fixed pattern, neglecting task-specific characteristics and reducing the retention of essential information. However, we observe distinct activation patterns across layers in various tasks, highlighting the need for adaptive strategies tailored to each task's unique demands. Based on this insight, we propose DynamicKV, a method that dynamically optimizes token retention by adjusting the number of tokens retained at each layer to adapt to the specific task. DynamicKV establishes global and per-layer maximum KV cache budgets, temporarily retaining the maximum budget for the current layer, and periodically updating the KV cache sizes of all preceding layers during inference. Our method retains only 1.7% of the KV cache size while achieving ~85% of the Full KV cache performance on LongBench. Notably, even under extreme compression (0.9%), DynamicKV surpasses state-of-the-art (SOTA) methods by 11% in the Needle-in-a-Haystack test using Mistral-7B-Instruct-v0.2. The code will be released.

As large language models (LLMs) continue to advance, the demand for higher quality and faster processing of long contexts across various applications is growing. KV cache is widely adopted as it stores previously generated key and value tokens, effectively reducing redundant computations during inference. However, as memory overhead becomes a significant concern, efficient compression of KV cache has gained increasing attention. Most existing methods perform compression from two perspectives: identifying important tokens and designing compression strategies. However, these approaches often produce biased distributions of important tokens due to the influence of accumulated attention scores or positional encoding. Furthermore, they overlook the sparsity and redundancy across different heads, which leads to difficulties in preserving the most effective information at the head level. To this end, we propose EMS to overcome these limitations, while achieving better KV cache compression under extreme compression ratios. Specifically, we introduce a Global-Local score that combines accumulated attention scores from both global and local KV tokens to better identify the token importance. For the compression strategy, we design an adaptive and unified Evict-then-Merge framework that accounts for the sparsity and redundancy of KV tokens across different heads. Additionally, we implement the head-wise parallel compression through a zero-class mechanism to enhance efficiency. Extensive experiments demonstrate our SOTA performance even under extreme compression ratios. EMS consistently achieves the lowest perplexity, improves scores by over 1.28 points across four LLMs on LongBench under a 256 cache budget, and preserves 95% retrieval accuracy with a cache budget less than 2% of the context length in the Needle-in-a-Haystack task.

Large language models (LLMs) often incorporate multiple text chunks in their inputs to provide the necessary contexts. To speed up the prefill of the long LLM inputs, one can pre-compute the KV cache of a text and re-use the KV cache when the context is reused as the prefix of another LLM input. However, the reused text chunks are not always the input prefix, and when they are not, their precomputed KV caches cannot be directly used since they ignore the text's cross-attention with the preceding text in the LLM input. Thus, the benefits of reusing KV caches remain largely unrealized. This paper tackles just one question: when an LLM input contains multiple text chunks, how to quickly combine their precomputed KV caches in order to achieve the same generation quality as the expensive full prefill (i.e., without reusing KV cache)? We present CacheBlend, a scheme that reuses the pre-computed KV caches, regardless prefix or not, and selectively recomputes the KV values of a small subset of tokens to partially update each reused KV cache. In the meantime,the small extra delay for recomputing some tokens can be pipelined with the retrieval of KV caches within the same job,allowing CacheBlend to store KV caches in slower devices with more storage capacity while retrieving them without increasing the inference delay. By comparing CacheBlend with the state-of-the-art KV cache reusing schemes on three open-source LLMs of various sizes and four popular benchmark datasets of different tasks, we show that CacheBlend reduces time-to-first-token (TTFT) by 2.2-3.3X and increases the inference throughput by 2.8-5X, compared with full KV recompute, without compromising generation quality or incurring more storage cost.

Efficient inference with Large Language Models (LLMs) increasingly relies on Key-Value (KV) caches to store previously computed key and value vectors at each layer. These caches are essential to minimize redundant computation during autoregressive token generation, lowering computational complexity from quadratic to linear. However, the growth of KV caches has posed significant system-level challenges, particularly as model sizes increase, context lengths grow, and concurrent requests compete for limited memory resources. Even though several recent frameworks for KV cache management have emerged, their comparative trade-offs in memory consumption and inference performance have not been fully understood, especially under varying request sizes and model configurations. In this work, we conduct an empirical study of three state-of-the-art KV cache management frameworks: vLLM, InfiniGen, and H2O. These frameworks employ techniques such as tensor offloading, token eviction heuristics, and speculative scheduling to balance memory usage and performance. We evaluate their performance in terms of a range of metrics such as latency, throughput, and memory usage across a spectrum of key parameters including request rates, model sizes, and sparsity levels. Our results pinpoint the conditions for each framework to perform the best, revealing the most suitable selection and configuration of KV cache strategies under memory and performance constraints.

The key-value (KV) cache accelerates LLMs decoding by storing KV tensors from previously generated tokens. It reduces redundant computation at the cost of increased memory usage. To mitigate this overhead, existing approaches compress KV tensors into lower-bit representations; however, quantization errors can accumulate as more tokens are generated, potentially resulting in undesired outputs. In this paper, we introduce SQuat (Subspace-orthogonal KV cache quantization). It first constructs a subspace spanned by query tensors to capture the most critical task-related information. During key tensor quantization, it enforces that the difference between the (de)quantized and original keys remains orthogonal to this subspace, minimizing the impact of quantization errors on the attention mechanism's outputs. SQuat requires no model fine-tuning, no additional calibration dataset for offline learning, and is grounded in a theoretical framework we develop. Through numerical experiments, we show that our method reduces peak memory by 2.17 to 2.82, improves throughput by 2.45 to 3.60, and achieves more favorable benchmark scores than existing KV cache quantization algorithms.

Recently, large vision-language models (LVLMs) have rapidly gained popularity for their strong generation and reasoning capabilities given diverse multimodal inputs. However, these models incur significant computational and memory overhead during inference, which greatly hinders the efficient deployment in practical scenarios. The extensive key-value (KV) cache, necessitated by the lengthy input and output sequences, notably contributes to the high inference cost. Based on this, recent works have investigated ways to reduce the KV cache size for higher efficiency. Although effective, they generally overlook the distinct importance distributions of KV vectors across layers and maintain the same cache size for each layer during the next token prediction. This results in the significant contextual information loss for certain layers, leading to notable performance decline. To address this, we present PrefixKV. It reframes the challenge of determining KV cache sizes for all layers into the task of searching for the optimal global prefix configuration. With an adaptive layer-wise KV retention recipe based on binary search, the maximum contextual information can thus be preserved in each layer, facilitating the generation. Extensive experiments demonstrate that our method achieves the state-of-the-art performance compared with others. It exhibits superior inference efficiency and generation quality trade-offs, showing promising potential for practical applications. Code is available at https://github.com/THU-MIG/PrefixKV.

Block coordinate descent (BCD) methods are widely used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block selection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can significantly improve the progress made by each BCD iteration. We (i) propose new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule; (ii) explore practical issues like how to implement the new rules when using "variable" blocks; (iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for problems with sparse dependencies between variables; and (iv) consider optimal active manifold identification, which leads to bounds on the "active-set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numerical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization.

k-Clustering in R^d (e.g., k-median and k-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality n, it remains open to find sublinear-time quantum algorithms. We give quantum algorithms that find coresets for k-clustering in R^d with O(nkd^{3/2}) query complexity. Our coreset reduces the input size from n to poly(kepsilon^{-1}d), so that existing alpha-approximation algorithms for clustering can run on top of it and yield (1 + epsilon)alpha-approximation. This eventually yields a quadratic speedup for various k-clustering approximation algorithms. We complement our algorithm with a nearly matching lower bound, that any quantum algorithm must make Omega(nk) queries in order to achieve even O(1)-approximation for k-clustering.

We compress KV cache entries by quantizing angles in the Fast Walsh-Hadamard domain, where a random diagonal rotation makes consecutive element pairs approximately uniformly distributed on the unit circle. We extend this angular quantizer with per-layer early-boost, which independently configures K and V codebook sizes at each layer, allocating higher precision to a model-specific subset of critical layers. Across seven models (1B to 7B parameters), per-layer early-boost achieves lossless compression on four models and near-lossless quality on six of seven, at 3.28 to 3.67 angle bits per element. Asymmetric norm quantization (8-bit for keys, 4-bit log-space for values) yields 6.56 total bits per element on Mistral-7B with perplexity degradation of +0.0014 and no calibration data. A layer-group sensitivity analysis reveals model-specific bottleneck patterns, including K-dominated versus V-dominated layers and negative-transfer layers where increased precision degrades quality.

We present Key-Value Means ("KVM"), a novel block-recurrence for attention that can accommodate either fixed-size or growing state. Equipping a strong transformer baseline with fixed-size KVM attention layers yields a strong O(N) chunked RNN, while adding only an insignificant number of new parameters. We train a transformer with a growable KVM cache and show it performs competitively on long-context tests with only subquadratic prefill time and sublinear state growth. KVM is implementable with standard operations and without custom kernels, and supports chunk-wise parallelizable training and prefill. It provides many of the benefits of both traditional transformers (expandable context memory, chunk-wise parallelizable training and prefill) and linear RNNs in a single unified package. It can be used on every layer, saving KV-cache memory, and allowing a continuous range of choices of prefill time complexity between O(N) and O(N^2). It can also be implemented in a hybrid solution in tandem with LRNN layers in place of traditional attention, to supplement the LRNN with improved sublinear memory growth context length usage and long context decoding. We release our code at https://github.com/recursal/KVM-paper and trained models at https://huggingface.co/collections/recursal/key-value-means under the Apache 2.0 license.

Sparse sketches such as the sparse Johnson-Lindenstrauss transform are a core primitive in randomized numerical linear algebra because they leverage random sparsity to reduce the arithmetic cost of sketching, while still offering strong approximation guarantees. Their random sparsity, however, is at odds with efficient implementations on modern GPUs, since it leads to irregular memory access patterns that degrade memory bandwidth utilization. Motivated by this tension, we pursue a sketch-kernel co-design approach: we design a new family of sparse sketches, BlockPerm-SJLT, whose sparsity structure is chosen to enable FlashSketch, a corresponding optimized CUDA kernel that implements these sketches efficiently. The design of BlockPerm-SJLT introduces a tunable parameter that explicitly trades off the tension between GPU-efficiency and sketching robustness. We provide theoretical guarantees for BlockPerm-SJLT under the oblivious subspace embedding (OSE) framework, and also analyze the effect of the tunable parameter on sketching quality. We empirically evaluate FlashSketch on standard RandNLA benchmarks, as well as an end-to-end ML data attribution pipeline called GraSS. FlashSketch pushes the Pareto frontier of sketching quality versus speed, across a range of regimes and tasks, and achieves a global geomean speedup of roughly 1.7x over the prior state-of-the-art GPU sketches.

Many LLM tasks are performed in large batches or even offline, and the performance indictor for which is throughput. These tasks usually show the characteristic of prefix sharing, where different prompt input can partially show the common prefix. However, the existing LLM inference engines tend to optimize the streaming requests and show limitations of supporting the large batched tasks with the prefix sharing characteristic. The existing solutions use the LRU-based cache to reuse the KV context of common prefix. The KV context that is about to be reused may prematurely be evicted with the implicit cache management. Even if not evicted, the lifetime of the shared KV context is extended since requests sharing the same context are not scheduled together, resulting in larger memory usage. These streaming oriented systems schedule the requests in the first-come-first-serve or similar order. As a result, the requests with larger ratio of decoding steps may be scheduled too late to be able to mix with the prefill chunks to increase the hardware utilization. Besides, the token and request number based batching can limit the size of token-batch, which keeps the GPU from saturating for the iterations dominated by decoding tokens. We propose BatchLLM to address the above problems. BatchLLM explicitly identifies the common prefixes globally. The requests sharing the same prefix will be scheduled together to reuse the KV context the best, which also shrinks the lifetime of common KV memory. BatchLLM reorders the requests and schedules the requests with larger ratio of decoding first to better mix the decoding tokens with the latter prefill chunks and applies memory-centric token batching to enlarge the token-batch sizes, which helps to increase the GPU utilization. Extensive evaluation shows that BatchLLM outperforms vLLM by 1.1x to 2x on a set of microbenchmarks and two typical industry workloads.

