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Apr 14

Logit Standardization in Knowledge Distillation

Knowledge distillation involves transferring soft labels from a teacher to a student using a shared temperature-based softmax function. However, the assumption of a shared temperature between teacher and student implies a mandatory exact match between their logits in terms of logit range and variance. This side-effect limits the performance of student, considering the capacity discrepancy between them and the finding that the innate logit relations of teacher are sufficient for student to learn. To address this issue, we propose setting the temperature as the weighted standard deviation of logit and performing a plug-and-play Z-score pre-process of logit standardization before applying softmax and Kullback-Leibler divergence. Our pre-process enables student to focus on essential logit relations from teacher rather than requiring a magnitude match, and can improve the performance of existing logit-based distillation methods. We also show a typical case where the conventional setting of sharing temperature between teacher and student cannot reliably yield the authentic distillation evaluation; nonetheless, this challenge is successfully alleviated by our Z-score. We extensively evaluate our method for various student and teacher models on CIFAR-100 and ImageNet, showing its significant superiority. The vanilla knowledge distillation powered by our pre-process can achieve favorable performance against state-of-the-art methods, and other distillation variants can obtain considerable gain with the assistance of our pre-process.

  • 5 authors
·
Mar 3, 2024

Talking Models: Distill Pre-trained Knowledge to Downstream Models via Interactive Communication

Many recent breakthroughs in machine learning have been enabled by the pre-trained foundation models. By scaling up model parameters, training data, and computation resources, foundation models have significantly advanced the state-of-the-art in many applications. However, it is still an open question of how to use these models to perform downstream tasks efficiently. Knowledge distillation (KD) has been explored to tackle this challenge. KD transfers knowledge from a large teacher model to a smaller student model. While KD has been successful in improving student model performance, recent research has discovered that a powerful teacher does not necessarily lead to a powerful student, due to their huge capacity gap. In addition, the potential distribution shifts between the pre-training data and downstream tasks can make knowledge transfer in KD sub-optimal for improving downstream task performance. In this paper, we extend KD with an interactive communication process to help students of downstream tasks learn effectively from pre-trained foundation models. Our design is inspired by the way humans learn from teachers who can explain knowledge in a way that meets the students' needs. Specifically, we let each model (i.e., student and teacher) train two components: (1) an encoder encoding the model's hidden states to a message and (2) a decoder decoding any messages to its own hidden states. With encoder and decoder, not only can the teacher transfer rich information by encoding its hidden states, but also the student can send messages with information of downstream tasks to the teacher. Therefore, knowledge passing from teacher to student can be tailored to the student's capacity and downstream tasks' distributions. We conducted experiments on benchmark datasets to show that our communication mechanism outperforms state-of-the-art distillation techniques.

  • 6 authors
·
Oct 4, 2023

Not All Correct Answers Are Equal: Why Your Distillation Source Matters

Distillation has emerged as a practical and effective approach to enhance the reasoning capabilities of open-source language models. In this work, we conduct a large-scale empirical study on reasoning data distillation by collecting verified outputs from three state-of-the-art teacher models-AM-Thinking-v1, Qwen3-235B-A22B, and DeepSeek-R1-on a shared corpus of 1.89 million queries. We construct three parallel datasets and analyze their distributions, revealing that AM-Thinking-v1-distilled data exhibits greater token length diversity and lower perplexity. Student models trained on each dataset are evaluated on reasoning benchmarks including AIME2024, AIME2025, MATH500, and LiveCodeBench. The AM-based model consistently achieves the best performance (e.g., 84.3 on AIME2024, 72.2 on AIME2025, 98.4 on MATH500, and 65.9 on LiveCodeBench) and demonstrates adaptive output behavior-producing longer responses for harder tasks and shorter ones for simpler tasks. These findings highlight the value of high-quality, verified reasoning traces. We release the AM-Thinking-v1 and Qwen3-235B-A22B distilled datasets to support future research on open and high-performing reasoning-oriented language models. The datasets are publicly available on Hugging FaceDatasets are available on Hugging Face: \href{https://huggingface.co/datasets/a-m-team/AM-Thinking-v1-Distilled{AM-Thinking-v1-Distilled}, https://huggingface.co/datasets/a-m-team/AM-Qwen3-Distilled{AM-Qwen3-Distilled}.}.

