Context Compression

Multimodal large language models (MLLMs) have recently demonstrated strong capabilities in understanding and generating responses from diverse visual inputs, including high-resolution images and long video sequences. As these models scale to richer visual representations, inference increasingly relies on storing large numbers of vision tokens in the key-value (KV) cache, making memory consumption a central bottleneck. Existing methods address this issue by identifying redundancy in vision tokens and compressing the cache, but such compression is typically applied only after all inputs are processed, resulting in high peak memory usage during the prefill stage. In this work, we show that MLLMs exhibit inherent structural regularities and representational redundancy that can be exploited to control memory growth throughout inference. Based on this insight, we propose a sequential input-compression mechanism that enforces a fixed memory budget by performing structure-aware key-value cache compression during the prefill process. This approach substantially reduces peak memory usage while maintaining generative performance with only minimal degradation, enabling more practical and memory-efficient multimodal inference.

Large Language Models (LLMs) have achieved remarkable success, underpinning diverse AI applications. However, they often suffer from performance degradation due to factors such as catastrophic forgetting during Supervised Fine-Tuning (SFT), quantization, and pruning. In this work, we introduce a performance recovery framework based on Self-Distillation Fine-Tuning (SDFT) that effectively restores model capabilities. Complementing this practical contribution, we provide a rigorous theoretical explanation for the underlying recovery mechanism. We posit that an LLM's generative capability fundamentally relies on the high-dimensional manifold constructed by its hidden layers. To investigate this, we employ Centered Kernel Alignment (CKA) to quantify the alignment between student and teacher activation trajectories, leveraging its invariance to orthogonal transformations and scaling. Our experiments demonstrate a strong correlation between performance recovery and manifold alignment, substantiating the claim that self-distillation effectively aligns the student's high-dimensional manifold with the optimal structure represented by the teacher. This study bridges the gap between practical recovery frameworks and geometric representation theory, offering new insights into the internal mechanisms of self-distillation.

This paper is dedicated to lossless data compression with probability estimation using neural networks. First, we propose a probability estimation architecture based on a chain of neural predictors, so that each unit of the chain is defined as a neural network with the minimum possible number of weights, which is sufficient for efficient compression of data generated by Markov sources of a given order. We show that this architecture allows us to minimize the overall number of weights participating in the probability estimation process depending on the statistical properties of the input data. Second, in order to improve compression efficiency, we introduce an information inheritance mechanism, where the probability estimate obtained by a low-order unit is used at the next higher-order unit. Experimental results show that the proposed lossless data compressor equipped with the chained probability estimation architecture provides compression ratios close to the state-of-the-art PAC compressor. At the same time, it outperforms PAC by a factor of 1.2 to 6.3 in encoding throughput and by a factor of 2.8 to 12.3 in decoding throughput on a consumer GPU.

Large Language Models (LLMs) incur significant computational and memory costs when processing long prompts, as full self-attention scales quadratically with input length. Token compression aims to address this challenge by reducing the number of tokens representing inputs. However, existing prompt-compression approaches primarily operate in token space and overlook inefficiencies in the latent embedding space. In this paper, we propose K-Token Merging, a latent-space compression framework that merges each contiguous block of K token embeddings into a single embedding via a lightweight encoder. The compressed sequence is processed by a LoRA-adapted LLM, while generation remains in the original vocabulary. Experiments on structural reasoning (Textualized Tree), sentiment classification (Amazon Reviews), and code editing (CommitPackFT) show that K-Token Merging lies on the Pareto frontier of performance vs. compression, achieving up to 75% input length reduction with minimal performance degradation. Code is available at https://github.com/shsjxzh/K-Token-Merging.

While chain-of-thought (CoT) reasoning enables LLMs to solve challenging reasoning tasks, the linear growth of the KV cache leads to substantial memory and inference overhead. Existing approaches such as context compression and multi-token prediction (MTP) improve efficiency from two complementary directions by compressing historical tokens and generating future tokens in parallel. However, effectively combining them remains challenging due to their different training paradigms and architectural assumptions. In this work, we propose MemoSight (Memory-Foresight-Based Reasoning), a unified framework that integrates context compression and MTP to improve inference efficiency while preserving CoT performance. MemoSight adopts a shared minimalist design based on special tokens and token-specific positional layouts for both compression and parallel prediction. Experiments on four reasoning benchmarks show that, compared to the vanilla SFT baseline, MemoSight reduces KV cache usage by up to 66% and improves inference speed by 56%, while incurring less than a 3% drop in average reasoning accuracy, yielding a better efficiency-accuracy trade-off than existing CoT compression methods.