Multi-controlled single-target (MC) gates are some of the most crucial building blocks for varied quantum algorithms. How to implement them optimally is thus a pivotal question. To answer this question in an architecture-independent manner, and to get a worst-case estimate, we should look at a linear nearest-neighbor (LNN) architecture, as this can be embedded in almost any qubit connectivity. Motivated by the above, here we describe a method which implements MC gates using no more than sim 4k+8n CNOT gates -- up-to 60% reduction over state-of-the-art -- while allowing for complete flexibility to choose the locations of n controls, the target, and a dirty ancilla out of k qubits. More strikingly, in case k approx n, our upper bound is sim 12n -- the best known for unrestricted connectivity -- and if n = 1, our upper bound is sim 4k -- the best known for a single long-range CNOT gate over k qubits -- therefore, if our upper bound can be reduced, then the cost of one or both of these simpler versions of MC gates will be immediately reduced accordingly. In practice, our method provides circuits that tend to require fewer CNOT gates than our upper bound for almost any given instance of MC gates.

Extended reasoning in large language models (LLMs) creates severe KV cache memory bottlenecks. Leading KV cache compression methods estimate KV importance using attention scores from recent post-RoPE queries. However, queries rotate with position during RoPE, making representative queries very few, leading to poor top-key selection and unstable reasoning. To avoid this issue, we turn to the pre-RoPE space, where we observe that Q and K vectors are highly concentrated around fixed non-zero centers and remain stable across positions -- Q/K concentration. We show that this concentration causes queries to preferentially attend to keys at specific distances (e.g., nearest keys), with the centers determining which distances are preferred via a trigonometric series. Based on this, we propose TriAttention to estimate key importance by leveraging these centers. Via the trigonometric series, we use the distance preference characterized by these centers to score keys according to their positions, and also leverage Q/K norms as an additional signal for importance estimation. On AIME25 with 32K-token generation, TriAttention matches Full Attention reasoning accuracy while achieving 2.5x higher throughput or 10.7x KV memory reduction, whereas leading baselines achieve only about half the accuracy at the same efficiency. TriAttention enables OpenClaw deployment on a single consumer GPU, where long context would otherwise cause out-of-memory with Full Attention.

Key-Value (KV) Caching has become an essential technique for accelerating the inference speed and throughput of generative Large Language Models~(LLMs). However, the memory footprint of the KV cache poses a critical bottleneck in LLM deployment as the cache size grows with batch size and sequence length, often surpassing even the size of the model itself. Although recent methods were proposed to select and evict unimportant KV pairs from the cache to reduce memory consumption, the potential ramifications of eviction on the generative process are yet to be thoroughly examined. In this paper, we examine the detrimental impact of cache eviction and observe that unforeseen risks arise as the information contained in the KV pairs is exhaustively discarded, resulting in safety breaches, hallucinations, and context loss. Surprisingly, we find that preserving even a small amount of information contained in the evicted KV pairs via reduced precision quantization substantially recovers the incurred degradation. On the other hand, we observe that the important KV pairs must be kept at a relatively higher precision to safeguard the generation quality. Motivated by these observations, we propose Mixed-precision KV cache~(MiKV), a reliable cache compression method that simultaneously preserves the context details by retaining the evicted KV pairs in low-precision and ensure generation quality by keeping the important KV pairs in high-precision. Experiments on diverse benchmarks and LLM backbones show that our proposed method offers a state-of-the-art trade-off between compression ratio and performance, compared to other baselines.

Large language models rely on kv-caches to avoid redundant computation during autoregressive decoding, but as context length grows, reading and writing the cache can quickly saturate GPU memory bandwidth. Recent work has explored KV-cache compression, yet most approaches neglect the data-dependent nature of kv-caches and their variation across layers. We introduce KV-CoRE KV-cache Compressibility by Rank Evaluation), an SVD-based method for quantifying the data-dependent low-rank compressibility of kv-caches. KV-CoRE computes the optimal low-rank approximation under the Frobenius norm and, being gradient-free and incremental, enables efficient dataset-level, layer-wise evaluation. Using this method, we analyze multiple models and datasets spanning five English domains and sixteen languages, uncovering systematic patterns that link compressibility to model architecture, training data, and language coverage. As part of this analysis, we employ the Normalized Effective Rank as a metric of compressibility and show that it correlates strongly with performance degradation under compression. Our study establishes a principled evaluation framework and the first large-scale benchmark of kv-cache compressibility in LLMs, offering insights for dynamic, data-aware compression and data-centric model development.

Large language models (LLMs) have achieved remarkable performance across a wide range of tasks, but their inference efficiency remains a critical bottleneck due to rapidly growing parameters. Recent advances in dynamic computation allocation address this challenge by exploiting the highly uneven contributions of different tokens and layers, enabling selective execution that significantly reduces redundant computation while preserving model accuracy. However, existing hardware platforms and accelerators are primarily optimized for uniform, static execution, limiting their ability to efficiently support such dynamic inference patterns. In this work, we propose SkipOPU, an FPGA-based overlay processor that dynamically allocates computation across tokens and layers with high flexibility through a lightweight routing mechanism. First, we decouple reduction operations from element-wise computation in nonlinear modules and perform reductions incrementally, which enables both stages to be fused with adjacent linear operations (router or matrix multiplication) for effective latency hiding. Second, motivated by asymmetric sensitivity to numerical precision between activation and weight, we design a PE array that efficiently supports float-fixed hybrid execution. A novel DSP overpacking technique is introduced to maximize hardware utilization while minimizing resource overhead. Finally, we develop a proactive on-chip KV history buffer that exploits cross-layer KV invariance of pruned tokens, eliminating irregular HBM accesses during decoding and supplementing off-chip bandwidth through high-locality on-chip reuse. Experimental results demonstrate that SkipOPU on an AMD U280 FPGA outperforms GPU and other FPGA-based accelerators by 1.23x-3.83x in bandwidth efficiency for LLMs inference with dynamic computation allocation and can reduce up to 25.4% KV storage overhead across varying sequence lengths.

Pruning neural networks, which involves removing a fraction of their weights, can often maintain high accuracy while significantly reducing model complexity, at least up to a certain limit. We present a neural network pruning technique that builds upon the Combinatorial Brain Surgeon, but solves an optimization problem over a subset of the network weights in an iterative, block-wise manner using block coordinate descent. The iterative, block-based nature of this pruning technique, which we dub ``iterative Combinatorial Brain Surgeon'' (iCBS) allows for scalability to very large models, including large language models (LLMs), that may not be feasible with a one-shot combinatorial optimization approach. When applied to large models like Mistral and DeiT, iCBS achieves higher performance metrics at the same density levels compared to existing pruning methods such as Wanda. This demonstrates the effectiveness of this iterative, block-wise pruning method in compressing and optimizing the performance of large deep learning models, even while optimizing over only a small fraction of the weights. Moreover, our approach allows for a quality-time (or cost) tradeoff that is not available when using a one-shot pruning technique alone. The block-wise formulation of the optimization problem enables the use of hardware accelerators, potentially offsetting the increased computational costs compared to one-shot pruning methods like Wanda. In particular, the optimization problem solved for each block is quantum-amenable in that it could, in principle, be solved by a quantum computer.

Quantum optimization holds promise for addressing classically intractable combinatorial problems, yet a standardized framework for benchmarking its performance, particularly in terms of solution quality, computational speed, and scalability is still lacking. In this work, we introduce a comprehensive benchmarking framework designed to systematically evaluate a range of quantum optimization techniques against well-established NP-hard combinatorial problems. Our framework focuses on key problem classes, including the Multi-Dimensional Knapsack Problem (MDKP), Maximum Independent Set (MIS), Quadratic Assignment Problem (QAP), and Market Share Problem (MSP). Our study evaluates gate-based quantum approaches, including the Variational Quantum Eigensolver (VQE) and its CVaR-enhanced variant, alongside advanced quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) and its extensions. To address resource constraints, we incorporate qubit compression techniques like Pauli Correlation Encoding (PCE) and Quantum Random Access Optimization (QRAO). Experimental results, obtained from simulated quantum environments and classical solvers, provide key insights into feasibility, optimality gaps, and scalability. Our findings highlight both the promise and current limitations of quantum optimization, offering a structured pathway for future research and practical applications in quantum-enhanced decision-making.

Similarity search finds application in specialized database systems handling complex data such as images or videos, which are typically represented by high-dimensional features and require specific indexing structures. This paper tackles the problem of better utilizing GPUs for this task. While GPUs excel at data-parallel tasks, prior approaches are bottlenecked by algorithms that expose less parallelism, such as k-min selection, or make poor use of the memory hierarchy. We propose a design for k-selection that operates at up to 55% of theoretical peak performance, enabling a nearest neighbor implementation that is 8.5x faster than prior GPU state of the art. We apply it in different similarity search scenarios, by proposing optimized design for brute-force, approximate and compressed-domain search based on product quantization. In all these setups, we outperform the state of the art by large margins. Our implementation enables the construction of a high accuracy k-NN graph on 95 million images from the Yfcc100M dataset in 35 minutes, and of a graph connecting 1 billion vectors in less than 12 hours on 4 Maxwell Titan X GPUs. We have open-sourced our approach for the sake of comparison and reproducibility.

The deployment of efficient long-context LLMs in applications like autonomous agents, long-chain reasoning, and creative writing is fundamentally bottlenecked by the linear growth of KV cache memory. Existing compression and eviction methods often struggle to balance accuracy, compression ratio, and hardware efficiency. We propose DeltaKV, a residual-based KV cache compression framework motivated by two empirical findings: long-range inter-token similarity and highly shared latent components in KV representations. Instead of discarding tokens, DeltaKV encodes semantic residuals relative to retrieved historical references, preserving fidelity while substantially reducing storage. To translate compression gains into real system speedups, we further introduce Sparse-vLLM, a high-performance inference engine with decoupled memory management and kernels optimized for sparse and irregular KV layouts. Experiments show that DeltaKV reduces KV cache memory to 29\% of the original while maintaining near-lossless accuracy on LongBench, SCBench, and AIME. When integrated with Sparse-vLLM, it achieves up to 2times throughput improvement over vLLM in long-context scenarios, demonstrating a practical path toward scalable long-context LLM deployment. Code, model checkpoints, and datasets are available at https://github.com/CURRENTF/Sparse-vLLM.

Key-Value (KV) caching is a common technique to enhance the computational efficiency of Large Language Models (LLMs), but its memory overhead grows rapidly with input length. Prior work has shown that not all tokens are equally important for text generation, proposing layer-level KV cache compression to selectively retain key information. Recognizing the distinct roles of attention heads in generation, we propose HeadKV, a head-level KV cache compression method, and HeadKV-R2, which leverages a novel contextual reasoning ability estimation for compression. Our approach operates at the level of individual heads, estimating their importance for contextual QA tasks that require both retrieval and reasoning capabilities. Extensive experiments across diverse benchmarks (LongBench, LooGLE), model architectures (e.g., Llama-3-8B-Instruct, Mistral-7B-Instruct), and long-context abilities tests demonstrate that our head-level KV cache compression significantly outperforms strong baselines, particularly in low-resource settings (KV size = 64 & 128). Notably, our method retains just 1.5% of the KV cache while achieving 97% of the performance of the full KV cache on the contextual question answering benchmark.

Large Language Model or LLM inference has two phases, the prompt (or prefill) phase to output the first token and the extension (or decoding) phase to the generate subsequent tokens. In this work, we propose an efficient parallelization scheme, KV-Runahead to accelerate the prompt phase. The key observation is that the extension phase generates tokens faster than the prompt phase because of key-value cache (KV-cache). Hence, KV-Runahead parallelizes the prompt phase by orchestrating multiple processes to populate the KV-cache and minimizes the time-to-first-token (TTFT). Dual-purposing the KV-cache scheme has two main benefits. Fist, since KV-cache is designed to leverage the causal attention map, we minimize computation and computation automatically. Second, since it already exists for the exten- sion phase, KV-Runahead is easy to implement. We further propose context-level load-balancing to handle uneven KV-cache generation (due to the causal attention) and to optimize TTFT. Compared with an existing parallelization scheme such as tensor or sequential parallelization where keys and values are locally generated and exchanged via all-gather collectives, our experimental results demonstrate that KV-Runahead can offer over 1.4x and 1.6x speedups for Llama 7B and Falcon 7B respectively.