  • 8 authors
·
May 20, 2025 2

Polyglot Teachers: Evaluating Language Models for Multilingual Synthetic Data Generation

Synthesizing supervised finetuning (SFT) data from language models (LMs) to teach smaller models multilingual tasks has become increasingly common. However, teacher model selection is often ad hoc, typically defaulting to the largest available option, even though such models may have significant capability gaps in non-English languages. This practice can result in poor-quality synthetic data and suboptimal student downstream performance. In this work, we systematically characterize what makes an effective multilingual teacher. We measure intrinsic measures of data quality with extrinsic student model performance in a metric we call Polyglot Score; evaluating 10 LMs across 6 typologically diverse languages, generating over 1.4M SFT examples and training 240 student models. Among the models tested, Gemma 3 27B and Aya Expanse 32B emerge as consistently effective teachers across different student base model families. Further analyses reveal that model scale alone does not significantly predict teacher effectiveness; instead, data qualities such as prompt diversity, length, and response fluency capture over 93.3% of variance in intrinsic data quality and predict student performance. Finally, we provide practical recommendations, including matching the model families of teacher-student pairs and translating from or responding to existing prompts, which can yield improvements for less-resourced languages. We hope that our work advances data-centric research in multilingual synthetic data and LM development.

Sparse Knowledge Distillation: A Mathematical Framework for Probability-Domain Temperature Scaling and Multi-Stage Compression

We develop a unified theoretical framework for sparse knowledge distillation based on probability-domain softening operators. While the equivalence p^{1/T} propto softmax(z/T) is well known, our contribution is an operator-level analytical framework built on this foundation rather than the equivalence itself. The framework comprises four core components: (i) operator-agnostic bias--variance decompositions that characterize when sparse students outperform dense teachers, (ii) a homotopy path formalization of multi-stage pruning in function space explaining why iterative compression succeeds where one-shot pruning fails, (iii) convergence guarantees establishing O(1/n) rates for n-stage distillation with explicit parameter dependence, and (iv) equivalence class characterizations identifying distinct probability-domain operators that yield identical student models under capacity constraints. We introduce an axiomatic definition of probability-domain softening operators based on ranking preservation, continuity, entropy monotonicity, identity, and boundary behavior, and show that multiple non-equivalent operator families satisfy these axioms. All learning-theoretic guarantees are shown to hold uniformly across this operator class, independent of implementation details. These results provide theoretical grounding for black-box teacher distillation, partial-access settings such as top-k truncation and text-only outputs, and privacy-preserving model compression.

  • 2 authors
·
Jan 6

Performance-Guided LLM Knowledge Distillation for Efficient Text Classification at Scale

Large Language Models (LLMs) face significant challenges at inference time due to their high computational demands. To address this, we present Performance-Guided Knowledge Distillation (PGKD), a cost-effective and high-throughput solution for production text classification applications. PGKD utilizes teacher-student Knowledge Distillation to distill the knowledge of LLMs into smaller, task-specific models. PGKD establishes an active learning routine between the student model and the LLM; the LLM continuously generates new training data leveraging hard-negative mining, student model validation performance, and early-stopping protocols to inform the data generation. By employing a cyclical, performance-aware approach tailored for highly multi-class, sparsely annotated datasets prevalent in industrial text classification, PGKD effectively addresses training challenges and outperforms traditional BERT-base models and other knowledge distillation methods on several multi-class classification datasets. Additionally, cost and latency benchmarking reveals that models fine-tuned with PGKD are up to 130X faster and 25X less expensive than LLMs for inference on the same classification task. While PGKD is showcased for text classification tasks, its versatile framework can be extended to any LLM distillation task, including language generation, making it a powerful tool for optimizing performance across a wide range of AI applications.

