Model collapse occurs in structured interactive learning if and only if the directed interaction graph satisfies a specific topological condition, with finite-sample guarantees for linear regression and asymptotic results for M-estimators.
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A Survey on Knowledge Distillation of Large Language Models
Canonical reference. 83% of citing Pith papers cite this work as background.
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abstract
In the era of Large Language Models (LLMs), Knowledge Distillation (KD) emerges as a pivotal methodology for transferring advanced capabilities from leading proprietary LLMs, such as GPT-4, to their open-source counterparts like LLaMA and Mistral. Additionally, as open-source LLMs flourish, KD plays a crucial role in both compressing these models, and facilitating their self-improvement by employing themselves as teachers. This paper presents a comprehensive survey of KD's role within the realm of LLM, highlighting its critical function in imparting advanced knowledge to smaller models and its utility in model compression and self-improvement. Our survey is meticulously structured around three foundational pillars: \textit{algorithm}, \textit{skill}, and \textit{verticalization} -- providing a comprehensive examination of KD mechanisms, the enhancement of specific cognitive abilities, and their practical implications across diverse fields. Crucially, the survey navigates the intricate interplay between data augmentation (DA) and KD, illustrating how DA emerges as a powerful paradigm within the KD framework to bolster LLMs' performance. By leveraging DA to generate context-rich, skill-specific training data, KD transcends traditional boundaries, enabling open-source models to approximate the contextual adeptness, ethical alignment, and deep semantic insights characteristic of their proprietary counterparts. This work aims to provide an insightful guide for researchers and practitioners, offering a detailed overview of current methodologies in KD and proposing future research directions. Importantly, we firmly advocate for compliance with the legal terms that regulate the use of LLMs, ensuring ethical and lawful application of KD of LLMs. An associated Github repository is available at https://github.com/Tebmer/Awesome-Knowledge-Distillation-of-LLMs.
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CoDistill-GRPO lets small and large models mutually improve via co-distillation in GRPO, raising small-model math accuracy by over 11 points while cutting large-model training time by about 18%.
Chain-based Distillation constructs a sequence of anchor models to enable efficient initialization of variable-sized SLMs through interpolation, with bridge distillation for cross-architecture transfer, yielding better performance than scratch training.
AOPD modifies on-policy distillation by using localized divergence minimization for non-positive advantages instead of negative reinforcement, yielding average gains of 4.09/8.34 over standard OPD on math reasoning benchmarks under strong/weak initialization.
LOVER creates an unsupervised logic-regularized verifier that reaches 95% of supervised verifier performance on reasoning tasks across 10 datasets.
ReflectMT internalizes reflection via two-stage RL to enable direct high-quality machine translation that outperforms explicit reasoning models like DeepSeek-R1 on WMT24 while using 94% fewer tokens.
A semi-supervised framework distills vision foundation models into compact instance segmentation experts that outperform their teachers by up to 11.9 AP on Cityscapes and 8.6 AP on ADE20K while being 11 times smaller.
CodeRL+ integrates variable-level execution trajectory inference into RLVR training to align textual code representations with execution semantics, delivering 4.6% relative pass@1 gains and generalization to code-reasoning and test-output tasks.
CODI compresses explicit CoT into continuous space via self-distillation and is the first implicit method to match explicit CoT performance on GSM8k at GPT-2 scale with 3.1x compression and 28.2% higher accuracy than prior implicit approaches.
DASD improves math reasoning in LLMs by adaptively directing self-distillation based on per-token entropy to balance exploration and step accuracy, outperforming prior self-distillation and RLVR baselines on six benchmarks.
FireFly inverts task synthesis by exploring real MCP servers first via pairwise tool graphs and sub-DAG sampling, then generates 5,144 verified tasks backward from outcomes to train a 4B model that matches Claude Sonnet 4.6 on tool-calling benchmarks.
OpenJarvis decomposes personal AI into Intelligence, Engine, Agents, Tools & Memory, and Learning primitives and applies LLM-guided spec search to produce on-device configurations that reach within 3.2 pp of cloud baselines on average across eight tasks.
PARSE trains a prompt-aware linear router on dense-model outputs to select dynamic SVD ranks, improving accuracy up to 10% at 0.6 compression ratio on LLaMA-7B while delivering 2.5x prefill and 2.4x decode speedups.