Nonconvex optimization is central in solving many machine learning problems, in which block-wise structure is commonly encountered. In this work, we propose cyclic block coordinate methods for nonconvex optimization problems with non-asymptotic gradient norm guarantees. Our convergence analysis is based on a gradient Lipschitz condition with respect to a Mahalanobis norm, inspired by a recent progress on cyclic block coordinate methods. In deterministic settings, our convergence guarantee matches the guarantee of (full-gradient) gradient descent, but with the gradient Lipschitz constant being defined w.r.t.~a Mahalanobis norm. In stochastic settings, we use recursive variance reduction to decrease the per-iteration cost and match the arithmetic operation complexity of current optimal stochastic full-gradient methods, with a unified analysis for both finite-sum and infinite-sum cases. We prove a faster linear convergence result when a Polyak-{\L}ojasiewicz (P{\L}) condition holds. To our knowledge, this work is the first to provide non-asymptotic convergence guarantees -- variance-reduced or not -- for a cyclic block coordinate method in general composite (smooth + nonsmooth) nonconvex settings. Our experimental results demonstrate the efficacy of the proposed cyclic scheme in training deep neural nets.

Efficient deployment of Large Language Models (LLMs) requires batching multiple requests together to improve throughput. As the batch size, context length, or model size increases, the size of the key and value (KV) cache can quickly become the main contributor to GPU memory usage and the bottleneck of inference latency. Quantization has emerged as an effective technique for KV cache compression, but existing methods still fail at very low bit widths. We observe that distinct channels of a key/value activation embedding are highly inter-dependent, and the joint entropy of multiple channels grows at a slower rate than the sum of their marginal entropies. Based on this insight, we propose Coupled Quantization (CQ), which couples multiple key/value channels together to exploit their inter-dependency and encode the activations in a more information-efficient manner. Extensive experiments reveal that CQ outperforms or is competitive with existing baselines in preserving model quality. Furthermore, we demonstrate that CQ can preserve model quality with KV cache quantized down to 1-bit.

We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximation improves as p is increased. The quantum circuit that implements the algorithm consists of unitary gates whose locality is at most the locality of the objective function whose optimum is sought. The depth of the circuit grows linearly with p times (at worst) the number of constraints. If p is fixed, that is, independent of the input size, the algorithm makes use of efficient classical preprocessing. If p grows with the input size a different strategy is proposed. We study the algorithm as applied to MaxCut on regular graphs and analyze its performance on 2-regular and 3-regular graphs for fixed p. For p = 1, on 3-regular graphs the quantum algorithm always finds a cut that is at least 0.6924 times the size of the optimal cut.

Efficient real-world deployments of large language models (LLMs) rely on Key-Value (KV) caching for processing and generating long outputs, reducing the need for repetitive computation. For large contexts, Key-Value caches can take up tens of gigabytes of device memory, as they store vector representations for each token and layer. Recent work has shown that the cached vectors can be compressed through quantization, pruning or merging, but these techniques often compromise quality towards higher compression rates. In this work, we aim to improve Key & Value compression by exploiting two observations: 1) the inherent dependencies between keys and values across different layers, and 2) high-compression mechanisms for internal network states. We propose AQUA-KV, an adaptive quantization for Key-Value caches that relies on compact adapters to exploit existing dependencies between Keys and Values, and aims to "optimally" compress the information that cannot be predicted. AQUA-KV significantly improves compression rates, while maintaining high accuracy on state-of-the-art LLM families. On Llama 3.2 LLMs, we achieve near-lossless inference at 2-2.5 bits per value with under 1% relative error in perplexity and LongBench scores. AQUA-KV is one-shot, simple, and efficient: it can be calibrated on a single GPU within 1-6 hours, even for 70B models.

k-means has historically been positioned primarily as an offline processing primitive, typically used for dataset organization or embedding preprocessing rather than as a first-class component in online systems. In this work, we revisit this classical algorithm under the lens of modern AI system design and enable k-means as an online primitive. We point out that existing GPU implementations of k-means remain fundamentally bottlenecked by low-level system constraints rather than theoretical algorithmic complexity. Specifically, the assignment stage suffers from a severe IO bottleneck due to the massive explicit materialization of the N times K distance matrix in High Bandwidth Memory (HBM). Simultaneously, the centroid update stage is heavily penalized by hardware-level atomic write contention caused by irregular, scatter-style token aggregations. To bridge this performance gap, we propose flash-kmeans, an IO-aware and contention-free k-means implementation for modern GPU workloads. Flash-kmeans introduces two core kernel-level innovations: (1) FlashAssign, which fuses distance computation with an online argmin to completely bypass intermediate memory materialization; (2) sort-inverse update, which explicitly constructs an inverse mapping to transform high-contention atomic scatters into high-bandwidth, segment-level localized reductions. Furthermore, we integrate algorithm-system co-designs, including chunked-stream overlap and cache-aware compile heuristics, to ensure practical deployability. Extensive evaluations on NVIDIA H200 GPUs demonstrate that flash-kmeans achieves up to 17.9times end-to-end speedup over best baselines, while outperforming industry-standard libraries like cuML and FAISS by 33times and over 200times, respectively.

Quantum computation is an emerging technology with important potential for solving certain problems pivotal in various scientific and engineering disciplines. This paper introduces an efficient quantum protocol for the explicit construction of the block-encoding for an important class of Hamiltonians. Using the Schrodingerisation technique -- which converts non-conservative PDEs into conservative ones -- this particular class of Hamiltonians is shown to be sufficient for simulating any linear partial differential equations that have coefficients which are polynomial functions. The class of Hamiltonians consist of discretisations of polynomial products and sums of position and momentum operators. This construction is explicit and leverages minimal one- and two-qubit operations. The explicit construction of this block-encoding forms a fundamental building block for constructing the unitary evolution operator for this Hamiltonian. The proposed algorithm exhibits polynomial scaling with respect to the spatial partitioning size, suggesting an exponential speedup over classical finite-difference methods. This work provides an important foundation for building explicit and efficient quantum circuits for solving partial differential equations.

KV cache quantization can improve Large Language Models (LLMs) inference throughput and latency in long contexts and large batch-size scenarios while preserving LLMs effectiveness. However, current methods have three unsolved issues: overlooking layer-wise sensitivity to KV cache quantization, high overhead of online fine-grained decision-making, and low flexibility to different LLMs and constraints. Therefore, we theoretically analyze the inherent correlation of layer-wise transformer attention patterns to KV cache quantization errors and study why key cache is generally more important than value cache for quantization error reduction. We further propose a simple yet effective framework KVTuner to adaptively search for the optimal hardware-friendly layer-wise KV quantization precision pairs for coarse-grained KV cache with multi-objective optimization and directly utilize the offline searched configurations during online inference. To reduce the computational cost of offline calibration, we utilize the intra-layer KV precision pair pruning and inter-layer clustering to reduce the search space. Experimental results show that we can achieve nearly lossless 3.25-bit mixed precision KV cache quantization for LLMs like Llama-3.1-8B-Instruct and 4.0-bit for sensitive models like Qwen2.5-7B-Instruct on mathematical reasoning tasks. The maximum inference throughput can be improved by 21.25\% compared with KIVI-KV8 quantization over various context lengths. Our code and searched configurations are available at https://github.com/cmd2001/KVTuner.

Modular quantum processors require a compiler to reason about two resources at the same time: local device connectivity and communication across QPUs. A mapping that is acceptable on a single coupling graph may be unsuitable for a modular machine if it creates excessive cross-QPU traffic, concentrates that traffic on a small number of interconnect links, or assigns many boundary qubits to a QPU with few communication ports. This paper presents QuPort, a Python and Qiskit-based compilation framework that studies this setting through an explicit three-level model: a weighted logical interaction graph, a directed physical coupling map, and an undirected QPU-level interconnect graph. The main partitioning method, TPCCAP, optimizes the implemented objective formed by weighted cut distance, communication-port overflow, and routed link-load congestion. The framework also includes heavy-edge clustering, balanced greedy partitioning, simulated-annealing refinement, communication-port-aware layout, extraction of remote two-qubit operations, local-only routing of per-QPU circuits, and topology-aware schedule estimation. The model is a compiler-level abstraction. It does not claim a calibrated hardware runtime or an implementation of a physical remote-gate protocol.

The Key-Value (KV) cache is crucial for efficient Large Language Models (LLMs) inference, but excessively long contexts drastically increase KV cache memory footprint. Existing KV cache compression methods typically rely on input-side attention patterns within a prompt observation window to estimate token importance during the prefill stage. They fail to preserve critical tokens for future generation since these assessments are not derived from the decoding process. Intuitively, an effective observation window should mirror the decoding-stage queries to accurately reflect which tokens the generation process will attend to. However, ground-truth decoding queries are inherently unavailable during inference. For constructing pseudo queries to approximate them, we find that positional information plays a more critical role than semantic content. Motivated by this insight, we propose decoding-aligned KV cache compression via position-aware pseudo queries (DapQ), a novel and lightweight eviction framework that leverages position-aware pseudo queries to simulate the output tokens, thereby establishing an effective observation window for importance assessment. It aligns closely with the actual generation context and enables precise token eviction. Extensive evaluations across multiple benchmarks and LLMs demonstrate that DapQ achieves superior performance, particularly under strict memory constraints (e.g., up to nearly lossless performance 99.5% on NIAH with 3% KV cache budgets).

The adversarial vulnerability of Deep Neural Networks (DNNs) has been well-known and widely concerned, often under the context of learning top-1 attacks (e.g., fooling a DNN to classify a cat image as dog). This paper shows that the concern is much more serious by learning significantly more aggressive ordered top-K clear-box~ This is often referred to as white/black-box attacks in the literature. We choose to adopt neutral terminology, clear/opaque-box attacks in this paper, and omit the prefix clear-box for simplicity. targeted attacks proposed in Adversarial Distillation. We propose a novel and rigorous quadratic programming (QP) method of learning ordered top-K attacks with low computing cost, dubbed as QuadAttacK. Our QuadAttacK directly solves the QP to satisfy the attack constraint in the feature embedding space (i.e., the input space to the final linear classifier), which thus exploits the semantics of the feature embedding space (i.e., the principle of class coherence). With the optimized feature embedding vector perturbation, it then computes the adversarial perturbation in the data space via the vanilla one-step back-propagation. In experiments, the proposed QuadAttacK is tested in the ImageNet-1k classification using ResNet-50, DenseNet-121, and Vision Transformers (ViT-B and DEiT-S). It successfully pushes the boundary of successful ordered top-K attacks from K=10 up to K=20 at a cheap budget (1times 60) and further improves attack success rates for K=5 for all tested models, while retaining the performance for K=1.

This work studies how to adaptively recompute key-value (KV) caches for diffusion large language models (DLMs) to maximize prediction accuracy while minimizing decoding latency. Prior methods' decoders recompute QKV for all tokens at every denoising step and layer, despite KV states changing little across most steps, especially in shallow layers, leading to substantial redundancy. We make three observations: (1) distant {bf MASK} tokens primarily act as a length-bias and can be cached block-wise beyond the active prediction window; (2) KV dynamics increase with depth, suggesting that selective refresh starting from deeper layers is sufficient; and (3) the most-attended token exhibits the smallest KV drift, providing a conservative lower bound on cache change for other tokens. Building on these, we propose {bf Elastic-Cache}, a training-free, architecture-agnostic strategy that jointly decides {when} to refresh (via an attention-aware drift test on the most-attended token) and {where} to refresh (via a depth-aware schedule that recomputes from a chosen layer onward while reusing shallow-layer caches and off-window MASK caches). Unlike fixed-period schemes, Elastic-Cache performs adaptive, layer-aware cache updates for diffusion LLMs, reducing redundant computation and accelerating decoding with negligible loss in generation quality. Experiments on LLaDA-Instruct, LLaDA-1.5, and LLaDA-V across mathematical reasoning and code generation tasks demonstrate consistent speedups: 8.7times on GSM8K (256 tokens), 45.1times on longer sequences, and 4.8times on HumanEval, while consistently maintaining higher accuracy than the baseline. Our method achieves significantly higher throughput (6.8times on GSM8K) than existing confidence-based approaches while preserving generation quality, enabling practical deployment of diffusion LLMs.

A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs). However, their applicability is limited by hardware constraints, including shallow circuit depth, limited qubit counts, and noise. To mitigate these issues, we propose a hybrid classical--quantum framework based on graph shrinking to reduce the number of variables and constraints in QUBO formulations of COPs, while preserving problem structure. Our approach introduces three key ideas: (i) constraint-aware shrinking that prevents merges that will likely violate problem-specific feasibility constraints, (ii) a verification-and-repair pipeline to correct infeasible solutions post-optimization, and (iii) adaptive strategies for recalculating correlations and controlling the graph shrinking process. We apply our approach to three standard benchmark problems: Multidimensional Knapsack (MDKP), Maximum Independent Set (MIS), and the Quadratic Assignment Problem (QAP). Empirical results show that our approach improves solution feasibility, reduces repair complexity, and enhances quantum optimization quality on hardware-limited instances. These findings demonstrate a scalable pathway for applying near-term quantum algorithms to classically challenging constrained optimization problems.