  • 3 authors
·
Nov 6, 2024

Context Aware Grounded Teacher for Source Free Object Detection

We focus on the Source Free Object Detection (SFOD) problem, when source data is unavailable during adaptation, and the model must adapt to the unlabeled target domain. In medical imaging, several approaches have leveraged a semi-supervised student-teacher architecture to bridge domain discrepancy. Context imbalance in labeled training data and significant domain shifts between domains can lead to biased teacher models that produce inaccurate pseudolabels, degrading the student model's performance and causing a mode collapse. Class imbalance, particularly when one class significantly outnumbers another, leads to contextual bias. To tackle the problem of context bias and the significant performance drop of the student model in the SFOD setting, we introduce Grounded Teacher (GT) as a standard framework. In this study, we model contextual relationships using a dedicated relational context module and leverage it to mitigate inherent biases in the model. This approach enables us to apply augmentations to closely related classes, across and within domains, enhancing the performance of underrepresented classes while keeping the effect on dominant classes minimal. We further improve the quality of predictions by implementing an expert foundational branch to supervise the student model. We validate the effectiveness of our approach in mitigating context bias under the SFOD setting through experiments on three medical datasets supported by comprehensive ablation studies. All relevant resources, including preprocessed data, trained model weights, and code, are publicly available at this https://github.com/Tajamul21/Grounded_Teacher.

  • 5 authors
·
Apr 21, 2025

A-SDM: Accelerating Stable Diffusion through Redundancy Removal and Performance Optimization

The Stable Diffusion Model (SDM) is a popular and efficient text-to-image (t2i) generation and image-to-image (i2i) generation model. Although there have been some attempts to reduce sampling steps, model distillation, and network quantization, these previous methods generally retain the original network architecture. Billion scale parameters and high computing requirements make the research of model architecture adjustment scarce. In this work, we first explore the computational redundancy part of the network, and then prune the redundancy blocks of the model and maintain the network performance through a progressive incubation strategy. Secondly, in order to maintaining the model performance, we add cross-layer multi-expert conditional convolution (CLME-Condconv) to the block pruning part to inherit the original convolution parameters. Thirdly, we propose a global-regional interactive (GRI) attention to speed up the computationally intensive attention part. Finally, we use semantic-aware supervision (SAS) to align the outputs of the teacher model and student model at the semantic level. Experiments show that this method can effectively train a lightweight model close to the performance of the original SD model, and effectively improve the model speed under limited resources. Experiments show that the proposed method can effectively train a light-weight model close to the performance of the original SD model, and effectively improve the model speed under limited resources. After acceleration, the UNet part of the model is 22% faster and the overall speed is 19% faster.

  • 6 authors
·
Dec 24, 2023

Historic Scripts to Modern Vision: A Novel Dataset and A VLM Framework for Transliteration of Modi Script to Devanagari

In medieval India, the Marathi language was written using the Modi script. The texts written in Modi script include extensive knowledge about medieval sciences, medicines, land records and authentic evidence about Indian history. Around 40 million documents are in poor condition and have not yet been transliterated. Furthermore, only a few experts in this domain can transliterate this script into English or Devanagari. Most of the past research predominantly focuses on individual character recognition. A system that can transliterate Modi script documents to Devanagari script is needed. We propose the MoDeTrans dataset, comprising 2,043 images of Modi script documents accompanied by their corresponding textual transliterations in Devanagari. We further introduce MoScNet (Modi Script Network), a novel Vision-Language Model (VLM) framework for transliterating Modi script images into Devanagari text. MoScNet leverages Knowledge Distillation, where a student model learns from a teacher model to enhance transliteration performance. The final student model of MoScNet has better performance than the teacher model while having 163times lower parameters. Our work is the first to perform direct transliteration from the handwritten Modi script to the Devanagari script. MoScNet also shows competitive results on the optical character recognition (OCR) task.

