Context Compression

Transformer models can adapt to new tasks from input--output examples at inference time, a capability known as in-context learning (ICL). A common interpretation is that transformers implement implicit learning algorithms in their forward pass, using the context to infer the task and predict the query. We test this interpretation beyond the training distribution in controlled regression settings where classical estimators can generalize exactly. Transformers achieve near-perfect in-distribution ICL, but fail sharply under scale and support shifts, exhibiting a cliff-shaped collapse that is absent from least-squares and kernel baselines. This failure is robust across polynomial degrees and a range of training interventions. We identify two architectural mechanisms that help explain this behavior. First, final normalization imposes a readout-side scale constraint, causing predictions to saturate at fixed boundary values. Removing this constraint eliminates hard saturation, but does not restore reliable ICL under coefficient or label scaling. Second, attention can become a context bottleneck: under distribution shift, softmax attention may concentrate on a small part of the prompt, limiting the context-dependent adaptation required for ICL. These results show that strong in-distribution ICL does not imply distribution-independent ICL, and suggest caution when using ICL instead of explicit retraining or adaptation under distribution shift.

The effectiveness of modern deep learning models in forecasting *groups of time series* is often attributed to their ability to capture (long-range) dependencies across long observation windows. In this paper, we show that this forecasting task involves two objectives: (i) *generative process identification* (GPI), i.e., inferring the specific process generating the input sequence, and (ii) *conditional forecasting* (CF), i.e., predicting future values given input observations. From this perspective, optimal predictions can be interpreted as an average over plausible data-generating processes, weighted by their likelihood given the input window. This suggests a different explanation for the benefits of long context windows: they reduce the uncertainty about which specific process is generating the input time series during operation. We prove that even for processes with memory length $P$, an input window size strictly larger than $P$ is *necessary* to achieve the minimum attainable error. Finally, we show how decoupling GPI and CF can improve computational scalability without compromising accuracy. Experiments on synthetic and real-world data validate our insights and their relevance for designing forecasting architectures.

Scaling up model parameters has long been a prevalent training paradigm driven by the assumption that larger models yield superior generation capabilities. However, under lossy context compression in a compressor--decoder setup, we find a \textbf{\textit{Size-Fidelity Paradox}}: increasing compressor size can lessen the faithfulness of reconstructed contexts though reconstruction error decreases. Across 27 compressor setups spanning model families, scales, and compression rates, we coin this paradox arising from two dominant factors: 1) \textit{knowledge overwriting}: larger models increasingly replace source facts with their own prior beliefs, \textit{e.g.}, ``the white strawberry`` $\to$ ``the red strawberry``; and 2) \textit{semantic drift}: larger models tend to paraphrase or restructure content instead of reproducing it verbatim, \textit{e.g.}, ``Alice hit Bob`` $\to$ ``Bob hit Alice``. Interestingly, this paradox persists across varied settings, with mid-sized compressors often outperforming larger ones in faithful recovery. By analyzing the compressed memory via embedding geometry and reconstruction determinacy, we further reveal that compressors tend to organize memory across broader semantic subspaces, yielding more ambiguous representations prone to overwriting, drift, and weakened recovery. These findings complement existing evaluations of context compression and expose a breakdown of scaling laws when the objective shifts from plausible generation to faithful preservation.

Visual text compression (VTC) promises efficient long-context processing by rendering text into an image and re-encoding it with a vision-language model, often producing $3$--$20\times$ fewer decoder tokens than subword tokenization. Yet token savings do not translate predictably into downstream utility: on some tasks the visual path matches or exceeds the text path, on others it collapses, and the compression ratio itself does not predict which regime will occur. The missing quantity is therefore not another summary of efficiency, but a principled measure of task-relevant information loss induced by visual encoding. We address this problem by formulating VTC in the language of measure transport. Treating text and visual tokens as empirical probability measures, we show that the ViT patch encoder induces a push-forward map whose transport cost decomposes into a precision cost from within-patch aggregation and a coverage cost from cross-patch fragmentation. Both terms are estimable from downstream-label-free probes. This formulation yields two operational consequences: a downstream-label-free routing criterion that selects whether to use the visual path for a given input or benchmark instance, and a transport-informed foveation mechanism that re-encodes high-cost regions at higher resolution. Across $24$ NLP datasets at Qwen3-4B, our label-free rule matches the per-dataset oracle on $17/24$ datasets ($70.8\%$), and improves the average task score by $+3.3\%$ with $-10.3\%$ average tokens relative to a pure-LLM.