Recent advances in long-text understanding have pushed the context length of large language models (LLMs) up to one million tokens. It boosts LLMs's accuracy and reasoning capacity but causes exorbitant computational costs and unsatisfactory Time to First Token (TTFT). KV cache reuse, which reuses the exact same KV cache of prefixes and templates or shares similar ones but with extra selective recomputation, offers a promising way to tackle this issue. However, prior studies overlook the cross-request KV reuse and the attention deviations introduced by new tokens during the decoding stage. In this paper, we present a KV cache management module that shares the KV cache across requests under multi-tenant scenarios without sacrificing model accuracy. Our system, KVShare, enables accurate and efficient LLM serving by 1) a Dual-Stage High Deviation algorithm (DHD) that conditionally selects a small portion of KV cache to be recomputed during both prefill and decode phases, and 2) a cache-aware scheduler that prioritizes requests based on their KV cache hit rates and orchestrates continuous batching to achieve enhanced system efficiency and faster TTFT. Multi-task experiments conducted on models such as Qwen2.5-7B,Llama3.1-8B and Yi1.5-9B demonstrate that KVShare reduces TTFT by up to 9.39x and increases 1.2x of the throughput compared to the full KV recompute. Moreover, KVShare achieves 20.38% boost in terms of accuracy compared to SOTA methods.

Large Language Models (LLMs) rely heavily on Key-Value (KV) caching to minimize inference latency. However, standard KV caches are context-dependent: reusing a cached document in a new context requires recomputing KV states to account for shifts in attention distribution. Existing solutions such as CacheBlend, EPIC, and SAM-KV mitigate this issue by selectively recomputing a subset of tokens; however, they still incur non-negligible computational overhead (FLOPs) and increased Time-to-First-Token (TTFT) latency. In this paper, we propose KV Packet, a recomputation-free cache reuse framework that treats cached documents as immutable ``packets'' wrapped in light-weight trainable soft-token adapters, which are trained via self-supervised distillation to bridge context discontinuities. Experiments on Llama-3.1 and Qwen2.5 demonstrate that the proposed KV Packet method achieves near-zero FLOPs and lower TTFT than recomputation-based baselines, while retaining F1 scores comparable to those of the full recomputation baseline.

We present a decomposition technique that uses non-deterministic circuits to approximate an arbitrary single-qubit unitary to within distance ε and requires significantly fewer non-Clifford gates than existing techniques. We develop "Repeat-Until-Success" (RUS) circuits and characterize unitaries that can be exactly represented as an RUS circuit. Our RUS circuits operate by conditioning on a given measurement outcome and using only a small number of non-Clifford gates and ancilla qubits. We construct an algorithm based on RUS circuits that approximates an arbitrary single-qubit Z-axis rotation to within distance ε, where the number of T gates scales as 1.26log_2(1/ε) - 3.53, an improvement of roughly three-fold over state-of-the-art techniques. We then extend our algorithm and show that a scaling of 2.4log_2(1/ε) - 3.28 can be achieved for arbitrary unitaries and a small range of ε, which is roughly twice as good as optimal deterministic decomposition methods.

How to efficiently serve Large Language Models (LLMs) has become a pressing issue because of their huge computational cost in their autoregressive generation process. To mitigate computational costs, LLMs often employ the KV Cache technique to improve the generation speed. While improving the computational efficiency, the storage requirements of the KV cache are substantial, particularly in long-context scenarios, leading to significant memory consumption. Existing KV cache eviction methods often degrade the performance of LLMs in long-context scenarios due to the information loss introduced by eviction. In this paper, we propose a novel KV cache merging approach, called KVMerger, to achieve adaptive KV cache compression for long-context tasks without significant performance degradation under constrained memory budgets. Our approach is inspired by the intriguing observation that key states exhibit high similarity at the token level within a single sequence. To facilitate merging, we develop an effective yet straightforward merging set identification algorithm to identify suitable KV states for merging. Our merging set identification algorithm stimulates the second observation that KV cache sparsity, from similarity perspective, is independent of the dataset and remains persistent at the model level. Subsequently, we propose a Gaussian kernel weighted merging algorithm to selectively merge all states within each merging set. We conduct extensive experiments to demonstrate the effectiveness of KVMerger for long-context tasks under constrained memory budgets, applying it to models including Llama2-7B-chat and Llama2-13B-chat. Using the LongBench and ZeroScroll benchmarks, we compare our method with other KV cache compression techniques, including H2O and CaM, showing that our method achieves superior performance across tasks with both 50% and 35% KV cache budgets.

The Muon optimizer, based on matrix orthogonalization, has recently shown faster convergence and up to 2x computational efficiency over AdamW in LLM pretraining. Like AdamW, Muon is stateful, requiring storage of both model weights and accumulated gradients. While 8-bit AdamW variants mitigate this overhead using blockwise quantization, they are typically stable only under dynamic quantization - which improves stability on linear quantization for extreme values. In this paper, we introduce the 8-bit Muon optimizer using blockwise quantization, supporting both linear and dynamic schemes. We demonstrate that 8-bit Muon maintains stability under both, while delivering sim74\% reduction in memory footprint compared to full-precision Muon. In extensive experiments, 8-bit Muon closely matches the performance of Muon while outperforming AdamW and 8-bit AdamW in pre-training a 1.6B model on 4B FineWeb tokens. It also shows competitive results when fine-tuning the Llama 3.2 3B model on post-training data. We also provide a theoretical perspective to help explain this robustness under quantization.

We consider the problem of constructing small coresets for k-Median in Euclidean spaces. Given a large set of data points Psubset R^d, a coreset is a much smaller set Ssubset R^d, so that the k-Median costs of any k centers w.r.t. P and S are close. Existing literature mainly focuses on the high-dimension case and there has been great success in obtaining dimension-independent bounds, whereas the case for small d is largely unexplored. Considering many applications of Euclidean clustering algorithms are in small dimensions and the lack of systematic studies in the current literature, this paper investigates coresets for k-Median in small dimensions. For small d, a natural question is whether existing near-optimal dimension-independent bounds can be significantly improved. We provide affirmative answers to this question for a range of parameters. Moreover, new lower bound results are also proved, which are the highest for small d. In particular, we completely settle the coreset size bound for 1-d k-Median (up to log factors). Interestingly, our results imply a strong separation between 1-d 1-Median and 1-d 2-Median. As far as we know, this is the first such separation between k=1 and k=2 in any dimension.

Memory consumption of the Key-Value (KV) cache represents a major bottleneck for efficient large language model inference. While attention-score-based KV cache pruning shows promise, it faces critical practical limitations: attention scores from future tokens are unavailable during compression, and modern implementations like Flash Attention do not materialize the full attention matrix, making past scores inaccessible. To overcome these challenges, we introduce Expected Attention, a training-free compression method that estimates KV pairs importance by predicting how future queries will attend to them. Our approach leverages the distributional properties of LLM activations to compute expected attention scores in closed form for each KV pair. These scores enable principled ranking and pruning of KV pairs with minimal impact on the residual stream, achieving effective compression without performance degradation. Importantly, our method operates seamlessly across both prefilling and decoding phases, consistently outperforming state-of-the-art baselines in both scenarios. Finally, we release KVPress, a comprehensive library to enable researchers to implement and benchmark KV cache compression methods, already including more than 20 techniques.

The growing demand for Large Language Models (LLMs) across diverse applications has prompted a paradigm shift in the design of deep learning serving systems. Deploying LLMs, especially in multi-tenant environments, presents considerable challenges due to their high computational and memory demands. We present BlockLLM, a serving system that exploits the potential of sharing components among fine-tuned LLM models to offer an efficient and flexible solution for LLM workloads. BlockLLM partitions the models into finer-grained blocks to enable the reuse of model components and independent provisioning to improve the computation efficiency. BlockLLM consists of an offline block zoo, for storing the blocks, and an online system to serve the requests through chains of blocks. It offers multi-fold flexibility: (1) Adaptive assembly of block chains on-the-fly is achieved with the help of equivalence evaluation among blocks in the zoo. (2) We enable per-block batch size and configure best-effort KV cache coordination at individual block level. (3) We adopt speculative execution and locality-aware block placement to mitigate the communication costs from dynamic block resource allocation. Our evaluation demonstrates that BlockLLM reduces memory and storage footprints and improves computation efficiency, outperforming existing serving approach in 95\%ile latency and GPU utilization by 33.5\% and 20.1\%, respectively.

Video large language models (VideoLLMs) have demonstrated the capability to process longer video inputs and enable complex reasoning and analysis. However, due to the thousands of visual tokens from the video frames, key-value (KV) cache can significantly increase memory requirements, becoming a bottleneck for inference speed and memory usage. KV cache quantization is a widely used approach to address this problem. In this paper, we find that 2-bit KV quantization of VideoLLMs can hardly hurt the model performance, while the limit of KV cache quantization in even lower bits has not been investigated. To bridge this gap, we introduce VidKV, a plug-and-play KV cache quantization method to compress the KV cache to lower than 2 bits. Specifically, (1) for key, we propose a mixed-precision quantization strategy in the channel dimension, where we perform 2-bit quantization for anomalous channels and 1-bit quantization combined with FFT for normal channels; (2) for value, we implement 1.58-bit quantization while selectively filtering semantically salient visual tokens for targeted preservation, for a better trade-off between precision and model performance. Importantly, our findings suggest that the value cache of VideoLLMs should be quantized in a per-channel fashion instead of the per-token fashion proposed by prior KV cache quantization works for LLMs. Empirically, extensive results with LLaVA-OV-7B and Qwen2.5-VL-7B on six benchmarks show that VidKV effectively compresses the KV cache to 1.5-bit and 1.58-bit precision with almost no performance drop compared to the FP16 counterparts.

Large Language Models have excelled in various domains but face efficiency challenges due to the growing Key-Value (KV) cache required for long-sequence inference. Recent efforts aim to reduce KV cache size by evicting vast non-critical cache elements during runtime while preserving generation quality. However, these methods typically allocate compression budgets uniformly across all attention heads, ignoring the unique attention patterns of each head. In this paper, we establish a theoretical loss upper bound between pre- and post-eviction attention output, explaining the optimization target of prior cache eviction methods, while guiding the optimization of adaptive budget allocation. Base on this, we propose {\it Ada-KV}, the first head-wise adaptive budget allocation strategy. It offers plug-and-play benefits, enabling seamless integration with prior cache eviction methods. Extensive evaluations on 13 datasets from Ruler and 16 datasets from LongBench, all conducted under both question-aware and question-agnostic scenarios, demonstrate substantial quality improvements over existing methods. Our code is available at https://github.com/FFY0/AdaKV.

KyFrog is a conservative Learning-with-Errors (LWE) key-encapsulation mechanism designed to explore an alternative operating point compared to schemes with relatively small public keys and ciphertexts. KyFrog uses a larger dimension (n = 1024) and a small prime modulus q = 1103, together with narrow error distributions with standard deviations σ_s = σ_e = 1.4, to target approximately 2^{325} classical and quantum security against state-of-the-art lattice attacks under standard cost models, as estimated using the Lattice Estimator. The price paid for this security margin is an extremely large KEM ciphertext (about 0.5 MiB), while public and secret keys remain in the same ballpark as ML-KEM. We describe the design rationale, parameter search methodology, and implementation details of KyFrog, and we compare its asymptotic security and concrete parameter sizes with the ML-KEM standard. All code and data for this work are released as free and open-source software, with the full C++23 implementation and experimental scripts available at: https://github.com/victormeloasm/kyfrog

Diffusion large language models (dLLMs) have emerged as a promising alternative for text generation, distinguished by their native support for parallel decoding. In practice, block inference is crucial for avoiding order misalignment in global bidirectional decoding and improving output quality. However, the widely-used fixed, predefined block (naive) schedule is agnostic to semantic difficulty, making it a suboptimal strategy for both quality and efficiency: it can force premature commitments to uncertain positions while delaying easy positions near block boundaries. In this work, we analyze the limitations of naive block scheduling and disclose the importance of dynamically adapting the schedule to semantic difficulty for reliable and efficient inference. Motivated by this, we propose Dynamic Sliding Block (DSB), a training-free block scheduling method that uses a sliding block with a dynamic size to overcome the rigidity of the naive block. To further improve efficiency, we introduce DSB Cache, a training-free KV-cache mechanism tailored to DSB. Extensive experiments across multiple models and benchmarks demonstrate that DSB, together with DSB Cache, consistently improves both generation quality and inference efficiency for dLLMs. Code is released at https://github.com/lizhuo-luo/DSB.