  • 4 authors
·
Mar 17, 2025

HTR-JAND: Handwritten Text Recognition with Joint Attention Network and Knowledge Distillation

Despite significant advances in deep learning, current Handwritten Text Recognition (HTR) systems struggle with the inherent complexity of historical documents, including diverse writing styles, degraded text quality, and computational efficiency requirements across multiple languages and time periods. This paper introduces HTR-JAND (HTR-JAND: Handwritten Text Recognition with Joint Attention Network and Knowledge Distillation), an efficient HTR framework that combines advanced feature extraction with knowledge distillation. Our architecture incorporates three key components: (1) a CNN architecture integrating FullGatedConv2d layers with Squeeze-and-Excitation blocks for adaptive feature extraction, (2) a Combined Attention mechanism fusing Multi-Head Self-Attention with Proxima Attention for robust sequence modeling, and (3) a Knowledge Distillation framework enabling efficient model compression while preserving accuracy through curriculum-based training. The HTR-JAND framework implements a multi-stage training approach combining curriculum learning, synthetic data generation, and multi-task learning for cross-dataset knowledge transfer. We enhance recognition accuracy through context-aware T5 post-processing, particularly effective for historical documents. Comprehensive evaluations demonstrate HTR-JAND's effectiveness, achieving state-of-the-art Character Error Rates (CER) of 1.23\%, 1.02\%, and 2.02\% on IAM, RIMES, and Bentham datasets respectively. Our Student model achieves a 48\% parameter reduction (0.75M versus 1.5M parameters) while maintaining competitive performance through efficient knowledge transfer. Source code and pre-trained models are available at https://github.com/DocumentRecognitionModels/HTR-JAND{Github}.

  • 3 authors
·
Dec 24, 2024

TITAN: Query-Token based Domain Adaptive Adversarial Learning

We focus on the source-free domain adaptive object detection (SF-DAOD) problem when source data is unavailable during adaptation and the model must adapt to an unlabeled target domain. The majority of approaches for the problem employ a self-supervised approach using a student-teacher (ST) framework where pseudo-labels are generated via a source-pretrained model for further fine-tuning. We observe that the performance of a student model often degrades drastically, due to the collapse of the teacher model, primarily caused by high noise in pseudo-labels, resulting from domain bias, discrepancies, and a significant domain shift across domains. To obtain reliable pseudo-labels, we propose a Target-based Iterative Query-Token Adversarial Network (TITAN), which separates the target images into two subsets: those similar to the source (easy) and those dissimilar (hard). We propose a strategy to estimate variance to partition the target domain. This approach leverages the insight that higher detection variances correspond to higher recall and greater similarity to the source domain. Also, we incorporate query-token-based adversarial modules into a student-teacher baseline framework to reduce the domain gaps between two feature representations. Experiments conducted on four natural imaging datasets and two challenging medical datasets have substantiated the superior performance of TITAN compared to existing state-of-the-art (SOTA) methodologies. We report an mAP improvement of +22.7, +22.2, +21.1, and +3.7 percent over the current SOTA on C2F, C2B, S2C, and K2C benchmarks, respectively.

  • 2 authors
·
Jun 26, 2025

Learning Occlusion-Robust Vision Transformers for Real-Time UAV Tracking

Single-stream architectures using Vision Transformer (ViT) backbones show great potential for real-time UAV tracking recently. However, frequent occlusions from obstacles like buildings and trees expose a major drawback: these models often lack strategies to handle occlusions effectively. New methods are needed to enhance the occlusion resilience of single-stream ViT models in aerial tracking. In this work, we propose to learn Occlusion-Robust Representations (ORR) based on ViTs for UAV tracking by enforcing an invariance of the feature representation of a target with respect to random masking operations modeled by a spatial Cox process. Hopefully, this random masking approximately simulates target occlusions, thereby enabling us to learn ViTs that are robust to target occlusion for UAV tracking. This framework is termed ORTrack. Additionally, to facilitate real-time applications, we propose an Adaptive Feature-Based Knowledge Distillation (AFKD) method to create a more compact tracker, which adaptively mimics the behavior of the teacher model ORTrack according to the task's difficulty. This student model, dubbed ORTrack-D, retains much of ORTrack's performance while offering higher efficiency. Extensive experiments on multiple benchmarks validate the effectiveness of our method, demonstrating its state-of-the-art performance. Codes is available at https://github.com/wuyou3474/ORTrack.