The fundamental limit of natural signal compression has traditionally been characterized by classical rate-distortion (RD) theory through the tradeoff between coding rate and reconstruction distortion, while the rate-distortion-perception (RDP) framework introduces a divergence-based measure of perceptual quality as a modeling principle, leaving its theoretical origin unclear. In this paper, motivated by a synonymity-based semantic information perspective, we reformulate perceptual reconstruction as recovering any admissible sample within an ideal synonymous set (synset) associated with the source, rather than the source sample itself, and establish a synonymous source coding architecture. On this basis, we develop a synonymous variational inference (SVI) analysis framework with a synonymous variational lower bound (SVLBO) for tractable analysis of synset-oriented compression. Within this framework, we establish a synonymity-perception consistency principle, showing that optimal identification of semantic information is theoretically consistent with perceptual optimization. Based on this result, we further derive a tight-bound synonymous source coding rate characterization and show that its Jensen-limit relaxation leads to a synonymous rate-distortion-perception form for practical optimization. These analytical results show that the distributional divergence term arises naturally from the synset-based reconstruction objective, clarify its compatibility with existing RDP formulations and classical RD theory, and suggest the potential advantages of synonymous source coding.

Communication in Large Language Model (LLM)-based multi-agent systems is moving beyond discrete tokens to preserve richer context. Recent work such as LatentMAS enables agents to exchange latent messages through full key-value (KV) caches. However, full KV relay incurs high memory and communication cost. We adapt KV-cache eviction methods to this setting and introduce \textbf{Orthogonal BackFill (OBF)} to mitigate information loss from hard eviction. OBF injects a low-rank orthogonal residual from discarded KV states into the retained KV states. We evaluate OBF against full KV relay on nine benchmarks spanning mathematical reasoning, expert and commonsense QA, and coding. With only 9.9%-20.2% of the prompt KV states retained, H-OBF delivers between $97$ and $120$ of full KV relay's per-benchmark accuracy across the nine benchmarks. This suggests that more information does not necessarily lead to better communication; preserving the most useful information matters more. Our codebase is included in the supplementary material. Our codebase is publicly available on https://github.com/markli404/When-Less-Latent-Leads-to-Better-Relay.

Deep Reinforcement Learning (DRL) is widely recognized as sample-inefficient, a limitation attributable in part to the high dimensionality and substantial functional redundancy inherent to the policy parameter space. A recent framework, which we refer to as Action-based Policy Compression (APC), mitigates this issue by compressing the parameter space $Θ$ into a low-dimensional latent manifold $\mathcal Z$ using a learned generative mapping $g:\mathcal Z \to Θ$. However, its performance is severely constrained by relying on immediate action-matching as a reconstruction loss, a myopic proxy for behavioral similarity that suffers from compounding errors across sequential decisions. To overcome this bottleneck, we introduce Occupancy-based Policy Compression (OPC), which enhances APC by shifting behavior representation from immediate action-matching to long-horizon state-space coverage. Specifically, we propose two principal improvements: (1) we curate the dataset generation with an information-theoretic uniqueness metric that delivers a diverse population of policies; and (2) we propose a fully differentiable compression objective that directly minimizes the divergence between the true and reconstructed mixture occupancy distributions. These modifications force the generative model to organize the latent space around true functional similarity, promoting a latent representation that generalizes over a broad spectrum of behaviors while retaining most of the original parameter space's expressivity. Finally, we empirically validate the advantages of our contributions across multiple continuous control benchmarks.