Self-forcing video generation extends a short-horizon video model to longer rollouts by repeatedly feeding generated content back in as context. This scaling path immediately exposes a systems bottleneck: the key-value (KV) cache grows with rollout length, so longer videos require not only better generation quality but also substantially better memory behavior. We present a comprehensive empirical study of KV-cache compression for self-forcing video generation on a Wan2.1-based Self-Forcing stack. Our study covers 33 quantization and cache-policy variants, 610 prompt-level observations, and 63 benchmark-level summaries across two evaluation settings: MovieGen for single-shot 10-second generation and StoryEval for longer narrative-style stability. We jointly evaluate peak VRAM, runtime, realized compression ratio, VBench imaging quality, BF16-referenced fidelity (SSIM, LPIPS, PSNR), and terminal drift. Three findings are robust. First, the strongest practical operating region is a FlowCache-inspired soft-prune INT4 adaptation, which reaches 5.42-5.49x compression while reducing peak VRAM from 19.28 GB to about 11.7 GB with only modest runtime overhead. Second, the highest-fidelity compressed methods, especially PRQ_INT4 and QUAROT_KV_INT4, are not the best deployment choices because they preserve quality at severe runtime or memory cost. Third, nominal compression alone is not sufficient: several methods shrink KV storage but still exceed BF16 peak VRAM because the current integration reconstructs or retains large BF16 buffers during attention and refresh stages. The result is a benchmark harness, analysis workflow, and empirical map of which KV-cache ideas are practical today and which are promising research directions for better memory integration. Code, data products, and the presentation dashboard are available at https://github.com/suraj-ranganath/kv-quant-longhorizon/.

Large Language Models (LLMs) with long context windows enable powerful applications but come at the cost of high memory consumption to store the Key and Value states (KV-Cache). Recent studies attempted to merge KV-cache from multiple layers into shared representations, yet these approaches either require expensive pretraining or rely on assumptions of high per-token cosine similarity across layers which generally does not hold in practice. We find that the dominant singular vectors are remarkably well-aligned across multiple layers of the KV-Cache. Exploiting this insight, we propose xKV, a simple post-training method that applies Singular Value Decomposition (SVD) on the KV-Cache of grouped layers. xKV consolidates the KV-Cache of multiple layers into a shared low-rank subspace, significantly reducing KV-Cache sizes. Through extensive evaluations on the RULER long-context benchmark with widely-used LLMs (e.g., Llama-3.1 and Qwen2.5), xKV achieves up to 6.8x higher compression rates than state-of-the-art inter-layer technique while improving accuracy by 2.7%. Moreover, xKV is compatible with the emerging Multi-Head Latent Attention (MLA) (e.g., DeepSeek-Coder-V2), yielding a notable 3x compression rates on coding tasks without performance degradation. These results highlight xKV's strong capability and versatility in addressing memory bottlenecks for long-context LLM inference. Our code is publicly available at: https://github.com/abdelfattah-lab/xKV.

Key-value (KV) cache compression has emerged as a critical technique for reducing the memory and latency overhead of autoregressive language models during inference. Prior approaches predominantly rely on query-key attention scores to rank and evict cached tokens, assuming that attention intensity correlates with semantic importance. However, this heuristic overlooks the contribution of value vectors, which directly influence the attention output. In this paper, we propose CurDKV, a novel, value-centric KV compression method that selects keys and values based on leverage scores computed from CUR matrix decomposition. Our approach approximates the dominant subspace of the attention output softmax(QK^T)V, ensuring that the retained tokens best preserve the model's predictive behavior. Theoretically, we show that attention score approximation does not guarantee output preservation, and demonstrate that CUR-based selection minimizes end-to-end attention reconstruction loss. Empirically, CurDKV achieves up to 9.6% higher accuracy than state-of-the-art methods like SnapKV and ChunkKV under aggressive compression budgets on LLaMA and Mistral, while maintaining compatibility with FlashAttention and Grouped Query Attention. In addition to improved accuracy, CurDKV reduces generation latency by up to 40% at high compression, offering a practical speed-accuracy tradeoff.

The correct use of model evaluation, model selection, and algorithm selection techniques is vital in academic machine learning research as well as in many industrial settings. This article reviews different techniques that can be used for each of these three subtasks and discusses the main advantages and disadvantages of each technique with references to theoretical and empirical studies. Further, recommendations are given to encourage best yet feasible practices in research and applications of machine learning. Common methods such as the holdout method for model evaluation and selection are covered, which are not recommended when working with small datasets. Different flavors of the bootstrap technique are introduced for estimating the uncertainty of performance estimates, as an alternative to confidence intervals via normal approximation if bootstrapping is computationally feasible. Common cross-validation techniques such as leave-one-out cross-validation and k-fold cross-validation are reviewed, the bias-variance trade-off for choosing k is discussed, and practical tips for the optimal choice of k are given based on empirical evidence. Different statistical tests for algorithm comparisons are presented, and strategies for dealing with multiple comparisons such as omnibus tests and multiple-comparison corrections are discussed. Finally, alternative methods for algorithm selection, such as the combined F-test 5x2 cross-validation and nested cross-validation, are recommended for comparing machine learning algorithms when datasets are small.

To reduce memory costs in long-context inference with Large Language Models (LLMs), many recent works focus on compressing the key-value (KV) cache of different tokens. However, we identify that the previous KV cache compression methods measure token importance individually, neglecting the dependency between different tokens in the real-world language characterics. In light of this, we introduce ChunkKV, grouping the tokens in a chunk as a basic compressing unit, and retaining the most informative semantic chunks while discarding the less important ones. Furthermore, observing that ChunkKV exhibits higher similarity in the preserved indices across different layers, we propose layer-wise index reuse to further reduce computational overhead. We evaluated ChunkKV on cutting-edge long-context benchmarks including LongBench and Needle-In-A-HayStack, as well as the GSM8K and JailbreakV in-context learning benchmark. Our experiments with instruction tuning and multi-step reasoning (O1 and R1) LLMs, achieve up to 10\% performance improvement under aggressive compression ratios compared to existing methods.

Large Language Models (LLMs) are increasingly deployed in multi-agent systems, where effective inter-model communication is crucial. Existing communication protocols either rely on natural language, incurring high inference costs and information loss, or on hidden states, which suffer from information concentration bias and inefficiency. To address these limitations, we propose KVComm, a novel communication framework that enables efficient communication between LLMs through selective sharing of KV pairs. KVComm leverages the rich information encoded in the KV pairs while avoiding the pitfalls of hidden states. We introduce a KV layer-wise selection strategy based on attention importance scores with a Gaussian prior to identify the most informative KV pairs for communication. Extensive experiments across diverse tasks and model pairs demonstrate that KVComm achieves comparable performance to the upper-bound method, which directly merges inputs to one model without any communication, while transmitting as few as 30\% of layers' KV pairs. Our study highlights the potential of KV pairs as an effective medium for inter-LLM communication, paving the way for scalable and efficient multi-agent systems.

The quadratic computational complexity of the standard attention mechanism constitutes a fundamental bottleneck for large language models in long-context inference. While existing KV cache compression methods alleviate memory pressure, they often sacrifice generation quality and fail to address the high overhead of floating-point arithmetic. This paper introduces DASH-KV, an innovative acceleration framework that reformulates attention as approximate nearest-neighbor search via asymmetric deep hashing. Under this paradigm, we design an asymmetric encoding architecture that differentially maps queries and keys to account for their distinctions in precision and reuse characteristics. To balance efficiency and accuracy, we further introduce a dynamic mixed-precision mechanism that adaptively retains full-precision computation for critical tokens. Extensive experiments on LongBench demonstrate that DASH-KV significantly outperforms state-of-the-art baseline methods while matching the performance of full attention, all while reducing inference complexity from O(N^2) to linear O(N). The code is available at https://github.com/Zhihan-Zh/DASH-KV

Multi-agent LLM applications organize execution in synchronized rounds where a central scheduler gathers outputs from all agents and redistributes the combined context. This All-Gather communication pattern creates massive KV Cache redundancy, because every agent's prompt contains the same shared output blocks, yet existing reuse methods fail to exploit it efficiently. We present TokenDance, a system that scales the number of concurrent agents by exploiting the All-Gather pattern for collective KV Cache sharing. TokenDance's KV Collector performs KV Cache reuse over the full round in one collective step, so the cost of reusing a shared block is paid once regardless of agent count. Its Diff-Aware Storage encodes sibling caches as block-sparse diffs against a single master copy, achieving 11-17x compression on representative workloads. Evaluation on GenerativeAgents and AgentSociety shows that TokenDance supports up to 2.7x more concurrent agents than vLLM with prefix caching under SLO requirement, reduces per-agent KV Cache storage by up to 17.5x, and achieves up to 1.9x prefill speedup over per-request position-independent caching.

Inference with transformer-based language models begins with a prompt processing step. In this step, the model generates the first output token and stores the KV cache needed for future generation steps. This prompt processing step can be computationally expensive, taking 10s of seconds or more for billion-parameter models on edge devices when prompt lengths or batch sizes rise. This degrades user experience by introducing significant latency into the model's outputs. To reduce the time spent producing the first output (known as the ``time to first token'', or TTFT) of a pretrained model, we introduce a novel method called KV Prediction. In our method, a small auxiliary model is used to process the prompt and produce an approximation of the KV cache used by a base model. This approximated KV cache is then used with the base model for autoregressive generation without the need to query the auxiliary model again. We demonstrate that our method produces a pareto-optimal efficiency-accuracy trade-off when compared to baselines. On TriviaQA, we demonstrate relative accuracy improvements in the range of 15%-50% across a range of TTFT FLOPs budgets. We also demonstrate accuracy improvements of up to 30% on HumanEval python code completion at fixed TTFT FLOPs budgets. Additionally, we benchmark models on an Apple M2 Pro CPU and demonstrate that our improvement in FLOPs translates to a TTFT speedup on hardware. We release our code at https://github.com/apple/corenet/tree/main/projects/kv-prediction .

The increasing complexity of AI tasks has shifted the paradigm from monolithic models toward multi-agent large language model (LLM) systems. However, these collaborative architectures introduce a critical bottleneck: redundant prefill computation for shared content generated by previous agents, which significantly increases KV cache memory usage and time-to-first-token (TTFT). While various KV cache methods have been proposed to mitigate prefill redundancy, they either fail to maintain accuracy on agent-generated outputs or exhibit low reuse rates due to rigid constraints. We present RelayCaching, a training-free inference method that directly reuses decoding phase KV caches from previous agents in subsequent prefill phases. Our key insight is that KV caches for identical content are highly consistent across phases, while prefix-induced deviations are sparse and localized within a limited range of layers and token positions. By selectively recomputing KV caches at these positions, RelayCaching preserves model accuracy with minimal overhead, yielding a superior accuracy-efficiency trade-off over existing methods. Experiments on diverse collaborative LLM tasks spanning mathematical reasoning, general knowledge, and code generation demonstrate that RelayCaching achieves over 80% KV cache reuse, reduces TTFT by up to 4.7times compared to the standard pipeline, all with negligible accuracy degradation.

The key-value (KV) cache is widely treated as essential state in transformer inference, and a large body of work engineers policies to compress, evict, or approximate its entries. We prove that this state is entirely redundant: keys and values at every layer are deterministic projections of the residual stream, and recomputing them from a single residual vector per token incurs exactly zero reconstruction error, not approximately, but bit-identically. We verify this across six models from four architecture families (135M to 4B parameters). Cross-task residual patching at every layer produces D_KL = 0 between patched and original output distributions, confirming that the residual stream satisfies a Markov property and is the sole information-carrying state. Removing the cache entirely and recomputing from scratch yields token-identical output under greedy decoding on all models tested. We build on this result with KV-Direct, a bounded-memory inference scheme that checkpoints residual vectors (5 KB per token on Gemma 3-4B) instead of full KV pairs (136 KB), recomputing keys and values on demand. Over 20 conversation turns, KV-Direct holds peak memory at 42 MB while the standard cache grows past 103 MB. Against five eviction baselines (H2O, StreamingLLM, SnapKV, TOVA, window-only), KV-Direct maintains 100% token match at every cache budget; all baselines degrade to 5-28%. A per-operation latency analysis shows recomputation runs up to 5x faster than reading cached tensors at moderate batch sizes. Code is available at https://github.com/Kaleemullahqasim/KV-Direct.