  • 7 authors
·
Apr 12, 2025 2

Effective Whole-body Pose Estimation with Two-stages Distillation

Whole-body pose estimation localizes the human body, hand, face, and foot keypoints in an image. This task is challenging due to multi-scale body parts, fine-grained localization for low-resolution regions, and data scarcity. Meanwhile, applying a highly efficient and accurate pose estimator to widely human-centric understanding and generation tasks is urgent. In this work, we present a two-stage pose Distillation for Whole-body Pose estimators, named DWPose, to improve their effectiveness and efficiency. The first-stage distillation designs a weight-decay strategy while utilizing a teacher's intermediate feature and final logits with both visible and invisible keypoints to supervise the student from scratch. The second stage distills the student model itself to further improve performance. Different from the previous self-knowledge distillation, this stage finetunes the student's head with only 20% training time as a plug-and-play training strategy. For data limitations, we explore the UBody dataset that contains diverse facial expressions and hand gestures for real-life applications. Comprehensive experiments show the superiority of our proposed simple yet effective methods. We achieve new state-of-the-art performance on COCO-WholeBody, significantly boosting the whole-body AP of RTMPose-l from 64.8% to 66.5%, even surpassing RTMPose-x teacher with 65.3% AP. We release a series of models with different sizes, from tiny to large, for satisfying various downstream tasks. Our codes and models are available at https://github.com/IDEA-Research/DWPose.

  • 4 authors
·
Jul 28, 2023

SuperCorrect: Supervising and Correcting Language Models with Error-Driven Insights

Large language models (LLMs) like GPT-4, PaLM, and LLaMA have shown significant improvements in various reasoning tasks. However, smaller models such as Llama-3-8B and DeepSeekMath-Base still struggle with complex mathematical reasoning because they fail to effectively identify and correct reasoning errors. Recent reflection-based methods aim to address these issues by enabling self-reflection and self-correction, but they still face challenges in independently detecting errors in their reasoning steps. To overcome these limitations, we propose SuperCorrect, a novel two-stage framework that uses a large teacher model to supervise and correct both the reasoning and reflection processes of a smaller student model. In the first stage, we extract hierarchical high-level and detailed thought templates from the teacher model to guide the student model in eliciting more fine-grained reasoning thoughts. In the second stage, we introduce cross-model collaborative direct preference optimization (DPO) to enhance the self-correction abilities of the student model by following the teacher's correction traces during training. This cross-model DPO approach teaches the student model to effectively locate and resolve erroneous thoughts with error-driven insights from the teacher model, breaking the bottleneck of its thoughts and acquiring new skills and knowledge to tackle challenging problems. Extensive experiments consistently demonstrate our superiority over previous methods. Notably, our SuperCorrect-7B model significantly surpasses powerful DeepSeekMath-7B by 7.8%/5.3% and Qwen2.5-Math-7B by 15.1%/6.3% on MATH/GSM8K benchmarks, achieving new SOTA performance among all 7B models. Code: https://github.com/YangLing0818/SuperCorrect-llm

  • 7 authors
·
Oct 11, 2024 3

GigaSpeech 2: An Evolving, Large-Scale and Multi-domain ASR Corpus for Low-Resource Languages with Automated Crawling, Transcription and Refinement