LiDAR point clouds are fundamental to various applications, yet the extreme sparsity of high-precision geometric details hinders efficient context modeling, thereby limiting the compression speed and performance of existing methods. To address this challenge, we propose a compact representation for efficient predictive lossless coding. Our framework comprises two lightweight modules. First, the Geometry Re-Densification Module iteratively densifies encoded sparse geometry, extracts features at a dense scale, and then sparsifies the features for predictive coding. This module avoids costly computation on highly sparse details while maintaining a lightweight prediction head. Second, the Cross-scale Feature Propagation Module leverages occupancy cues from multiple resolution levels to guide hierarchical feature propagation, enabling information sharing across scales and reducing redundant feature extraction. Additionally, we introduce an integer-only inference pipeline to enable bit-exact cross-platform consistency, which avoids the entropy-coding collapse observed in existing neural compression methods and further accelerates coding. Experiments demonstrate competitive compression performance at real-time speed. Code will be released upon acceptance. Code is available at https://github.com/pengpeng-yu/FastPCC.

Dataset distillation, a training-aware data compression technique, has recently attracted increasing attention as an effective tool for mitigating costs of optimization and data storage. However, progress remains largely empirical. Mechanisms underlying the extraction of task-relevant information from the training process and the efficient encoding of such information into synthetic data points remain elusive. In this paper, we theoretically analyze practical algorithms of dataset distillation applied to the gradient-based training of two-layer neural networks with width $L$. By focusing on a non-linear task structure called multi-index model, we prove that the low-dimensional structure of the problem is efficiently encoded into the resulting distilled data. This dataset reproduces a model with high generalization ability for a required memory complexity of \tildeΘ$$(r^2d+L), where $d$ and $r$ are the input and intrinsic dimensions of the task. To the best of our knowledge, this is one of the first theoretical works that include a specific task structure, leverage its intrinsic dimensionality to quantify the compression rate and study dataset distillation implemented solely via gradient-based algorithms.

Tokenization is a hardcoded compression step which remains in the training pipeline of Large Language Models (LLMs), despite a general trend towards architectures becoming increasingly end-to-end. Prior work has shown promising results at scale in bringing this compression step inside the LLMs' architecture with heuristics to draw token boundaries, and also attempts to learn these token boundaries with straight-through estimates, which treat the problem of drawing discrete token boundaries as a continuous one. We show that these token boundaries can instead be learned using score function estimates, which have tighter theoretical guarantees due to directly optimizing the problem of drawing discrete token boundaries to minimize loss. We observe that techniques from reinforcement learning, such as time discounting, are necessary to reduce the variance of this score function sufficiently to make it practicable. We demonstrate that the resultant method outperforms prior proposed straight-through estimates, both qualitatively and quantitatively at the $100$ million parameter scale.

Multi-hop all-reduce is the de facto backbone of large model training. As the training scale increases, the network often becomes a bottleneck, motivating the reduction of the volume of transmitted data. Accordingly, recent systems have demonstrated significant acceleration of the training process using gradient quantization. However, these systems are not optimized for multi-hop aggregation, where entries are partially summed multiple times along their aggregation topology. We present DynamiQ, a quantization framework that bridges the gap between quantization best practices and multi-hop aggregation. DynamiQ introduces novel techniques to better represent partial sums, codesigned with a decompress accumulate recompress fused kernel to facilitate fast execution. We extend PyTorch DDP to support DynamiQ over NCCL P2P, and across different LLMs, tasks, and scales, we demonstrate consistent improvement of up to 34.2% over the best among state-of-the-art methods such as Omni-Reduce, THC, and emerging standards such as MXFP4, MXFP6, and MXFP8. Further, DynamiQ is the only evaluated method that consistently reaches near-baseline accuracy (e.g., 99.9% of the BF16 baseline) and does so while significantly accelerating the training.

Large reasoning models (LRMs) typically solve reasoning-intensive tasks by generating long chain-of-thought (CoT) traces, leading to substantial inference overhead. We identify a reproducible inference-time phenomenon, termed Self-Compression: when multiple independent and answerable questions are presented within a single prompt, the model spontaneously produces shorter reasoning traces for each question. This phenomenon arises from multi-question contextual pressure during generation and consistently manifests across models and benchmarks. Building on this observation, we propose ConPress (Learning from Contextual Pressure), a lightweight self-supervised fine-tuning approach. ConPress constructs multi-question prompts to induce self-compression, samples the resulting model outputs, and parses and filters per-question traces to obtain concise yet correct reasoning trajectories. These trajectories are directly used for supervised fine-tuning, internalizing compressed reasoning behavior in single-question settings without external teachers, manual pruning, or reinforcement learning. With only 8k fine-tuning examples, ConPress reduces reasoning token usage by 59% on MATH500 and 33% on AIME25, while maintaining competitive accuracy.

