Chain-of-thought (CoT) reasoning improves multi-step problem solving, but long reasoning traces inflate inference cost. Token-level CoT compression reduces this cost by pruning full reasoning chains into shorter traces for model adaptation, making token selection the central challenge. Existing methods often rely on external scorers or heuristic signals only indirectly tied to the model's internal answer computation. We instead adopt a model-internal perspective: as the model forms an answer, each reasoning token leaves a ripple in the residual stream, the model's \emph{stream of thought}, and the magnitude of this ripple reflects the token's contribution to the answer computation. Building on this view, we propose \textsc{MIST} (Model-Internal Saliency for Token-level CoT compression), which defines token importance along two complementary axes: \emph{necessity}, the drop in answer likelihood when a token's internal contribution is removed, and \emph{sufficiency}, the gain in answer likelihood when that contribution alone is provided. Combining the two yields a unified importance score for pruning. Across four reasoning benchmarks and four models, \textsc{MIST} consistently outperforms baseline methods, suggesting that model-internal saliency provides an effective proxy for reasoning-token importance.
Large language models often rely on Chain-of-Thought (CoT) reasoning to solve complex tasks, but verbose reasoning traces introduce substantial inference overhead. CoT compression shortens generation, yet aggressive compression may disrupt logical coherence and degrade performance. We formalize this trade-off as the Context-Generation Substitution Law, where explicit reasoning context substitutes for part of decode-time generation. Based on this principle, we propose Memory-Augmented Compression, a training-free framework that constructs reusable reasoning memories from historical traces and retrieves them as prefill-side scaffolds. Rather than using raw demonstrations, these memories summarize reusable reasoning patterns, key constraints, and critical operations to compensate for information lost during compression. Experiments show that Memory consistently improves prompt-based Chain-of-Draft (CoD) compression across mathematical reasoning, complex reasoning, and science question answering tasks, yielding accuracy gains of 21.4, 28.0, 29.5, and 6.61 points over CoD on GSM8K, MATH, BBH, and MMLU-Sci, while achieving a 1.14-1.49x latency speedup latency speedup over standard CoT. Memory is also compatible with token-level, reasoning-trace-level, and inference-state compression mechanisms.
GPT-style models achieve strong performance by representing language with finite vocabularies of reusable discrete tokens. This success has motivated symbolic music tokenizations to treat recurring musical structures, such as chords, motifs, and phrases, as reusable units analogous to linguistic tokens. However, tokenization derives its advantage not from reusable combinations alone, but from compression: effective compression requires coordinates in which recurring regularities form stable and predictable conditional distributions. The key problem is therefore not to find larger musical combinations, but to discover the coordinate system in which musical facts become predictively compressible. We formulate the Effectiveness--Losslessness Framework and define tokenization as the construction of a predictively effective and relationally lossless coordinate system. The Predictive Effectiveness Principle defines the Fact--Token Boundary: decoupling and denesting construct coordinate interfaces that expose predictive regularities. The Relational Losslessness Principle defines the Token--State Boundary: tokenization stops before context-dependent relations are fixed, leaving their computation to model states. Controlled symbolic-music experiments validate these boundaries. Effective coordinate construction improves predictive compressibility, while fixed relational projections constrain contextual modeling. Sequence compaction alone does not guarantee predictive compression, while preserving contextual freedom allows higher-order musical organization to emerge without explicit structural labels. These results reveal why GPT-style models do not transfer directly across modalities: architectures transfer, but tokenization interfaces do not. Tokenization must discover effective representations while preserving the relational freedom from which contextual structure can emerge.