The evolution of speech technology has been spurred by the rapid increase in dataset sizes. Traditional speech models generally depend on a large amount of labeled training data, which is scarce for low-resource languages. This paper presents GigaSpeech 2, a large-scale, multi-domain, multilingual speech recognition corpus. It is designed for low-resource languages and does not rely on paired speech and text data. GigaSpeech 2 comprises about 30,000 hours of automatically transcribed speech, including Thai, Indonesian, and Vietnamese, gathered from unlabeled YouTube videos. We also introduce an automated pipeline for data crawling, transcription, and label refinement. Specifically, this pipeline uses Whisper for initial transcription and TorchAudio for forced alignment, combined with multi-dimensional filtering for data quality assurance. A modified Noisy Student Training is developed to further refine flawed pseudo labels iteratively, thus enhancing model performance. Experimental results on our manually transcribed evaluation set and two public test sets from Common Voice and FLEURS confirm our corpus's high quality and broad applicability. Notably, ASR models trained on GigaSpeech 2 can reduce the word error rate for Thai, Indonesian, and Vietnamese on our challenging and realistic YouTube test set by 25% to 40% compared to the Whisper large-v3 model, with merely 10% model parameters. Furthermore, our ASR models trained on Gigaspeech 2 yield superior performance compared to commercial services. We believe that our newly introduced corpus and pipeline will open a new avenue for low-resource speech recognition and significantly facilitate research in this area.

  • 16 authors
·
Jun 17, 2024

One-for-All: Bridge the Gap Between Heterogeneous Architectures in Knowledge Distillation

Knowledge distillation~(KD) has proven to be a highly effective approach for enhancing model performance through a teacher-student training scheme. However, most existing distillation methods are designed under the assumption that the teacher and student models belong to the same model family, particularly the hint-based approaches. By using centered kernel alignment (CKA) to compare the learned features between heterogeneous teacher and student models, we observe significant feature divergence. This divergence illustrates the ineffectiveness of previous hint-based methods in cross-architecture distillation. To tackle the challenge in distilling heterogeneous models, we propose a simple yet effective one-for-all KD framework called OFA-KD, which significantly improves the distillation performance between heterogeneous architectures. Specifically, we project intermediate features into an aligned latent space such as the logits space, where architecture-specific information is discarded. Additionally, we introduce an adaptive target enhancement scheme to prevent the student from being disturbed by irrelevant information. Extensive experiments with various architectures, including CNN, Transformer, and MLP, demonstrate the superiority of our OFA-KD framework in enabling distillation between heterogeneous architectures. Specifically, when equipped with our OFA-KD, the student models achieve notable performance improvements, with a maximum gain of 8.0% on the CIFAR-100 dataset and 0.7% on the ImageNet-1K dataset. PyTorch code and checkpoints can be found at https://github.com/Hao840/OFAKD.

  • 7 authors
·
Oct 30, 2023

DriveAdapter: Breaking the Coupling Barrier of Perception and Planning in End-to-End Autonomous Driving

End-to-end autonomous driving aims to build a fully differentiable system that takes raw sensor data as inputs and directly outputs the planned trajectory or control signals of the ego vehicle. State-of-the-art methods usually follow the `Teacher-Student' paradigm. The Teacher model uses privileged information (ground-truth states of surrounding agents and map elements) to learn the driving strategy. The student model only has access to raw sensor data and conducts behavior cloning on the data collected by the teacher model. By eliminating the noise of the perception part during planning learning, state-of-the-art works could achieve better performance with significantly less data compared to those coupled ones. However, under the current Teacher-Student paradigm, the student model still needs to learn a planning head from scratch, which could be challenging due to the redundant and noisy nature of raw sensor inputs and the casual confusion issue of behavior cloning. In this work, we aim to explore the possibility of directly adopting the strong teacher model to conduct planning while letting the student model focus more on the perception part. We find that even equipped with a SOTA perception model, directly letting the student model learn the required inputs of the teacher model leads to poor driving performance, which comes from the large distribution gap between predicted privileged inputs and the ground-truth. To this end, we propose DriveAdapter, which employs adapters with the feature alignment objective function between the student (perception) and teacher (planning) modules. Additionally, since the pure learning-based teacher model itself is imperfect and occasionally breaks safety rules, we propose a method of action-guided feature learning with a mask for those imperfect teacher features to further inject the priors of hand-crafted rules into the learning process.