Audio-Visual Large Language Models (AV-LLMs) face prohibitive computational costs of processing massive, redundant audio-visual tokens. Existing unimodal compression techniques fail to capture the heterogeneous and mutually influential information density of joint audio-visual signals. Furthermore, we identify a fundamental and overlooked theoretical bottleneck in sparse token reduction: positional aliasing. We demonstrate that aggressive sparse sampling on standard position-encoded sequences violates the Nyquist limit relative to the effective token interval, causing phase-wrapping collisions that corrupt temporal monotonicity. To address this, we introduce EchoingPixels, a framework for aliasing-resistant joint token reduction. Our Cross-Modal Semantic Sieve performs extractive selection on the synergistic audio-visual stream, dynamically allocating budgets based on joint-modality saliency rather than fixed per-modality ratios. To resolve positional aliasing, we derive Sync-RoPE, a spectral low-pass filter for Rotary Positional Embeddings that adapts encoding bandwidth to the sparse sampling rate, preserving monotonic temporal relationships in the reduced stream. Experiments show that EchoingPixels achieves performance comparable to full models using only 5-20% of original tokens, validating theoretically grounded sparse learning as a robust solution for efficient AV-LLMs. Code is available at https://github.com/CharlesGong12/EchoingPixels.

Mixture-of-Experts (MoE) models have shown strong potential in scaling language models efficiently by activating only a small subset of experts per input. However, their widespread deployment remains limited due to the high memory overhead associated with storing all expert parameters, particularly as the number of experts increases. To address this challenge, prior works have explored expert dropping and merging strategies, yet they often suffer from performance drop at high compression ratios. In this paper, we introduce PuzzleMoE, a training-free MoE compression method that achieves both high accuracy and efficient inference through two key innovations: First, PuzzleMoE performs sparse expert merging by identifying element-wise weight redundancy and specialization. It uses a dual-mask to capture both shared and expert-specific parameters. Second, to avoid the overhead of storing binary masks and signs, PuzzleMoE introduces a bit-packed encoding scheme that reuses underutilized exponent bits, enabling efficient MoE inference on GPUs. Extensive experiments demonstrate that PuzzleMoE can compress MoE models by up to 50% while maintaining accuracy across various tasks. Specifically, it outperforms prior MoE compression methods by up to 16.7% on MMLU at 50% compression ratio, and achieves up to 1.28\times inference speedup.

Neural video compression (NVC) technologies have advanced rapidly in recent years, yielding state-of-the-art schemes such as DCVC-RT that offer superior compression efficiency to H.266/VVC and real-time encoding/decoding capabilities. Nonetheless, existing NVC schemes have several limitations, including inefficiency in dealing with disocclusion and new content, interframe error propagation and accumulation, among others. To eliminate these limitations, we borrow the idea from classic video coding schemes, which allow intra coding within inter-coded frames. With the intra coding tool enabled, disocclusion and new content are properly handled, and interframe error propagation is naturally intercepted without the need for manual refresh mechanisms. We present an NVC framework with unified intra and inter coding, where every frame is processed by a single model that is trained to perform intra/inter coding adaptively. Moreover, we propose a simultaneous two-frame compression design to exploit interframe redundancy not only forwardly but also backwardly. Experimental results show that our scheme outperforms DCVC-RT by an average of 12.1% BD-rate reduction, delivers more stable bitrate and quality per frame, and retains real-time encoding/decoding performances. Code and models will be released.

Humans can uniquely assign value to novel, abstract outcomes to support reinforcement learning. However, this flexibility is cognitively costly and reduces learning efficiency. We propose that goal-dependent learning initially relies on capacity-limited working memory. With consistent experience, learners create a "compressed" reward function - a simplified goal rule -- that transfers to long-term memory for a more automatic evaluation upon receiving feedback. This automaticity frees working memory resources, thereby boosting learning efficiency. Across six experiments, we demonstrate that learning is impaired by the size of the goal space but improves when this space allows for compression. Additionally, faster reward processing correlates with better learning. Although the algorithmic details remain to be established, our behavioral results and computational models suggest that efficient goal-directed learning relies on compressing complex goal information into a stable reward function. These findings illuminate the cognitive mechanisms of intrinsic motivation and can inform behavioral interventions supporting human goal achievement.