Compressed short-text generators can fail in two different places: the codec may discard information before generation starts, or the latent generator may produce weak codes. Without separating these failure modes, researchers can spend compute improving the wrong component. We study this problem in a controlled 64-to-16 TinyStories case study built from a hierarchical VQ-VAE-2 codec and a masked discrete diffusion generator (MDLM). We use a staged validation protocol that separates codec reconstruction fidelity, latent generation quality, and auxiliary latent diagnostics under one shared external GPT-2 scorer, while reporting complementary semantic metrics for the geometry study. In the tested configuration, codec reconstruction alone raises median external perplexity from 15.17 to 27.36 (+80.4%) and p95 from 25.10 to 98.91 (+294.1%), showing that the dominant quality loss appears before latent generation begins. Under the same scorer, code-space MDLM remains materially stronger than token-space diffusion, reducing mean, median, and p95 by 32.9%, 30.9%, and 36.6%, respectively. Geometry-aware regularization improves local latent proxies but does not improve decoded-text metrics in the available runs. The contribution is methodological rather than algorithmic: the paper presents a reusable staged diagnosis for one concrete pipeline and shows that, in this setting, codec fidelity rather than latent denoising sets the practical quality ceiling.
Adhiraj Singh, Deepanshu Mody, Ghina Al Shdaifat +4cs.CL
Recent work has shown that subword vocabularies can be trained to optimize compression for a specific inference rule rather than relying on greedy heuristics such as Byte Pair Encoding (BPE). We extend this approach to greedy left-to-right longest-match decoding, the fast and widely used inference rule underlying WordPiece. We introduce Joint Optimization for Greedy Longest-Match Tokenization (JOLT), which formulates vocabulary learning as an integer program over vocabulary-selection and segmentation-choice variables. Greedy-consistency constraints ensure that each optimized segmentation exactly matches the segmentation produced by longest-match decoding under the selected vocabulary, aligning the training objective with deployment-time tokenization. To scale the optimization, we solve a linear programming relaxation and selectively introduce higher-order segmentations only for unresolved pretokens. The resulting relaxation is nearly integral: rounded solutions fall within 0.008 - 0.176 % of the LP lower bound on the training scope. The bound also shows that BPE is already within 1 - 2 % of the best achievable compression under greedy longest-match decoding, while JOLT closes 89.6 - 99.4 % of the remaining gap. On held-out validation data across four training scopes and vocabulary sizes of 32,000 and 64,000, JOLT produces up to 0.78 % fewer tokens than BPE, with improvements generally increasing as the training scope grows. These results demonstrate that inference-aligned vocabulary optimization can recover most of the limited compression headroom left by BPE while providing a certificate of near-optimality.
Modern multilingual tokenizers often fragment Ukrainian and other underrepresented Cyrillic-script languages more heavily than English, creating disparities in cost and context capacity. We quantify this overhead across nine production tokenizers and five languages with standardized Cyrillic and Latin representations, covering 8.37 million word forms. On a corpus benchmark, Ukrainian shows 68-121% token overhead on modern tokenizers and 220% on the older cl100k, measured through full-text fertility on the BrUK and Brown corpora. Overhead is negatively associated with Cyrillic vocabulary allocation in the subset with independently verified English baselines, although the association is not statistically significant (Spearman rho = -0.536, p = 0.215, n = 7). We evaluate two mitigation strategies. LLMLingua-2 reduces Ukrainian input length by 47-49% on an e-commerce RAG benchmark of 1,536 products and 145 queries, with no compression-induced value losses among 80 retrievable cases. A balanced byte-level BPE tokenizer trained with a 200K vocabulary cap, converging at 158,184 actual entries, reduces the held-out UK/EN ratio from 2.22x to 1.30x. Romanization increases Ukrainian token counts by 2-19% on most tokenizers. Across the five languages, tokenization efficiency favors the script more prevalent in web data. These findings indicate that training data allocation contributes to Cyrillic tokenization overhead and that mitigation is possible at both inference and tokenizer-design stages.