  • 6 authors
·
Aug 1, 2023

Using Advanced LLMs to Enhance Smaller LLMs: An Interpretable Knowledge Distillation Approach

Advanced Large language models (LLMs) like GPT-4 or LlaMa 3 provide superior performance in complex human-like interactions. But they are costly, or too large for edge devices such as smartphones and harder to self-host, leading to security and privacy concerns. This paper introduces a novel interpretable knowledge distillation approach to enhance the performance of smaller, more economical LLMs that firms can self-host. We study this problem in the context of building a customer service agent aimed at achieving high customer satisfaction through goal-oriented dialogues. Unlike traditional knowledge distillation, where the "student" model learns directly from the "teacher" model's responses via fine-tuning, our interpretable "strategy" teaching approach involves the teacher providing strategies to improve the student's performance in various scenarios. This method alternates between a "scenario generation" step and a "strategies for improvement" step, creating a customized library of scenarios and optimized strategies for automated prompting. The method requires only black-box access to both student and teacher models; hence it can be used without manipulating model parameters. In our customer service application, the method improves performance, and the learned strategies are transferable to other LLMs and scenarios beyond the training set. The method's interpretabilty helps safeguard against potential harms through human audit.

  • 3 authors
·
Aug 13, 2024

Prototype-guided Cross-task Knowledge Distillation for Large-scale Models

Recently, large-scale pre-trained models have shown their advantages in many tasks. However, due to the huge computational complexity and storage requirements, it is challenging to apply the large-scale model to real scenes. A common solution is knowledge distillation which regards the large-scale model as a teacher model and helps to train a small student model to obtain a competitive performance. Cross-task Knowledge distillation expands the application scenarios of the large-scale pre-trained model. Existing knowledge distillation works focus on directly mimicking the final prediction or the intermediate layers of the teacher model, which represent the global-level characteristics and are task-specific. To alleviate the constraint of different label spaces, capturing invariant intrinsic local object characteristics (such as the shape characteristics of the leg and tail of the cattle and horse) plays a key role. Considering the complexity and variability of real scene tasks, we propose a Prototype-guided Cross-task Knowledge Distillation (ProC-KD) approach to transfer the intrinsic local-level object knowledge of a large-scale teacher network to various task scenarios. First, to better transfer the generalized knowledge in the teacher model in cross-task scenarios, we propose a prototype learning module to learn from the essential feature representation of objects in the teacher model. Secondly, for diverse downstream tasks, we propose a task-adaptive feature augmentation module to enhance the features of the student model with the learned generalization prototype features and guide the training of the student model to improve its generalization ability. The experimental results on various visual tasks demonstrate the effectiveness of our approach for large-scale model cross-task knowledge distillation scenes.

  • 4 authors
·
Dec 26, 2022

DDK: Distilling Domain Knowledge for Efficient Large Language Models

Despite the advanced intelligence abilities of large language models (LLMs) in various applications, they still face significant computational and storage demands. Knowledge Distillation (KD) has emerged as an effective strategy to improve the performance of a smaller LLM (i.e., the student model) by transferring knowledge from a high-performing LLM (i.e., the teacher model). Prevailing techniques in LLM distillation typically use a black-box model API to generate high-quality pretrained and aligned datasets, or utilize white-box distillation by altering the loss function to better transfer knowledge from the teacher LLM. However, these methods ignore the knowledge differences between the student and teacher LLMs across domains. This results in excessive focus on domains with minimal performance gaps and insufficient attention to domains with large gaps, reducing overall performance. In this paper, we introduce a new LLM distillation framework called DDK, which dynamically adjusts the composition of the distillation dataset in a smooth manner according to the domain performance differences between the teacher and student models, making the distillation process more stable and effective. Extensive evaluations show that DDK significantly improves the performance of student models, outperforming both continuously pretrained baselines and existing knowledge distillation methods by a large margin.