Constraint handling remains a key bottleneck in quantum combinatorial optimization. While slack-variable-based encodings are straightforward, they significantly increase qubit counts and circuit depth, challenging the scalability of quantum solvers. In this work, we investigate a suite of Lagrangian-based optimization techniques including dual ascent, bundle methods, cutting plane approaches, and augmented Lagrangian formulations for solving constrained combinatorial problems on quantum simulators and hardware. Our framework is applied to three representative NP-hard problems: the Travelling Salesman Problem (TSP), the Multi-Dimensional Knapsack Problem (MDKP), and the Maximum Independent Set (MIS). We demonstrate that MDKP and TSP, with their inequality-based or degree-constrained structures, allow for slack-free reformulations, leading to significant qubit savings without compromising performance. In contrast, MIS does not inherently benefit from slack elimination but still gains in feasibility and objective quality from principled Lagrangian updates. We benchmark these methods across classically hard instances, analyzing trade-offs in qubit usage, feasibility, and optimality gaps. Our results highlight the flexibility of Lagrangian formulations as a scalable alternative to naive QUBO penalization, even when qubit savings are not always achievable. This work provides practical insights for deploying constraint-aware quantum optimization pipelines, with applications in logistics, network design, and resource allocation.

Video generation is pivotal to digital media creation, and recent advances in autoregressive video generation have markedly enhanced the efficiency of real-time video synthesis. However, existing approaches generally rely on heuristic KV Cache policies, which ignore differences in token importance in long-term video generation. This leads to the loss of critical spatiotemporal information and the accumulation of redundant, invalid cache, thereby degrading video generation quality and efficiency. To address this limitation, we first observe that token contributions to video generation are highly time-heterogeneous and accordingly propose a novel Past- and Future-Informed KV Cache Policy (PaFu-KV). Specifically, PaFu-KV introduces a lightweight Salience Estimation Head distilled from a bidirectional teacher to estimate salience scores, allowing the KV cache to retain informative tokens while discarding less relevant ones. This policy yields a better quality-efficiency trade-off by shrinking KV cache capacity and reducing memory footprint at inference time. Extensive experiments on benchmarks demonstrate that our method preserves high-fidelity video generation quality while enables accelerated inference, thereby enabling more efficient long-horizon video generation. Our code will be released upon paper acceptance.

We demonstrate that unstructured sparsity significantly improves KV cache compression for LLMs, enabling sparsity levels up to 70% without compromising accuracy or requiring fine-tuning. We conduct a systematic exploration of pruning strategies and find per-token magnitude-based pruning as highly effective for both Key and Value caches under unstructured sparsity, surpassing prior structured pruning schemes. The Key cache benefits from prominent outlier elements, while the Value cache surprisingly benefits from a simple magnitude-based pruning despite its uniform distribution. KV cache size is the major bottleneck in decode performance due to high memory overhead for large context lengths. To address this, we use a bitmap-based sparse format and a custom attention kernel capable of compressing and directly computing over compressed caches pruned to arbitrary sparsity patterns, significantly accelerating memory-bound operations in decode computations and thereby compensating for the overhead of runtime pruning and compression. Our custom attention kernel coupled with the bitmap-based format delivers substantial compression of KV cache upto 45% of dense inference and thereby enables longer context length and increased tokens/sec throughput of upto 2.23x compared to dense inference. Our pruning mechanism and sparse attention kernel is available at https://github.com/dhjoo98/mustafar.

Gaussian processes (GP) are one of the most successful frameworks to model uncertainty. However, GP optimization (e.g., GP-UCB) suffers from major scalability issues. Experimental time grows linearly with the number of evaluations, unless candidates are selected in batches (e.g., using GP-BUCB) and evaluated in parallel. Furthermore, computational cost is often prohibitive since algorithms such as GP-BUCB require a time at least quadratic in the number of dimensions and iterations to select each batch. In this paper, we introduce BBKB (Batch Budgeted Kernel Bandits), the first no-regret GP optimization algorithm that provably runs in near-linear time and selects candidates in batches. This is obtained with a new guarantee for the tracking of the posterior variances that allows BBKB to choose increasingly larger batches, improving over GP-BUCB. Moreover, we show that the same bound can be used to adaptively delay costly updates to the sparse GP approximation used by BBKB, achieving a near-constant per-step amortized cost. These findings are then confirmed in several experiments, where BBKB is much faster than state-of-the-art methods.

Adversarial attacks expose important vulnerabilities of deep learning models, yet little attention has been paid to settings where data arrives as a stream. In this paper, we formalize the online adversarial attack problem, emphasizing two key elements found in real-world use-cases: attackers must operate under partial knowledge of the target model, and the decisions made by the attacker are irrevocable since they operate on a transient data stream. We first rigorously analyze a deterministic variant of the online threat model by drawing parallels to the well-studied k-secretary problem in theoretical computer science and propose Virtual+, a simple yet practical online algorithm. Our main theoretical result shows Virtual+ yields provably the best competitive ratio over all single-threshold algorithms for k<5 -- extending the previous analysis of the k-secretary problem. We also introduce the stochastic k-secretary -- effectively reducing online blackbox transfer attacks to a k-secretary problem under noise -- and prove theoretical bounds on the performance of Virtual+ adapted to this setting. Finally, we complement our theoretical results by conducting experiments on MNIST, CIFAR-10, and Imagenet classifiers, revealing the necessity of online algorithms in achieving near-optimal performance and also the rich interplay between attack strategies and online attack selection, enabling simple strategies like FGSM to outperform stronger adversaries.

We give a simple, fully correct, and assumption-light replacement for the contested "domain-extension" in Step 9 of a recent windowed-QFT lattice algorithm with complex-Gaussian windows~chen2024quantum. The published Step~9 suffers from a periodicity/support mismatch. We present a pair-shift difference construction that coherently cancels all unknown offsets, produces an exact uniform CRT-coset state over Z_{P}, and then uses the QFT to enforce the intended modular linear relation. The unitary is reversible, uses poly(log M_2) gates, and preserves the algorithm's asymptotics. Project Page: https://github.com/yifanzhang-pro/quantum-lattice.

Block attention, which processes the input as separate blocks that cannot attend to one another, offers significant potential to improve KV cache reuse in long-context scenarios such as Retrieval-Augmented Generation (RAG). However, its broader application is hindered by two key challenges: the difficulty of segmenting input text into meaningful, self-contained blocks, and the inefficiency of existing block fine-tuning methods that risk degrading performance. To address these, we first construct SemanticSeg, a large and diverse semantic segmentation dataset containing over 30k instances across 16 categories-including books, code, web text, and conversations with text lengths ranging from 2k to 32k. Using this dataset, we train a lightweight segmenter to automatically partition text into human-instinct-aligned blocks with controllable granularity. Second, we propose block distillation, a training framework that is more efficient than block fine-tuning, which uses a frozen full-attention teacher model to guide the block-attention student. This framework integrates three novel components: block sink tokens to mitigate information loss at block boundaries, block dropout to leverage training signals from all blocks, and token-level loss weighting to focus learning on block-attention-sensitive tokens. Experiments across multiple models and benchmarks demonstrate that our segmenter outperforms heuristic and statistical baselines, and block distillation achieves near-full-attention performance under block attention, establishing a practical and scalable pathway for deploying block attention.

Block-causal video generation faces a stark speed-quality trade-off: small 1.3B models manage only 16 FPS while large 14B models crawl at 4.5 FPS, forcing users to choose between responsiveness and quality. Block Cascading significantly mitigates this trade-off through training-free parallelization. Our key insight: future video blocks do not need fully denoised current blocks to begin generation. By starting block generation with partially denoised context from predecessors, we transform sequential pipelines into parallel cascades where multiple blocks denoise simultaneously. With 5 GPUs exploiting temporal parallelism, we achieve ~2x acceleration across all model scales: 1.3B models accelerate from 16 to 30 FPS, 14B models from 4.5 to 12.5 FPS. Beyond inference speed, Block Cascading eliminates overhead from KV-recaching (of ~200ms) during context switches for interactive generation. Extensive evaluations validated against multiple block-causal pipelines demonstrate no significant loss in generation quality when switching from block-causal to Block Cascading pipelines for inference. Project Page: https://hmrishavbandy.github.io/block_cascading_page/

Disaggregated inference has become an essential framework that separates the prefill (P) and decode (D) stages in large language model inference to improve throughput. However, the KV cache transfer faces significant delays between prefill and decode nodes. The block-wise calling method and discontinuous KV cache memory allocation increase the number of calls to the transmission kernel. Additionally, existing frameworks often fix the roles of P and D nodes, leading to computational imbalances. In this paper, we propose FlowKV, a novel disaggregated inference framework, which reduces the average transmission latency of KV cache by 96%, from 0.944s to 0.053s, almost eliminating the transfer time relative to the total request latency by optimizing the KV cache transfer. FlowKV introduces the Load-Aware Scheduler for balanced request scheduling and flexible PD node allocation. This design maximizes hardware resource utilization, achieving peak system throughput across various scenarios, including normal, computational imbalance, and extreme overload conditions. Experimental results demonstrate that FlowKV significantly accelerates inference by 15.2%-48.9% on LongBench dataset compared to the baseline and supports applications with heterogeneous GPUs.

Key-Value (KV) cache facilitates efficient large language models (LLMs) inference by avoiding recomputation of past KVs. As the batch size and context length increase, the oversized KV caches become a significant memory bottleneck, highlighting the need for efficient compression. Existing KV quantization rely on fine-grained quantization or the retention of a significant portion of high bit-widths caches, both of which compromise compression ratio and often fail to maintain robustness at extremely low average bit-widths. In this work, we explore the potential of rotation technique for 2-bit KV quantization and propose RotateKV, which achieves accurate and robust performance through the following innovations: (i) Outlier-Aware Rotation, which utilizes channel-reordering to adapt the rotations to varying channel-wise outlier distributions without sacrificing the computational efficiency of the fast Walsh-Hadamard transform (FWHT); (ii) Pre-RoPE Grouped-Head Rotation, which mitigates the impact of rotary position embedding (RoPE) on proposed outlier-aware rotation and further smooths outliers across heads; (iii) Attention-Sink-Aware Quantization, which leverages the massive activations to precisely identify and protect attention sinks. RotateKV achieves less than 0.3 perplexity (PPL) degradation with 2-bit quantization on WikiText-2 using LLaMA-2-13B, maintains strong CoT reasoning and long-context capabilities, with less than 1.7\% degradation on GSM8K, outperforming existing methods even at lower average bit-widths. RotateKV also showcases a 3.97x reduction in peak memory usage, supports 5.75x larger batch sizes, and achieves a 2.32x speedup in decoding stage.

KV cache compression promises increased throughput and efficiency with negligible loss in performance. While the gains in throughput are indisputable and recent literature has indeed shown minimal degradation on particular benchmarks, in general the consequences of compression in realistic scenarios such as multi-instruction prompting have been insufficiently studied. In this paper, we identify several pitfalls practitioners should be aware of when deploying KV cache compressed LLMs. Importantly, we show that certain instructions degrade much more rapidly with compression, effectively causing them to be completely ignored by the LLM. As a practical example of that, we highlight system prompt leakage as a case study, empirically showing the impact of compression on leakage and general instruction following. We show several factors that play a role in prompt leakage: compression method, instruction order, and KV eviction bias. We then propose simple changes to KV cache eviction policies that can reduce the impact of these factors and improve the overall performance in multi-instruction tasks.

Large Language Models (LLMs), despite their recent impressive accomplishments, are notably cost-prohibitive to deploy, particularly for applications involving long-content generation, such as dialogue systems and story writing. Often, a large amount of transient state information, referred to as the KV cache, is stored in GPU memory in addition to model parameters, scaling linearly with the sequence length and batch size. In this paper, we introduce a novel approach for implementing the KV cache which significantly reduces its memory footprint. Our approach is based on the noteworthy observation that a small portion of tokens contributes most of the value when computing attention scores. We call these tokens Heavy Hitters (H_2). Through a comprehensive investigation, we find that (i) the emergence of H_2 is natural and strongly correlates with the frequent co-occurrence of tokens in the text, and (ii) removing them results in significant performance degradation. Based on these insights, we propose Heavy Hitter Oracle (H_2O), a KV cache eviction policy that dynamically retains a balance of recent and H_2 tokens. We formulate the KV cache eviction as a dynamic submodular problem and prove (under mild assumptions) a theoretical guarantee for our novel eviction algorithm which could help guide future work. We validate the accuracy of our algorithm with OPT, LLaMA, and GPT-NeoX across a wide range of tasks. Our implementation of H_2O with 20% heavy hitters improves the throughput over three leading inference systems DeepSpeed Zero-Inference, Hugging Face Accelerate, and FlexGen by up to 29times, 29times, and 3times on OPT-6.7B and OPT-30B. With the same batch size, H2O can reduce the latency by up to 1.9times. The code is available at https://github.com/FMInference/H2O.