Chain-of-Thought (CoT) prompting has significantly advanced the reasoning capabilities of Large Language Models (LLMs), yet it often incurs substantial computational costs due to over-reasoning: the generation of redundant, verbose, or irrelevant steps. While existing reasoning step evaluators effectively detect logical fallacies and factual errors, our analysis reveals a critical blind spot: they fail to penalize valid but inefficient reasoning steps that inflate token usage without contributing to the solution. To systematically diagnose this limitation, we introduce RIV-GSM8K, a diagnostic benchmark injected with five distinct types of inefficiencies, including circular reasoning and excessive decomposition. Diagnostic experiments reveal that state-of-the-art evaluators struggle to distinguish these inefficiencies from necessary reasoning. To address this gap, we propose CAID (Context-Aware Information Density), a training-free metric grounded in information theory that identifies low-utility steps. To validate the metric's practical utility, we apply it within PACE, a post-hoc compression strategy. Additional control experiments show that the gains of PACE are not explained by trivial pruning: compared with random step removal and PRM-based compression baselines, it preserves accuracy at substantially higher compression rates. Empirical results on GSM8K, StrategyQA, and ARC-Challenge demonstrate that PACE reduces token consumption by 31-53% while maintaining accuracy, confirming that CAID successfully distills informational froth from reasoning chains without compromising deductive validity.
Chain of thought prompting improves complex reasoning, but its long intermediate traces create substantial inference cost and hinder practical deployment in financial settings. We present a Hierarchical Semantic Distillation Network, HSDN, for compressing reasoning chains while preserving answer accuracy and logical coherence. The framework combines semantic segmentation, dependency graph construction, dual encoder importance scoring, constrained segment selection, and local boundary rewriting. A frozen Qwen3 4B model is used only for feature extraction and final answer generation, while the compression process remains structured and interpretable. On the AFAC2025 benchmark, HSDN achieves 91.0% accuracy with 68.4% compression, outperforming strong compression baselines in overall score and reasoning coherence. The results show that graph guided compression is effective for high stakes financial reasoning tasks.
How far can a language model improve under a strict artifact budget? Parameter Golf posed this question as an open community challenge in which participants trained the best language model, with the complete artifact (training code + compressed weights) required to fit within 16 MB and be trained in under ten minutes on 8xH100 SXM GPUs. Quality was measured in bits-per-byte (BPB), the average number of bits required to encode each byte of unseen text. We analyze 2,037 pull requests and 1,430 clean scored submissions from the contest, build a taxonomy of 84 optimization techniques, and measure each technique's contribution to BPB. The verified leaderboard score dropped from 1.2244 to 1.058 BPB across three phases -- a 13.6% reduction, despite individual techniques rarely improving BPB by more than 1%. We show that most gains in techniques shrink across competitive submissions, isolating the few methods that improve performance across stacks.
Large language models achieve high reasoning performance via explicit chain-of-thought and reinforcement learning, but require long output sequences and extended inference time. Latent reasoning reduces this cost by shifting computation into a latent space; however, continuous latent methods are hard to train, suffering from unstable and uninterpretable reasoning trajectories. We argue these issues stem from a misalignment between continuous-space reasoning and discrete symbolic supervision, as continuous states lack explicit anchors for step-by-step alignment. To resolve this, we propose \textbf{Discrete Latent Reasoning~(DLR)}, the first method that converts continuous latent states into explicit discrete tokens. Inspired by render-based compression, we render textual chains of thought into images, extract visual features, and construct a discrete latent vocabulary via clustering-based fine-tuning. Expanding the vocabulary and output head enables standard autoregressive modeling over both natural language and latent tokens, supporting pretraining alignment, SFT, and RL. Experiments on five reasoning benchmarks and two model series~(Qwen3-VL and LLaMA-3) confirm that \textbf{DLR} outperforms prior latent reasoning baselines with up to \textbf{20$\times$ compression}. Furthermore, the learned latent trajectories retain an interpretable semantic structure. Overall, discrete latent tokens provide a controllable and interpretable basis for efficient latent reasoning.