Large Language Models have achieved remarkable performance across a large number of tasks, but face critical deployment and usage barriers due to substantial computational requirements. Model compression methods, which aim to reduce model size while preserving its capacity, are an important means to mitigate these issues. Promising approaches along these lines, such as structured pruning, typically require costly manual hyperparameter exploration or rely on local heuristics that may run the risk of ignoring better solutions. In this work we introduce GeLaCo, an evolutionary approach to LLM compression via layer collapse. Our approach supports an efficient exploration of the compression solution space via population-based search and a novel layer collapse formulation based on parametrized weight merging, with a fitness function based on similarity over residual updates and language modeling KL divergence. GeLaCo also supports both single and multi-objective evolutionary compression search, establishing the first Pareto front estimation along compression and quality axes. We evaluate GeLaCo solutions via both perplexity-based and generative evaluations over foundational and instruction-tuned models, outperforming state-of-the-art alternatives.

A proposition that connects randomness and compression is put forward via Gibbs entropy over set of measurement vectors associated with a compression process. In building this connection, we use a performance of a learning task as a probe of compression, over series of compression cycles within a cascade. The Gibbs entropy at each cycle measures the degree of randomness. Consequently a lossy compression process can be seen as an equivalent to {\it directed randomness} that preserves information content under certain bounds of Gibbs entropy and the performance of the learning task. The term directed means we guide the compression process with set of mathematical rules on how to reduce the model size. We formulate this connection with a theorem using a $δ$ and $ε$ bounds, and demonstrated a logical proof via comonotonic relationship within a very small decrease in compression ratio and the performance. We have showcase the validity of this proposition with a canonical vision task in deep learning with three different model compression processes as {\it a baseline model}. We use the following, simpler to more complex model compression approaches: (1) random pruning, (2) magnitude pruning, and (3) a more complex compression by using dual tomographic compression, which utilizes compressed sensing in dual fashion. We use remaining weights of deep learning network as a measurement vector where we measure the Gibbs entropy. The proposition is supported with the experimental evidence, resulting in very high correlation between learning performance and the Gibbs entropy over compression ratios for all different compression processes. We show case the idea that there is an inherent computable connection between compression probed by performance degradation and randomness from an entropy measure on the learned model.

Reflectance attributes in LiDAR point clouds provide essential information for downstream tasks but remain underexplored in neural compression methods. To address this, we introduce SerLiC, a serialization-based neural compression framework to fully exploit the intrinsic characteristics of LiDAR reflectance. SerLiC first transforms 3D LiDAR point clouds into 1D sequences via scan-order serialization, offering a device-centric perspective for reflectance analysis. Each point is then tokenized into a contextual representation comprising its sensor scanning index, radial distance, and prior reflectance, for effective dependencies exploration. For efficient sequential modeling, Mamba is incorporated with a dual parallelization scheme, enabling simultaneous autoregressive dependency capture and fast processing. Extensive experiments demonstrate that SerLiC attains over 2x volume reduction against the original reflectance data, outperforming the state-of-the-art method by up to 22% reduction of compressed bits while using only 2% of its parameters. Moreover, a lightweight version of SerLiC achieves > 10 fps (frames per second) with just 111K parameters, which is attractive for real-world applications.

Chain-of-Thought (CoT) prompting trades inference speed for reasoning accuracy. Existing compressors force a compromise as static gradient techniques treat tokens independently, severing sequential logic, while uncertainty-based pruning ignores the final answer. We introduce Adaptive GoGI-Skip, a framework that resolves this tension by non-linearly coupling Goal-Gradient Importance (GoGI) with Adaptive Dynamic Skipping (ADS). GoGI quantifies each token's functional contribution to answer correctness via gradient sensitivity. ADS leverages runtime entropy to dynamically modulate the GoGI threshold, preserving low-gradient tokens essential for structural coherence at high-uncertainty junctions. Trained on 7,472 MATH traces, our policy transfers zero-shot to AIME, GPQA, and GSM8K, reducing token volume by $>$45% and accelerating inference up to 2.0$\times$ without accuracy loss. These results suggest that thinking-optimal compression demands synergy between teleological goals and epistemic uncertainty.