Large Language Models (LLMs) rely on the Key-Value (KV) Cache to store token history, enabling efficient decoding of tokens. As the KV-Cache grows, it becomes a major memory and computation bottleneck, however, there is an opportunity to alleviate this bottleneck, especially because prior research has shown that only a small subset of tokens contribute meaningfully to each decoding step. A key challenge in finding these critical tokens is that they are dynamic, and heavily input query-dependent. Existing methods either risk quality by evicting tokens permanently, or retain the full KV-Cache but rely on retrieving chunks (pages) of tokens at generation, failing at dense, context-rich tasks. Additionally, many existing KV-Cache sparsity methods rely on inaccurate proxies for token importance. To address these limitations, we introduce TokenButler, a high-granularity, query-aware predictor that learns to identify these critical tokens. By training a light-weight predictor with less than 1.2% parameter overhead, TokenButler prioritizes tokens based on their contextual, predicted importance. This improves perplexity & downstream accuracy by over 8% relative to SoTA methods for estimating token importance. We evaluate TokenButler on a novel synthetic small-context co-referential retrieval task, demonstrating near-oracle accuracy. Code, models and benchmarks: https://github.com/abdelfattah-lab/TokenButler

As quantum hardware scales toward fault tolerant operation, the demand for correct quantum error correction (QEC) circuits far outpaces manual design capacity. AI agents offer a promising path to automating this synthesis, yet no benchmark exists to measure their progress on the specialized task of generating QEC circuits. We introduce StabilizerBench, a benchmark suite of 192 stabilizer codes spanning 12 families, 4-196 qubits, and distances 2-21, organized into three tasks of increasing difficulty: state preparation circuit generation, circuit optimization under semantic constraints, and fault tolerant circuit synthesis. Although motivated by QEC, stabilizer circuits exercise core competencies required for general quantum programming, including gate decomposition, qubit routing, and semantic preserving transformations, while admitting efficient verification via the Gottesman Knill theorem, enabling the benchmark to scale to large codes without the exponential cost of full unitary comparison. We define a unified generator weighted scoring system with two tiers: a capability score measuring breadth of success and a quality score capturing circuit merit. We also introduce continuous fault tolerance and optimization metrics that grade error resilience and circuit improvements beyond binary pass or fail. Following the design of classical benchmarks such as SWE-bench, StabilizerBench specifies inputs, verification oracles, and scoring but leaves prompts and agent strategies open. We evaluate three frontier AI agents and find the benchmark discriminates across models and tasks with substantial headroom for improvement.

In this paper, we consider non-convex multi-block bilevel optimization (MBBO) problems, which involve mgg 1 lower level problems and have important applications in machine learning. Designing a stochastic gradient and controlling its variance is more intricate due to the hierarchical sampling of blocks and data and the unique challenge of estimating hyper-gradient. We aim to achieve three nice properties for our algorithm: (a) matching the state-of-the-art complexity of standard BO problems with a single block; (b) achieving parallel speedup by sampling I blocks and sampling B samples for each sampled block per-iteration; (c) avoiding the computation of the inverse of a high-dimensional Hessian matrix estimator. However, it is non-trivial to achieve all of these by observing that existing works only achieve one or two of these properties. To address the involved challenges for achieving (a, b, c), we propose two stochastic algorithms by using advanced blockwise variance-reduction techniques for tracking the Hessian matrices (for low-dimensional problems) or the Hessian-vector products (for high-dimensional problems), and prove an iteration complexity of O(mepsilon^{-3I(I<m)}{II} + mepsilon^{-3}{IB}) for finding an epsilon-stationary point under appropriate conditions. We also conduct experiments to verify the effectiveness of the proposed algorithms comparing with existing MBBO algorithms.

In this note we establish a 1-to-1 correspondence between the class of generalized quadrangles with ovoids and the class of balanced incomplete block designs that posses a non-triangular local resolution system and have the appropriate parameters. We present a non-triangular local resolution system for a difference family BIBD construction of Sprott.

We study sets of delta tubes in R^3, with the property that not too many tubes can be contained inside a common convex set V. We show that the union of tubes from such a set must have almost maximal volume. As a consequence, we prove that every Kakeya set in R^3 has Minkowski and Hausdorff dimension 3.

Quantum algorithms based on variational approaches are one of the most promising methods to construct quantum solutions and have found a myriad of applications in the last few years. Despite the adaptability and simplicity, their scalability and the selection of suitable ans\"atzs remain key challenges. In this work, we report an algorithmic framework based on nested Monte-Carlo Tree Search (MCTS) coupled with the combinatorial multi-armed bandit (CMAB) model for the automated design of quantum circuits. Through numerical experiments, we demonstrated our algorithm applied to various kinds of problems, including the ground energy problem in quantum chemistry, quantum optimisation on a graph, solving systems of linear equations, and finding encoding circuit for quantum error detection codes. Compared to the existing approaches, the results indicate that our circuit design algorithm can explore larger search spaces and optimise quantum circuits for larger systems, showing both versatility and scalability.

One-shot coreset selection aims to select a representative subset of the training data, given a pruning rate, that can later be used to train future models while retaining high accuracy. State-of-the-art coreset selection methods pick the highest importance examples based on an importance metric and are found to perform well at low pruning rates. However, at high pruning rates, they suffer from a catastrophic accuracy drop, performing worse than even random sampling. This paper explores the reasons behind this accuracy drop both theoretically and empirically. We first propose a novel metric to measure the coverage of a dataset on a specific distribution by extending the classical geometric set cover problem to a distribution cover problem. This metric helps explain why coresets selected by SOTA methods at high pruning rates perform poorly compared to random sampling because of worse data coverage. We then propose a novel one-shot coreset selection method, Coverage-centric Coreset Selection (CCS), that jointly considers overall data coverage upon a distribution as well as the importance of each example. We evaluate CCS on five datasets and show that, at high pruning rates (e.g., 90%), it achieves significantly better accuracy than previous SOTA methods (e.g., at least 19.56% higher on CIFAR10) as well as random selection (e.g., 7.04% higher on CIFAR10) and comparable accuracy at low pruning rates. We make our code publicly available at https://github.com/haizhongzheng/Coverage-centric-coreset-selection.

Finite unions of convex sets are a central object of study in discrete and computational geometry. In this paper we initiate a systematic study of complements of such unions -- i.e., sets of the form S=R^d setminus (cup_{i=1}^n K_i), where K_i are convex sets. In the first part of the paper we study isolated points in S, whose number is related to the Betti numbers of cup_{i=1}^n K_i and to its non-convexity properties. We obtain upper bounds on the number of such points, which are sharp for n=3 and significantly improve previous bounds of Lawrence and Morris (2009) for all n ll 2^d{d}. In the second part of the paper we study coverings of S by well-behaved sets. We show that S can be covered by at most g(d,n) flats of different dimensions, in such a way that each x in S is covered by a flat whose dimension equals the `local dimension' of S in the neighborhood of x. Furthermore, we determine the structure of a minimum cover that satisfies this property. Then, we study quantitative aspects of this minimum cover and obtain sharp upper bounds on its size in various settings.

This paper presents a parallel random-search method for reducing additive complexity in fast matrix multiplication. The approach replaces expensive exact evaluation with fast heuristic scoring, including the new Greedy-Intersections strategy. The method runs many independent common subexpression elimination processes in parallel, exploring the search space through random pair substitutions and diverse selection strategies while sharing promising partial solutions. Tested on 164 ternary-coefficient schemes, the method achieves lower addition counts than the state-of-the-art Greedy-Potential on 103 schemes, matches it on 59, and is outperformed on 2. For most schemes, it gives equal or better results while being much faster, making it practical for algorithm exploration. All software and results are open source.

Serving disaggregated large language models (LLMs) over tens of thousands of xPU devices (GPUs or NPUs) with reliable performance faces multiple challenges. 1) Ignoring the diversity (various prefixes and tidal requests), treating all the prompts in a mixed pool is inadequate. To facilitate the similarity per scenario and minimize the inner mismatch on P/D (prefill and decoding) processing, fine-grained organization is required, dynamically adjusting P/D ratios for better performance. 2) Due to inaccurate estimation on workload (queue status or maintained connections), the global scheduler easily incurs unnecessary timeouts in prefill. 3) Block-fixed device-to-device (D2D) KVCache transfer over cluster-level RDMA (remote direct memory access) fails to achieve desired D2D utilization as expected. To overcome previous problems, this paper proposes an end-to-end system P/D-Serve, complying with the paradigm of MLOps (machine learning operations), which models end-to-end (E2E) P/D performance and enables: 1) fine-grained P/D organization, mapping the service with RoCE (RDMA over converged ethernet) as needed, to facilitate similar processing and dynamic adjustments on P/D ratios; 2) on-demand forwarding upon rejections for idle prefill, decoupling the scheduler from regular inaccurate reports and local queues, to avoid timeouts in prefill; and 3) efficient KVCache transfer via optimized D2D access. P/D-Serve is implemented upon Ascend and MindSpore, has been deployed over tens of thousands of NPUs for more than eight months in commercial use, and further achieves 60\%, 42\% and 46\% improvements on E2E throughput, time-to-first-token (TTFT) SLO (service level objective) and D2D transfer time. As the E2E system with optimizations, P/D-Serve achieves 6.7x increase on throughput, compared with aggregated LLMs.

An open-source C++ framework for discovering fast matrix multiplication schemes using the flip graph approach is presented. The framework supports multiple coefficient rings -- binary (Z_2), modular ternary (Z_3) and integer ternary (Z_T = {-1,0,1}) -- and implements both fixed-dimension and meta-dimensional search operators. Using efficient bit-level encoding of coefficient vectors and OpenMP parallelism, the tools enable large-scale exploration on commodity hardware. The study covers 680 schemes ranging from (2 times 2 times 2) to (16 times 16 times 16), with 276 schemes now in Z_T coefficients and 117 in integer coefficients. With this framework, the multiplicative complexity (rank) is improved for 79 matrix multiplication schemes. Notably, a new 4 times 4 times 10 scheme requiring only 115 multiplications is discovered, achieving ωapprox 2.80478 and beating Strassen's exponent for this specific size. Additionally, 93 schemes are rediscovered in ternary coefficients that were previously known only over rationals or integers, and 68 schemes in integer coefficients that previously required fractions. All tools and discovered schemes are made publicly available to enable reproducible research.

Vector quantization, a problem rooted in Shannon's source coding theory, aims to quantize high-dimensional Euclidean vectors while minimizing distortion in their geometric structure. We propose TurboQuant to address both mean-squared error (MSE) and inner product distortion, overcoming limitations of existing methods that fail to achieve optimal distortion rates. Our data-oblivious algorithms, suitable for online applications, achieve near-optimal distortion rates (within a small constant factor) across all bit-widths and dimensions. TurboQuant achieves this by randomly rotating input vectors, inducing a concentrated Beta distribution on coordinates, and leveraging the near-independence property of distinct coordinates in high dimensions to simply apply optimal scalar quantizers per each coordinate. Recognizing that MSE-optimal quantizers introduce bias in inner product estimation, we propose a two-stage approach: applying an MSE quantizer followed by a 1-bit Quantized JL (QJL) transform on the residual, resulting in an unbiased inner product quantizer. We also provide a formal proof of the information-theoretic lower bounds on best achievable distortion rate by any vector quantizer, demonstrating that TurboQuant closely matches these bounds, differing only by a small constant (approx 2.7) factor. Experimental results validate our theoretical findings, showing that for KV cache quantization, we achieve absolute quality neutrality with 3.5 bits per channel and marginal quality degradation with 2.5 bits per channel. Furthermore, in nearest neighbor search tasks, our method outperforms existing product quantization techniques in recall while reducing indexing time to virtually zero.