In-context learning plays a central role in transformer-based large language models, yet its theoretical understanding remains limited. In this work, we study multiclass in-context classification under more realistic settings, including anisotropic class centers and label imbalance, by introducing a spectral data generation framework that constructs class-center matrices with a prescribed singular spectrum. We first show that the isotropy of class-center vectors, as quantified by the stable rank, improves ICL generalization performance. From a meta-learning perspective, our theorem shows that linear transformers can learn multiclass in-context classification with near-optimal per-label sample complexity, extending prior guarantees beyond the binary setting. In the test label imbalance regime, our analysis reveals that queries from majority classes are easier to classify, while those from minority classes are more error-prone; moreover, robustness to this bias improves with the stable rank. Finally, we empirically demonstrate that our theory is consistent with observations on transformers and pretrained large language models.

In-context learning is usually analyzed as if the examples in the prompt were sampled before the learner is chosen. In deployed systems they are not: examples are retrieved, filtered, re-ranked, edited, and repeatedly tested after seeing the query and the data store. We formalize this gap by treating prompt construction as adaptive data analysis through a conditional stochastic-kernel calculus. Our main quantity is the \emph{context capacity}, the mutual information or approximate max-information between the data store and the final prompt transcript. For any frozen in-context learner and any adaptive context pipeline with capacity $\kappa$, we prove a finite-sample context generalization bound of order $\sqrt{\kappa/k}$, where $k$ is the number of examples that enter the prompt. We strengthen it to a sub-gamma transport inequality with Bernstein curvature, prove a matching lower bound, and derive two PAC-Bayesian retrieval rules: a first-order Gibbs rule and a self-normalized second-order rule. Finally, we instantiate the theory for Bayesian linear in-context regression, including an order-statistics analysis of query-aligned top-$k$ Gaussian retrieval. The results separate context quality from context certification: longer or more relevant contexts improve risk only when the procedure used to choose them is stable enough for selected-context evidence to transfer.

The rapid proliferation of large-scale machine learning models, such as LLMs, has driven remarkable progress across application domains. Nevertheless, their scale comes with significant deployment challenges and inherent redundancies that remain open challenges to this day. To this end, we propose the Tile-Reuse Index (T-ReX), a structured model compression method that identifies and indexes reusable, contiguous parameter groups (tiles) across a model's architecture. By learning a compact set of matching tiles, we compress the model's memory footprint while preserving its performance. Furthermore, by reconstructing dense layers on the fly at inference time, T-ReX compressed models remain efficient at runtime. In our experiments, we show that T-ReX outperforms existing compression methods across benchmarks by most closely matching the original model's performance. We furthermore show how post-training on top of T-ReX enables small footprint models to recover most of the performance loss introduced by compression.

Contemporary systems serving large language models (LLMs) have adopted prefill-decode disaggregation to better load-balance between the compute-bound prefill phase and the memory-bound decode phase. Under this design, prefill workers generate a KV cache that must be transferred to decode workers before token generation can begin. With these workers residing on different physical systems, this transfer becomes a significant bottleneck to serving LLMs at scale. This bottleneck gets exacerbated for long-input and agentic workloads. Existing lossless codecs are not suited to this setting as they primarily target offline weight compression, run on the CPU, or use variable-length coding whose decompression is fast but compression is too slow to keep up with KV production during prefill. We introduce SplitZip, a GPU-friendly lossless compressor for KV-cache transfer that preserves KV tensors bitwise and integrates into existing serving frameworks without changes to model execution. SplitZip exploits redundancy in floating-point exponents of KV activations, encoding the most frequent exponent values with fixed-length codes and routing rare exponents through a sparse escape stream of (position, value). An offline calibrated top-16 exponent codebook eliminates online-histogramming, while the regular dense path and sparse escape correction make both encoding and decoding efficient on GPUs. On real BF16 activation tensors, SplitZip achieves 613.3 GB/s compression throughput and 2181.8 GB/s decompression throughput, substantially outperforming prior lossless compressors on the latency-critical codec path. End-to-end transfer experiments show up to 1.32× speedup for BF16 KV-cache transfer, 1.30× speedup for TTFT, and 1.23× increase on Request Throughput. The same approach extends to FP8 KV caches, providing up to 1.14× compression over native E5M2.