Large Language Models (LLMs) have achieved significant success across various NLP tasks. However, their massive computational costs limit their widespread use, particularly in real-time applications. Structured pruning offers an effective solution by compressing models and directly providing end-to-end speed improvements, regardless of the hardware environment. Meanwhile, different components of the model exhibit varying sensitivities towards pruning, calling for non-uniform model compression. However, a pruning method should not only identify a capable substructure, but also account for post-compression training. To this end, we propose DarwinLM, a method for training-aware structured pruning. DarwinLM builds upon an evolutionary search process, generating multiple offspring models in each generation through mutation, and selecting the fittest for survival. To assess the effect of post-training, we incorporate a lightweight, multistep training process within the offspring population, progressively increasing the number of tokens and eliminating poorly performing models in each selection stage. We validate our method through extensive experiments on Llama-2-7B, Llama-3.1-8B and Qwen-2.5-14B-Instruct, achieving state-of-the-art performance for structured pruning. For instance, DarwinLM surpasses ShearedLlama while requiring 5x less training data during post-compression training. Code is at: https://github.com/IST-DASLab/DarwinLM

Task arithmetic, representing downstream tasks through linear operations on task vectors, has emerged as a simple yet powerful paradigm for transferring knowledge across diverse settings. However, maintaining a large collection of task vectors introduces scalability challenges in both storage and computation. We propose Task Vector Bases, a framework compressing $T$ task vectors into $M < T$ basis vectors while preserving the functionality of task arithmetic. By representing each task vector as a structured linear combination of basis atoms, our approach supports standard operations such as addition, negation, as well as more advanced arithmetic ones. The framework is orthogonal to other efficiency-oriented improvements in task arithmetic and can be used in combination with them. We provide theoretical analysis showing that basis compression retains addition generalization guarantees and enables principled unlearning, with error bounds depending on reconstruction quality. Empirically, our proposed basis construction methods consistently outperform heuristic basis construction baselines and, in some cases, even surpass the performance of full task vector collections across diverse downstream applications while reducing storage and computational requirements. The code is available at https://github.com/uiuctml/TaskVectorBasis.

The expansion of time-series data from sensors and monitoring systems has made compact representations increasingly important. Such representations should retain signal structure while cutting storage, transmission and computation costs. Adaptive Brownian Bridge-based Aggregation (ABBA) addresses this need by converting long numerical series into short symbolic sequences, but reductions in parameter storage and computational precision remain desirable. We propose Quantized ABBA (QABBA), a quantized version of ABBA. By quantizing the symbolic centers, QABBA reduces the parameter footprint and enables integer arithmetic while maintaining high reconstruction quality. We establish several error bounds for the additional approximation introduced by quantization: a dimension-free bound on the excess error of each segment, a time-domain reconstruction-error bound, a stability condition for symbolic assignment, and a rule for allocating bits between segment lengths and increments. The resulting symbolic strings can be passed directly to a pretrained large language model (LLM) without any extra time-series embedding layer. Experiments on the Monash regression archive, UCR Time Series Classification Archive, and UEA Multivariate Time Series Classification Archive demonstrate a practical trade-off among storage, reconstruction accuracy and downstream predictive performance. QABBA therefore provides an error-controlled, low-precision symbolic representation for time-series compression and LLM-based analysis.

Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data. However, it remains an open question how deep networks perform hierarchical feature learning across layers. In this work, we attempt to unveil this mystery by investigating the structures of intermediate features. Motivated by our empirical findings that linear layers mimic the roles of deep layers in nonlinear networks for feature learning, we explore how deep linear networks transform input data into output by investigating the output (i.e., features) of each layer after training in the context of multi-class classification problems. Toward this goal, we first define metrics to measure within-class compression and between-class discrimination of intermediate features, respectively. Through theoretical analysis of these two metrics, we show that the evolution of features follows a simple and quantitative pattern from shallow to deep layers when the input data is nearly orthogonal and the network weights are minimum-norm, balanced, and approximate low-rank: Each layer of the linear network progressively compresses within-class features at a geometric rate and discriminates between-class features at a linear rate with respect to the number of layers that data have passed through. To the best of our knowledge, this is the first quantitative characterization of feature evolution in hierarchical representations of deep linear networks. Empirically, our extensive experiments not only validate our theoretical results numerically but also reveal a similar pattern in deep nonlinear networks which aligns well with recent empirical studies. Moreover, we demonstrate the practical implications of our results in transfer learning. Our code is available at https://github.com/Heimine/PNC_DLN.