The Unigram tokenizer uses an elegant representation which makes it straightforward to edit vocabularies, but its training is comparatively heavy and complex. We introduce MinGram (Minimalist Unigram), which keeps the token-list representation but simplifies training using a BPE-derived seed vocabulary, Hard EM on a minimum-token path, and a single flat score-pruning step. This removes the suffix array, the forward-backward pass, and the iterative prune loop, leaving a procedure that requires little beyond tokenizer inference itself. By making token count the primary objective and using a Unigram score only as a tiebreak, MinGram keeps the compression of pure token-count methods while retaining much of the morphological alignment and downstream quality of probabilistic ones. Across six languages, MinGram compresses better than both BPE and standard Unigram, and a compression-oriented variant matches the strongest token-count compressors while retaining substantially higher morphological alignment. In controlled downstream language-model training, Unigram-family tokenizers, with MinGram among the best, consistently beat BPE in bits-per-byte.
Chain-of-Thought (CoT) distillation transfers multi-step reasoning from large reasoning models to smaller students, but verbose teacher traces inflate both training and inference cost. Existing CoT compression methods fall into two families, selective pruning and generative rewriting, yet prior studies have left key factors entangled: granularity is confounded with importance criteria in pruning, restructuring level is rarely isolated in rewriting, and compression budgets are not systematically evaluated across domains or regimes. We recast CoT compression along three dimensions: importance criterion, restructuring level, and compression budget. Sweeping these across two model families, Math and General domains, and Long-/Short-CoT regimes, we find that (i) importance criterion utility is strictly governed by granularity: step-level criteria converge on a shared reasoning backbone, while token-level pruning requires symbol-aware signals to preserve the logical core; (ii) restructuring level inverts across domains: Math degrades monotonically with structural disruption, while aggressive rewriting acts as a denoiser on General tasks; (iii) training-time compression does not necessarily translate to inference-time savings: Long-CoT students retain verbose habits despite concise supervision, making the training ratio an optimistic lower bound on deployment cost. These findings yield condition-aware guidelines for matching compression to deployment context.
Maxime Griot, Paul Steven Scotti, Tanishq Mathew Abrahamcs.LG cs.CL
Reasoning models produce long chain-of-thought traces that are costly to distill and encourage verbose student outputs. We study post-hoc compression of such traces before knowledge distillation. Two teachers, Qwen3.5-397B-A17B and gpt-oss-120B, generate about 283k correct traces each; two instruction-tuned models then compress them to 8.6-21.0% of their original character length. Across a 48-run main grid plus seven Qwen-teacher truncation ablations, compressed traces reduce training tokens to 12-30% of raw, speed up training by 2.0-7.6x, and shorten inference outputs by 3-19x with smaller reductions under the shorter gpt-oss teacher. However, raw traces retain the highest downstream accuracy at every scale and for both teachers. A length-matched raw-trace truncation ablation shows that compression is not merely benefiting from a smaller token budget: model-compressed traces usually beat or match naive truncation, especially for smaller students, while maintaining shorter inference outputs. Overall, reasoning-trace compression offers an accuracy-efficiency trade-off rather than a free improvement: students retain up to 96% of raw-trace accuracy while gaining up to 18x higher per-token efficiency, and at the 0.8B scale under LoRA compressed traces narrow the raw-vs-compressed gap but do not exceed raw.
Extended chain-of-thought (CoT) traces improve LLM reasoning but incur substantial computational and memory costs. While existing CoT compression methods mitigate this by condensing thought steps into compact representations via memory tokens and retaining only these representations at inference time, the loss of fine-grained information makes subsequent steps more error-prone. To alleviate this, we propose \textbf{HybridThinker}, where in addition to preserved these representations, thought steps are also temporarily retained to provide fine-grained details. However, we observe that naively keeping thought steps accessible to subsequent steps \emph{during training} lets the model bypass memory tokens by retrieving information directly from these steps, leaving the model's ability to compress and retrieve information through memory tokens insufficiently trained. We therefore introduce a hybrid training scheme, in which only some thought steps are directly accessible through attention to subsequent steps, while the other thought steps are masked, forcing the model to use memory tokens for compression and retrieval. Across 4 reasoning benchmarks, HybridThinker matches the uncompressed baseline, advancing the state of the art in CoT compression by 5.8 points on average accuracy with similar inference time. Ablation studies confirm that both temporary thought-step retention and the hybrid training scheme contribute to these gains.