The key-value (KV) cache has become a dominant memory and bandwidth bottleneck for serving long-context large language models, motivating a growing body of work on KV cache compression. Most existing methods follow a common recipe: a uniform per-layer budget and attention top-$k$ token selection, but this recipe is \emph{data-oblivious} (ignoring cross-layer variation in attention concentration) and \emph{redundancy-blind} (retaining near-duplicate key--value entries). We propose \textbf{SpectralKV}, a training-free framework that addresses both issues jointly. Across layers, a lightweight concentration-based criterion redistributes a fixed global budget based on the entropy of observation-window attention, giving more slots to layers whose attention is more concentrated. Within each layer, a spectral coreset selector treats keys and values as geometric objects in a metric-aligned joint feature space and selects tokens via residual pivoting, suppressing near-duplicates while preserving geometrically distinct directions. On Llama-3.1-8B and Qwen3-8B, SpectralKV consistently outperforms seven strong baselines on 15 LongBench tasks and PG-19 perplexity at 16K and 32K contexts, with the largest gains at aggressive compression ratios down to $6.25\%$ keep. And a static-budget variant reduces peak prefill VRAM by up to $44\%$ with negligible quality loss. Code and data are available at \url{https://anonymous.4open.science/r/spectralKV-2FF7}.

We investigate the short-context dominance hypothesis: that for most sequences, a small local prefix suffices to predict their next tokens. Using large language models as statistical oracles, we measure the minimum context length (MCL) needed to reproduce accurate full-context predictions across datasets with sequences of varying lengths. For sequences with 1–7k tokens from long-context documents, we consistently find that 75–80\% require only the last 96 tokens at most. Given the dominance of short-context tokens, we then ask whether it is possible to detect challenging long-context sequences for which a short local prefix does not suffice for prediction. We introduce a practical proxy to MCL, called Distributionally Aware MCL (DaMCL), that does not require knowledge of the actual next-token and is compatible with sampling strategies beyond greedy decoding. Our experiments validate that simple thresholding of the metric defining DaMCL achieves high performance in detecting long vs. short context sequences. Finally, to counter the bias that short-context dominance induces in LLM output distributions, we develop an intuitive decoding algorithm that leverages our detector to identify and boost tokens that are long-range-relevant. Across Q\&A tasks and model architectures, we confirm that mitigating the bias improves performance.

Training-memory reduction requires identifying which saved tensors drive peak usage and ensuring high-fidelity backward contractions from compressed states. We formalize saved-activation compression as a target-surface prediction problem: a pre-training framework to estimate the replaceable memory surface, computational overhead, and parameter-gradient error. We introduce STAC-R (Subspace Tracked Activation Compression with Residuals), a saved-tensor wrapper storing activations as persistent low-rank coefficients paired with a sparse quantized residual. Weight gradients are contracted directly from these factors, bypassing full decompression. To guide deployment, we propose the Saved-Surface Predictor ($\mathrm{SSP} = A_C^+ / P$), a statistic that upper-bounds peak memory reduction. We also derive a gradient bridge linking reconstruction error to parameter-gradient cosine similarity, determining if a low-precision state preserves update fidelity.Evaluations across GPT-2 (Medium/Large) and Pythia-1.4B pre-training show STAC-R reduces peak memory by 7.2-12.4\% while keeping long-horizon validation perplexity within 1.5\% of baseline (Pythia-1.4B 10k steps: +1.14\%) with mean gradient cosine $\geq$ 0.98. On BERT fine-tuning (SST-2), STAC-R achieves 12.45\% memory reduction with a 0.15pp accuracy decrease. Mechanistic benchmarks yield a mean gradient cosine of 0.9813, outperforming iso-byte SVD (0.9236) and untracked-subspace (0.6949) controls. On the empirical rate-distortion frontier, STAC-R is Pareto-dominant over controls across stored-byte budgets. Composed with GaLore, a "Turbo-fast" variant matches full STAC-R's memory footprint within 0.005 GiB while reaching 0.67𝑥 wall time. Finally, our analysis identifies memory-increasing regimes in SwiGLU architectures (Qwen-2.5/Llama-3.2), establishing STAC-R as a compressor with predictable memory and fidelity conditions checkable before training.

3D Gaussian Splatting (3DGS) has emerged as a promising method that enables fast and high-quality novel-view rendering. However, its large parameter size remains a bottleneck for storage and transmission. We propose *RacerGS*, a compact 3DGS compression framework that achieves scene reconstruction at significantly reduced storage sizes with preserved fidelity. To obtain compact and spatially coherent features, we design a hash projection model that projects the anchor hash encodings into compact context features. Additionally, we introduce a FiLM-modulated autoregressive GRU context model that utilizes causal dependencies among anchor feature groups and uses recurrent hidden states to refine entropy-model parameters, improving bitrate efficiency. Furthermore, we adaptively entropy-code quantized residuals of anchor attributes around their context-predicted means, reducing symbol entropy by leveraging spatial consistency. Overall, *RacerGS* achieves more than **$\mathbf{150}\boldsymbol{\times}$** compression over vanilla 3DGS and **$\mathbf{28}\boldsymbol{\times}$** over Scaffold-GS, while providing comparable rendering quality. Extensive experiments across five datasets demonstrate our superiority over prior 3DGS compression methods in both storage reduction and rate-distortion performance.