Lossy compression is conventionally driven by a task-agnostic distortion (e.g., MSE or MS-SSIM), yet in many emerging applications the receiver cares not about uniform fidelity but about a downstream task whose relevant content varies across the signal and evolves over time. We formulate task-aware compression as a weighted rate-distortion problem, in which a single codec is driven by a separable, per-component weighted distortion whose weights encode task importance and may depend on the source. We introduce task consistency, i.e., that minimizing the weighted distortion also minimizes the true task loss, and characterize when it holds: for linear tasks, the task loss admits a weighted-MSE form with signal-independent weights under suitable cross-term conditions, while for nonlinear tasks, an integrated-gradients analysis motivates separable task-aware weights. We show how task symmetry and irrelevance further constrain the admissible weights. Guided by this theory, we realize the weight-conditioned code in a single learned Vision Transformer (ViT) codec whose token-level attention natively consumes a per-component importance vector, so one fixed backbone is re-targeted at runtime, from universal (task-agnostic) to task-specialized operation, purely by swapping the injected weights, without retraining, while producing a single human-viewable reconstruction steered to the active task. On downstream face-analysis tasks, a single model reaches 91.4% accuracy at 0.034 bpp on a localized task, within 1.9% of a task-specific codec (93.3%) and well above a universal codec (76.9%). Such task-adaptive compression suits bandwidth-constrained perception systems, e.g., in Physical AI, where the active task drifts and per-task retraining is infeasible.

The basic problem of semantic compression is to minimize the length of a message while preserving its meaning. This differs from classical notions of compression in that the distortion is not measured directly at the level of bits, but rather in an abstract semantic space. In order to make this precise, we take inspiration from cognitive neuroscience and machine learning and model semantic space as a continuous Euclidean vector space. In such a space, stimuli like speech, images, or even ideas, are mapped to high-dimensional real vectors, and the location of these embeddings determines their meaning relative to other embeddings. This suggests that a natural metric for semantic similarity is just the Euclidean distance, which is what we use in this work. We map the optimization problem of determining the minimal-length, meaning-preserving message to a spin glass Hamiltonian and solve the resulting statistical mechanics problem using replica theory. We map out the replica symmetric phase diagram, identifying distinct phases of semantic compression: a first-order transition occurs between phases marked by the emergence of paraphrases, whereas a continuous crossover is seen from extractive to abstractive compression. We speculate on which features of the phase diagram are captured by replica symmetry, and which features change under replica symmetry breaking. We conclude by showing numerical simulations of compressions obtained by simulated annealing and greedy algorithms, and argue that while the problem of finding a meaning-preserving compression is computationally hard in the worst case, there exist efficient algorithms which achieve near optimal performance in the typical case.

Long-context inference with large language models (LLMs) is costly: self-attention during prefill scales quadratically with sequence length, and the key-value (KV) cache grows with the number of processed tokens. Larger context windows also do not ensure reliable evidence use. Context compression reduces this cost, but many soft-compression methods use LLMs as compressors and rely on compact memory tokens both to preserve information and to condition the decoder. We propose SeDeM, a selective decompression framework that decouples compact memory storage from decoder conditioning. SeDeM stores context as compact hidden-state memory blocks, selects query-relevant blocks, and decompresses only the selected blocks for decoder conditioning. Thus, the decoder avoids both full-context processing and direct generation from highly compressed memory slots. On four long-context QA benchmarks, SeDeM achieves higher QA scores than the compression baselines in our main comparison in both 1B and 3B same-backbone settings, and with the 3B backbone exceeds full-context fine-tuning on three datasets. SeDeM also provides favorable quality--efficiency trade-offs, achieving 1.74--2.46$\times$ lower online time-to-first-token and 1.08--1.10$\times$ higher autoregressive decoding throughput relative to ICAE while maintaining strong answer quality.