SOD reweights on-policy distillation strength step-by-step using divergence to stabilize tool use in small language model agents, yielding up to 20.86% gains and 26.13% on AIME 2025 for a 0.6B model.
SimCT enlarges the supervision space in cross-tokenizer on-policy distillation using short jointly tokenizable multi-token continuations, producing consistent gains over shared-token baselines on math and code benchmarks.
UniSD unifies self-distillation components for autoregressive LLMs and its full integrated version improves base models by 5.4 points and baselines by 2.8 points across six benchmarks.
DeCo-DETR builds hierarchical semantic prototypes offline and uses decoupled training streams to deliver competitive zero-shot open-vocabulary detection with improved inference speed.
LLM agents iteratively generate and optimize data processing strategies for fine-tuning, delivering over 80% win rates versus unprocessed data and 65% versus LLM-based AutoML baselines while cutting search time by up to 10x.
VERDI aligns perception, prediction, and planning outputs of end-to-end AD models with VLM-generated text features at training time to embed structured reasoning, yielding up to 11% better l2 distance and 10% higher non-collision rate in closed-loop tests.
ReAD applies a contextual bandit to allocate fixed-token distillation budget across interdependent LLM capabilities, yielding higher task utility and fewer negative spillovers than standard methods.
LLM post-training is unified as off-policy or on-policy interventions that expand support for useful behaviors, reshape policies within reachable states, or consolidate behavior across training stages.
A multi-scale weakly supervised framework converts underwater point classifications into coarse masks to train UAV coral segmentation models, then refines them via self-training to reach 86.07% pixel accuracy and 52.23% mIoU without pixel-level labels.
Empirical tests show compressed code language models retain task performance but suffer markedly lower robustness under four standard adversarial attacks.
RAP is a reinforcement learning framework for runtime-adaptive pruning of LLMs that jointly optimizes model weights and KV-cache usage under varying memory budgets.
citing papers explorer
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Chain-based Distillation for Effective Initialization of Variable-Sized Small Language Models
Chain-based Distillation constructs a sequence of anchor models to enable efficient initialization of variable-sized SLMs through interpolation, with bridge distillation for cross-architecture transfer, yielding better performance than scratch training.
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Logic-Regularized Verifier Elicits Reasoning from LLMs
LOVER creates an unsupervised logic-regularized verifier that reaches 95% of supervised verifier performance on reasoning tasks across 10 datasets.
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ReflectMT: Internalizing Reflection for Efficient and High-Quality Machine Translation
ReflectMT internalizes reflection via two-stage RL to enable direct high-quality machine translation that outperforms explicit reasoning models like DeepSeek-R1 on WMT24 while using 94% fewer tokens.
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CODI: Compressing Chain-of-Thought into Continuous Space via Self-Distillation
CODI compresses explicit CoT into continuous space via self-distillation and is the first implicit method to match explicit CoT performance on GSM8k at GPT-2 scale with 3.1x compression and 28.2% higher accuracy than prior implicit approaches.
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SOD: Step-wise On-policy Distillation for Small Language Model Agents
SOD reweights on-policy distillation strength step-by-step using divergence to stabilize tool use in small language model agents, yielding up to 20.86% gains and 26.13% on AIME 2025 for a 0.6B model.
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SimCT: Recovering Lost Supervision for Cross-Tokenizer On-Policy Distillation
SimCT enlarges the supervision space in cross-tokenizer on-policy distillation using short jointly tokenizable multi-token continuations, producing consistent gains over shared-token baselines on math and code benchmarks.
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UniSD: Towards a Unified Self-Distillation Framework for Large Language Models
UniSD unifies self-distillation components for autoregressive LLMs and its full integrated version improves base models by 5.4 points and baselines by 2.8 points across six benchmarks.
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ReAD: Reinforcement-Guided Capability Distillation for Large Language Models
ReAD applies a contextual bandit to allocate fixed-token distillation budget across interdependent LLM capabilities, yielding higher task utility and fewer negative spillovers than standard methods.
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Large Language Model Post-Training: A Unified View of Off-Policy and On-Policy Learning
LLM post-training is unified as off-policy or on-policy interventions that expand support for useful behaviors, reshape policies within reachable states, or consolidate behavior across training stages.
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ADMEDTAGGER: an annotation framework for distillation of expert knowledge for the Polish medical language
Llama 3.1 annotates Polish medical texts to train DistilBERT classifiers achieving F1 scores above 0.80 that are 500 times smaller than the teacher model.