Large language models achieve remarkable performance via extended chain-of-thought (CoT) reasoning, yet this lengthy process incurs substantial inference overhead. Existing CoT compression methods struggle with inflexible manual length budgets, computationally expensive multi-stage training pipelines, and fragile scalability restricted to small models. We propose HMPO (Hybrid Median-length Policy Optimization), a cost-effective, single-stage reinforcement learning framework. HMPO efficiently compresses CoT via three synergistic components: an adaptive median-based budget derived from successful rollouts to eliminate manual tuning, a cosine-decay token reward for smooth length penalization, and a multiplicative reward formulation that substantially mitigates trivial reward hacking by strictly prioritizing answer correctness. Trained exclusively on mathematical data, HMPO generalizes seamlessly across math, code, science, and instruction-following tasks. Extensive experiments scaling from 9B to 122B parameters across dense and Mixture-of-Experts (MoE) architectures demonstrate that HMPO achieves 19%--46% token compression with negligible accuracy degradation, all while drastically reducing training costs compared to existing multi-stage baselines.
Craig W. Schmidt, Michael Krumdick, Adam Wiemerslage +4cs.CL
We introduce Tokenization with Split Trees (ToaST), a subword tokenization method that directly optimizes compression under a new recursive inference procedure. ToaST greedily splits each pretoken into a full binary tree using precomputed byte n-gram counts, independent of any vocabulary. Given a vocabulary, inference recursively descends each split tree and emits the first in-vocabulary node reached on each path. Vocabulary selection is formulated as an Integer Program (IP) that minimizes the total token count over all split trees under this inference procedure. The Linear Programming (LP) relaxation is near-integral in practice, yielding provably near-optimal vocabularies, with training time empirically scaling quadratically in the number of split trees. On English text, ToaST reduces token counts by more than 11% compared to BPE, WordPiece, and UnigramLM at vocabulary sizes of 40,960 and above, reducing the number of inference tokens for models using this tokenizer, thus extending the effective context length. ToaST also uses common single-byte tokens less frequently than these baselines, leading to a substantial improvement in Renyi efficiency. In experiments training 1.5B parameter language models, ToaST achieves the highest CORE score, outperforming baselines by 2.6%--7.6%, with significance for two of three, and scoring best on 13 of 22 individual tasks.
Reasoning in Large Language Models incurs significant inference-time compute, yet the token-level information structure of reasoning traces remains underexplored. We observe that reasoning tokens split into two functional types: low-entropy \textit{structural} tokens (recurring phrases that scaffold the reasoning process) and higher-entropy \textit{organic} tokens (problem-specific content that drives toward a solution). This asymmetry motivates a simple, model-agnostic compression pipeline: apply cross-word BPE merges on a model's own reasoning traces to derive \textit{supertokens} that capture frequent structural patterns, then teach the model to adopt them via supervised fine-tuning. Across three model families and five mathematical reasoning benchmarks, our approach shortens reasoning traces by 8.1\% on average with no statistically significant accuracy loss on any model--benchmark pair. Beyond compression, supertokens act as interpretable reasoning-move annotations (backtracking, verification, strategy shifts), exposing the model's high-level strategy at a glance. Analyzing transitions between structural categories reveals systematic differences between correct and incorrect traces: correct traces show productive recovery (backtracking followed by strategy shifts and verification), while incorrect traces are dominated by confusion cycles (repeated hedging and unresolved contradictions). These diagnostic signals suggest applications in reward shaping and early stopping for RL-based reasoning training.