In modern LLM applications, the demand for extended context lengths continues to surge, making KV cache a major performance bottleneck in long-context inference. Channel-wise pruning has emerged as a prevalent KV cache compression paradigm; however, existing solutions overlook inherent similarities among KV vectors, resulting in limited pruning ratios and noticeable performance degradation. To tackle this issue, we present ResKV, a novel residual-driven channel-wise pruning framework that fully exploits KV vector similarity for effective compression. ResKV first clusters highly similar KV vectors via cosine similarity metrics, then calculates residual vectors by subtracting each cluster’s centroid from the original features. Subsequent channel-wise unstructured pruning and per-token quantization are exclusively applied to these residual components. During inference, preserved residuals are combined with their corresponding centroids to accurately recover dense KV representations. Benefiting from the low magnitude and sparse, near-zero properties of centroid residuals, both pruning and quantization incur only negligible approximation errors. Experimental results show that ResKV reduces peak memory consumption by 45.6% and improves inference throughput by 4.27× against dense FlashAttention inference, while sustaining competitive model performance. Under identical sparsity constraints, ResKV outperforms state-of-the-art channel-wise KV pruning methods by achieving up to 2.26 points higher accuracy and 2.63× faster end-to-end throughput.

The growing context lengths of large language models (LLMs) have made key-value (KV) cache memory a critical bottleneck during inference. Vector quantization (VQ) with commutative codebooks provides an effective Rotary Position Embedding (RoPE)-aware solution by enabling reconstruction-free attention over quantized key indices. However, existing commutative VQ methods still parameterize scalar codebook coefficients across RoPE subspaces and codewords largely independently, leaving parameter-side redundancy underexploited. We propose $\textbf{RankVQ}$, a low-rank parameterized commutative vector quantization method for KV cache compression. Instead of factorizing the deployed codebooks, RankVQ factorizes the underlying scalar coefficient matrices used to construct key and value codebooks. This design preserves the pseudo-symmetric structure required for RoPE commutativity on the key side, while improving the quality and compactness of offline codebook construction. The low-rank factors are discarded after codebook construction, so RankVQ keeps the same online inference form as standard commutative VQ and introduces no additional decoding overhead. Experiments on LongBench, InfiniteBench, and GSM8K show that RankVQ achieves a stronger accuracy--compression trade-off than directly comparable KV quantization baselines, with particularly clear gains in the 1-bit regime.

Motivated by applications in reinforcement learning from human feedback, we consider a setting where a given collection of rankings needs to be compressed into a smaller collection of rankings. This can also be seen as a combination of two fundamental social choice frameworks: ranking aggregation and multiwinner voting. We propose three proportionality notions that capture different types of representation in this setting: positional proportionality, pairwise proportionality, and proportionality for solid coalitions (PSC). On the one hand, we show that positional proportionality and PSC are always satisfiable for any input rankings and target compression size, and a desired output can be found in polynomial time. On the other hand, we prove that pairwise proportionality cannot be satisfied in general, but can nevertheless be attained when the input rankings are single-peaked or single-crossing.

State Space Models (SSMs) have emerged as a compelling alternative to Transformers, enabling sequence modeling with constant memory and linear compute. While SSMs excel in certain settings like length generalization, they continue to lag behind Transformers on tasks that require in-context learning and precise retrieval, slowing their adoption for large-scale language modeling. In this work, we demonstrate that both the success and failure of SSMs in these domains can be explained by studying the role of the gating mechanism, a prevalent component in modern recurrent networks. Specifically, we show through theory and experiments that this gating mechanism causes SSMs to first learn an in-weights ``memorization'' solution, while delaying, or even preventing, convergence to a correct in-context learning solution. Importantly, this happens even in cases where there are no fundamental limitations due to the architecture or its memory capacity. On the other hand, we find that gating is often beneficial for improving generalization to long sequence lengths. Our results illuminate the crucial role of the gating mechanism in shaping both the training dynamics and generalization of SSMs, and provide a basis for understanding and improving linear-time models.