Efficient key-value (KV) cache management is crucial for the practical deployment of large language models (LLMs), yet existing compression techniques often incur a trade-off between performance degradation and computational overhead. We propose a novel gating-based KV cache eviction method for frozen-weight LLMs that achieves high compression ratios with negligible computational cost. Our approach introduces lightweight sink-attention gating modules to identify and retain critical KV pairs, and integrates seamlessly into both the prefill and decoding stages. The proposed gate training algorithm relies on forward passes of an LLM, avoiding expensive backpropagation, while achieving strong task generalization through a task-agnostic reconstruction objective. Extensive experiments across the Qwen2.5-1M, Qwen3, and Gemma3 families show that our method maintains near-lossless performance while evicting up to 70% of the KV cache. The results are consistent across a wide range of tasks, including long-context understanding, code comprehension, and mathematical reasoning, demonstrating the generality of our approach.

While Key-Value (KV) cache succeeds in reducing redundant computations in auto-regressive models, it introduces significant memory overhead, limiting its practical deployment in long-sequence scenarios. Existing KV retrieval methods mitigate this by dynamically retaining only a subset of KV entries on the GPU. However, they still suffer from notable efficiency and accuracy bottlenecks due to per-token retrieval and coarse-grained page-level KV management, especially in long-output reasoning scenarios. With the emergence of large reasoning models, efficiently handling such scenarios has become increasingly important. To address this issue, we present two key observations: (1) critical KVs exhibit strong temporal locality during decoding, and (2) these KVs exhibit distinct distribution patterns across the input prompt and generated output. Building on these observations, we propose LouisKV, an efficient KV cache retrieval framework designed for various long-sequence scenarios. Specifically, LouisKV introduces a semantic-aware retrieval strategy leveraging temporal locality to trigger retrieval only at semantic boundaries, drastically reducing computation and data transfer overhead. LouisKV also designs a decoupled, fine-grained management scheme that tailors differentiated strategies for input and output sequences to create retrieval units that better match the model's attention patterns, enabling precise identification of critical KVs. Furthermore, to boost efficiency, LouisKV incorporates several kernel-level optimizations, including custom Triton and CUDA kernels to accelerate the KV clustering and retrieval. Evaluations show that LouisKV achieves up to 4.7times speedup over state-of-the-art KV retrieval methods while maintaining near-lossless accuracy across diverse long-sequence tasks, including long-input short-output, short-input long-output, and long-input long-output scenarios.

High-dimensional datasets require effective feature selection to improve predictive performance, interpretability, and robustness. We propose and evaluate feature selection methods for tabular datasets based on Kolmogorov-Arnold networks (KANs), which parameterize feature transformations through splines, enabling direct access to interpretable importance measures. We introduce four KAN-based selectors (KAN-L1, KAN-L2, KAN-SI, KAN-KO) and compare them against classical baselines (LASSO, Random Forest, Mutual Information, SVM-RFE) across multiple classification and regression tabular dataset benchmarks. Average (over three retention levels: 20\%, 40\%, and 60\%) F1 scores and R^2 score results reveal that KAN-based selectors, particularly KAN-L2, KAN-L1, KAN-SI, and KAN-KO, are competitive with and sometimes superior to classical baselines in structured and synthetic datasets. However, KAN-L1 is often too aggressive in regression, removing useful features, while KAN-L2 underperforms in classification, where simple coefficient shrinkage misses complex feature interactions. KAN-L2 and KAN-SI provide robust performance on noisy regression datasets and heterogeneous datasets, aligning closely with ensemble predictors. In classification tasks, KAN selectors such as KAN-L1, KAN-KO, and KAN-SI sometimes surpass the other selectors by eliminating redundancy, particularly in high-dimensional multi-class data. Overall, our findings demonstrate that KAN-based feature selection provides a powerful and interpretable alternative to traditional methods, capable of uncovering nonlinear and multivariate feature relevance beyond sparsity or impurity-based measures.

Matryoshka Quantization (MatQuant) is a recent quantization approach showing that a single integer-quantized model can be served across multiple precisions, by slicing the most significant bits (MSB) at inference time. This enables a single checkpoint to cover a wide range of memory and latency budgets, but renders quantization much more challenging. In particular, the initial MatQuant relies on expensive quantization-aware training (QAT) variants, rather than fast one-shot post training quantization (PTQ), and lacks open-source and kernel support. We address all of these limitations by introducing Post-Training Matryoshka Quantization (MatGPTQ), a new PTQ pipeline that produces a single parent model jointly optimized for multiple target precisions in one-shot, based on a small calibration set. MatGPTQ casts Matryoshka quantization as a multi-precision objective with bit-slicing and cross-bit error compensation, resulting in an algorithm that produces a multi-bit-width, "sliceable" model in a single pass. We also incorporate a new budget-aware search for heterogeneous per-layer bit-witdhs and provide efficient kernels that implement slicing and mixed-precision execution. Across standard LLMs and benchmarks, MatGPTQ preserves high-bit accuracy while substantially improving performance at low-bit-witdh settings. Overall, we establish a new state of the art for Matryoshka-style post-training quantization and make single-checkpoint, multi-precision deployment open and practical. Code is available at https://github.com/IST-DASLab/MatGPTQ.

We present PolyKV, a system in which multiple concurrent inference agents share a single, asymmetrically compressed KV cache pool. Rather than allocating a separate KV cache per agent -- the standard paradigm -- PolyKV writes a compressed cache once and injects it into N independent agent contexts via HuggingFace DynamicCache objects. Compression is asymmetric: Keys are quantized at int8 (q8_0) to preserve softmax stability, while Values are compressed using TurboQuant MSE -- a Fast Walsh-Hadamard Transform (FWHT) rotation followed by 3-bit Lloyd-Max quantization with centroids tuned to N(0,1). We evaluate across two model scales (SmolLM2-1.7B-Instruct and Llama-3-8B-Instruct), three context lengths (600-7,194 tokens), and up to 15 concurrent agents. PolyKV achieves a stable 2.91x compression ratio across all configurations. On Llama-3-8B with 15 agents sharing a 4K-token context, PolyKV reduces KV cache memory from 19.8 GB to 0.45 GB -- a 97.7% reduction -- while maintaining only +0.57% perplexity degradation and a mean BERTScore F1 of 0.928. PPL delta does not grow with agent count and improves as context length increases, inverting to -0.26% at 1,851 coherent tokens. To our knowledge, no prior work combines a single shared, lossy-compressed KV pool with multi-reader concurrent agent access.

Large Language Models (LLMs) have revolutionized a wide range of domains such as natural language processing, computer vision, and multi-modal tasks due to their ability to comprehend context and perform logical reasoning. However, the computational and memory demands of LLMs, particularly during inference, pose significant challenges when scaling them to real-world, long-context, and real-time applications. Key-Value (KV) cache management has emerged as a critical optimization technique for accelerating LLM inference by reducing redundant computations and improving memory utilization. This survey provides a comprehensive overview of KV cache management strategies for LLM acceleration, categorizing them into token-level, model-level, and system-level optimizations. Token-level strategies include KV cache selection, budget allocation, merging, quantization, and low-rank decomposition, while model-level optimizations focus on architectural innovations and attention mechanisms to enhance KV reuse. System-level approaches address memory management, scheduling, and hardware-aware designs to improve efficiency across diverse computing environments. Additionally, the survey provides an overview of both text and multimodal datasets and benchmarks used to evaluate these strategies. By presenting detailed taxonomies and comparative analyses, this work aims to offer useful insights for researchers and practitioners to support the development of efficient and scalable KV cache management techniques, contributing to the practical deployment of LLMs in real-world applications. The curated paper list for KV cache management is in: https://github.com/TreeAI-Lab/Awesome-KV-Cache-Management{https://github.com/TreeAI-Lab/Awesome-KV-Cache-Management}.

The K-core of a graph is the unique maximum subgraph within which each vertex connects to K or more other vertices. The optimal K-core attack problem asks to delete the minimum number of vertices from the K-core to induce its complete collapse. A hierarchical cycle-tree packing model is introduced here for this challenging combinatorial optimization problem. We convert the temporally long-range correlated K-core pruning dynamics into locally tree-like static patterns and analyze this model through the replica-symmetric cavity method of statistical physics. A set of coarse-grained belief propagation equations are derived to predict single vertex marginal probabilities efficiently. The associated hierarchical cycle-tree guided attack ({\tt hCTGA}) algorithm is able to construct nearly optimal attack solutions for regular random graphs and Erd\"os-R\'enyi random graphs. Our cycle-tree packing model may also be helpful for constructing optimal initial conditions for other irreversible dynamical processes on sparse random graphs.

Large language models (LLMs) are increasingly utilized for complex tasks requiring longer context lengths, with some models supporting up to 128K or 1M tokens. This trend, however, presents significant challenges in inference speed and memory management. Quantization emerges as a promising approach to address the widening gap between LLM size and memory capacity. However, traditional quantization schemes often yield suboptimal compression results for KV caches due to two key factors: i) On-the-fly quantization and de-quantization, causing significant performance overhead; ii) Prevalence of outliers in KV values, challenging low-bitwidth uniform quantization. To this end, we propose MILLION, a novel quantization framework achieving low-bitwidth KV cache through product quantization. First, we conduct a thorough analysis of KV cache distribution, revealing the limitations of existing quantization schemes. Second, we introduce a non-uniform quantization algorithm based on product quantization, which efficiently compresses data while preserving accuracy. Third, we develop a high-performance GPU inference framework with efficient attention kernel and pipeline design for MILLION that leverages sparse computation and asynchronous quantization, significantly enhancing inference speed. Comprehensive evaluation results demonstrate that MILLION can achieve 4 bits quantization with trivial perplexity and accuracy loss, and achieve 2.09x end-to-end performance gains at 32K context length. Code is released at https://github.com/ZongwuWang/MILLION.

The Entropic Optimal Transport (EOT) problem and its dynamic counterpart, the Schrödinger bridge (SB) problem, play an important role in modern machine learning, linking generative modeling with optimal transport theory. While recent advances in discrete diffusion and flow models have sparked growing interest in applying SB methods to discrete domains, there is still no reliable way to evaluate how well these methods actually solve the underlying problem. We address this challenge by introducing a benchmark for SB on discrete spaces. Our construction yields pairs of probability distributions with analytically known SB solutions, enabling rigorous evaluation. As a byproduct of building this benchmark, we obtain two new SB algorithms, DLightSB and DLightSB-M, and additionally extend prior related work to construct the α-CSBM algorithm. We demonstrate the utility of our benchmark by evaluating both existing and new solvers in high-dimensional discrete settings. This work provides the first step toward proper evaluation of SB methods on discrete spaces, paving the way for more reproducible future studies.

This paper re-examines a continuous optimization framework dubbed NOTEARS for learning Bayesian networks. We first generalize existing algebraic characterizations of acyclicity to a class of matrix polynomials. Next, focusing on a one-parameter-per-edge setting, it is shown that the Karush-Kuhn-Tucker (KKT) optimality conditions for the NOTEARS formulation cannot be satisfied except in a trivial case, which explains a behavior of the associated algorithm. We then derive the KKT conditions for an equivalent reformulation, show that they are indeed necessary, and relate them to explicit constraints that certain edges be absent from the graph. If the score function is convex, these KKT conditions are also sufficient for local minimality despite the non-convexity of the constraint. Informed by the KKT conditions, a local search post-processing algorithm is proposed and shown to substantially and universally improve the structural Hamming distance of all tested algorithms, typically by a factor of 2 or more. Some combinations with local search are both more accurate and more efficient than the original NOTEARS.

The k-means++ seeding algorithm (Arthur & Vassilvitskii, 2007) is widely used in practice for the k-means clustering problem where the goal is to cluster a dataset X subset R ^d into k clusters. The popularity of this algorithm is due to its simplicity and provable guarantee of being O(log k) competitive with the optimal solution in expectation. However, its running time is O(|X|kd), making it expensive for large datasets. In this work, we present a simple and effective rejection sampling based approach for speeding up k-means++. Our first method runs in time O(nnz (X) + beta k^2d) while still being O(log k ) competitive in expectation. Here, beta is a parameter which is the ratio of the variance of the dataset to the optimal k-means cost in expectation and O hides logarithmic factors in k and |X|. Our second method presents a new trade-off between computational cost and solution quality. It incurs an additional scale-invariant factor of k^{-Omega( m/beta)} Var (X) in addition to the O(log k) guarantee of k-means++ improving upon a result of (Bachem et al, 2016a) who get an additional factor of m^{-1}Var(X) while still running in time O(nnz(X) + mk^2d). We perform extensive empirical evaluations to validate our theoretical results and to show the effectiveness of our approach on real datasets.