BFloat16 weights of large language models carry only ${\sim}10.5$ bits of information per 16-bit value, yet exploiting this redundancy on GPUs, where weights bottleneck both per-token bandwidth and concurrent capacity, has not produced wall-clock speedup. Existing variable-length lossless codes are compute-bound on SIMT decode. We present NyoomFloat12 (NF12), a lossless 12-bit fixed-length format for BF16 weights that addresses both bottlenecks. Over $99.7\%$ of trained BF16 weights have the upper four exponent bits set to $\texttt{0111}$ after a per-matrix power-of-two scale; dropping them yields a fixed-length 12-bit format with 16-instruction SIMT-friendly decode. Out-of-range groups reuse the encoded slot to index a per-matrix verbatim BF16 buffer at zero per-group storage overhead. In the bandwidth-bound regime, fused NF12 GEMV achieves up to $1.21\times$ matched-BF16 and $1.35\times$ cuBLAS, $71\%$ of the entropy-bound optimum (a hypothetical implementation reading the joint entropy floor at full HBM bandwidth). In the capacity-bound regime on Qwen3-32B, NF12's smaller footprint opens $4.5\times$ more KV-cache room; with decode at near-peak HBM bandwidth ($3.3\times$ faster than prior lossless decoders), NF12 raises throughput up to $2.67\times$.

Mixture-of-Experts (MoE) language models scale model capacity efficiently by activating a small subset of parameters per token. However, in long-context inference, memory remains a major bottleneck because the KV cache grows linearly with sequence length. Existing KV cache compression methods reduce this cost for dense transformers, but overlook a problem specific to MoE: KV eviction can change which experts are selected during answer generation, degrading the generation quality. We propose MoEZip, a routing-aware KV cache compression for sparse MoE language models. To estimate the sensitivity of expert routing to perturbation, we propose a novel metric based on the Fisher information matrix of routing distributions. MoEZip combines this metric with attention weights for routing-aware scoring of contexts. Finally, we compose a complementary scoring system that combines eviction methods for dense and sparse-MoE architectures. Experiments show that MoEZip achieves robust performance under aggressive cache compression on various benchmarks. At a KV retention ratio of 10\%, MoEZip improves over the SoTA baseline by +24 and +20 points on average on LongBench and RULER, corresponding to 2.3$\times$ and 4.9$\times$ higher scores, respectively.

The key--value (KV) cache is a major bottleneck in long-context inference, where memory and computation grow with sequence length. Existing KV eviction methods reduce this cost but typically degrade performance relative to full-cache inference. Our key insight is that full-cache attention is not always optimal: in long contexts, irrelevant tokens can dilute attention away from useful evidence, so selective, learnable eviction can improve generation rather than merely approximate the full cache. We introduce a global retention-based KV eviction method that learns each token's future utility under a unified memory budget. Lightweight retention gates assign utility scores to cached KV entries, and a shared final scoring projection calibrates these scores across all layers and heads. This enables a single global eviction policy in which tokens from different layers, heads, and modalities compete directly for cache capacity. We further provide theoretical analysis showing that preferentially retaining useful tokens reduces attention dilution, and we justify geometric retention as a query-agnostic proxy for future utility. Across long-context language and vision--language benchmarks, our method substantially reduces KV memory while matching or surpassing full-cache inference. These results suggest that learned, globally calibrated KV eviction is not only a compression technique, but also a mechanism for improving long-context reasoning.

We study the $K$-armed logistic bandit problem, where at each round, the agent observes $K$ feature vectors associated with $K$ actions. Existing approaches that achieve a rate-optimal $\widetilde{\cal O}(\sqrt{dT})$ regret bound rely heavily on context diversity assumptions, such as strict positivity of the minimum eigenvalue of a context covariance matrix. These assumptions, however, impose strong restrictions on the context process, as they rule out the situation where the context vectors are concentrated in a low-dimensional subspace. In this paper, we propose SupSplitLog, which, to the best of our knowledge, is the first algorithm for logistic bandits that achieves $\widetilde{\cal O}(\sqrt{dT})$ regret without any context diversity assumption. The key idea is to split the collected samples into two disjoint subsets when constructing estimators; one is used to compute an initial-point estimator, while the other is used to apply a Newton-type one-step correction procedure. The splitting rule is carefully designed to balance the accuracy requirements of the initial-point estimator and the one-step correction procedure. Moreover, SupSplitLog strictly improves on the existing algorithms in terms of the dependence on dimension $d$ in the regret upper bound. Furthermore, SupSplitLog can be adapted simply to deduce a regret bound that grows with a data-dependent complexity measure, avoiding a direct dependence on $d$, which is favorable when the context vectors are concentrated in a low-dimensional subspace. We also provide experimental results that demonstrate numerically the superiority of our algorithm, validating the theoretical results.