  • 16 authors
·
Jul 22, 2024 2

Consistency Trajectory Matching for One-Step Generative Super-Resolution

Current diffusion-based super-resolution (SR) approaches achieve commendable performance at the cost of high inference overhead. Therefore, distillation techniques are utilized to accelerate the multi-step teacher model into one-step student model. Nevertheless, these methods significantly raise training costs and constrain the performance of the student model by the teacher model. To overcome these tough challenges, we propose Consistency Trajectory Matching for Super-Resolution (CTMSR), a distillation-free strategy that is able to generate photo-realistic SR results in one step. Concretely, we first formulate a Probability Flow Ordinary Differential Equation (PF-ODE) trajectory to establish a deterministic mapping from low-resolution (LR) images with noise to high-resolution (HR) images. Then we apply the Consistency Training (CT) strategy to directly learn the mapping in one step, eliminating the necessity of pre-trained diffusion model. To further enhance the performance and better leverage the ground-truth during the training process, we aim to align the distribution of SR results more closely with that of the natural images. To this end, we propose to minimize the discrepancy between their respective PF-ODE trajectories from the LR image distribution by our meticulously designed Distribution Trajectory Matching (DTM) loss, resulting in improved realism of our recovered HR images. Comprehensive experimental results demonstrate that the proposed methods can attain comparable or even superior capabilities on both synthetic and real datasets while maintaining minimal inference latency.

  • 6 authors
·
Mar 26, 2025

Dual-Head Knowledge Distillation: Enhancing Logits Utilization with an Auxiliary Head

Traditional knowledge distillation focuses on aligning the student's predicted probabilities with both ground-truth labels and the teacher's predicted probabilities. However, the transition to predicted probabilities from logits would obscure certain indispensable information. To address this issue, it is intuitive to additionally introduce a logit-level loss function as a supplement to the widely used probability-level loss function, for exploiting the latent information of logits. Unfortunately, we empirically find that the amalgamation of the newly introduced logit-level loss and the previous probability-level loss will lead to performance degeneration, even trailing behind the performance of employing either loss in isolation. We attribute this phenomenon to the collapse of the classification head, which is verified by our theoretical analysis based on the neural collapse theory. Specifically, the gradients of the two loss functions exhibit contradictions in the linear classifier yet display no such conflict within the backbone. Drawing from the theoretical analysis, we propose a novel method called dual-head knowledge distillation, which partitions the linear classifier into two classification heads responsible for different losses, thereby preserving the beneficial effects of both losses on the backbone while eliminating adverse influences on the classification head. Extensive experiments validate that our method can effectively exploit the information inside the logits and achieve superior performance against state-of-the-art counterparts.

  • 5 authors
·
Nov 13, 2024

Multiple Instance Learning Framework with Masked Hard Instance Mining for Whole Slide Image Classification

The whole slide image (WSI) classification is often formulated as a multiple instance learning (MIL) problem. Since the positive tissue is only a small fraction of the gigapixel WSI, existing MIL methods intuitively focus on identifying salient instances via attention mechanisms. However, this leads to a bias towards easy-to-classify instances while neglecting hard-to-classify instances. Some literature has revealed that hard examples are beneficial for modeling a discriminative boundary accurately. By applying such an idea at the instance level, we elaborate a novel MIL framework with masked hard instance mining (MHIM-MIL), which uses a Siamese structure (Teacher-Student) with a consistency constraint to explore the potential hard instances. With several instance masking strategies based on attention scores, MHIM-MIL employs a momentum teacher to implicitly mine hard instances for training the student model, which can be any attention-based MIL model. This counter-intuitive strategy essentially enables the student to learn a better discriminating boundary. Moreover, the student is used to update the teacher with an exponential moving average (EMA), which in turn identifies new hard instances for subsequent training iterations and stabilizes the optimization. Experimental results on the CAMELYON-16 and TCGA Lung Cancer datasets demonstrate that MHIM-MIL outperforms other latest methods in terms of performance and training cost. The code is available at: https://github.com/DearCaat/MHIM-MIL.

  • 6 authors
·
Jul 27, 2023

BPKD: Boundary Privileged Knowledge Distillation For Semantic Segmentation

Current knowledge distillation approaches in semantic segmentation tend to adopt a holistic approach that treats all spatial locations equally. However, for dense prediction, students' predictions on edge regions are highly uncertain due to contextual information leakage, requiring higher spatial sensitivity knowledge than the body regions. To address this challenge, this paper proposes a novel approach called boundary-privileged knowledge distillation (BPKD). BPKD distills the knowledge of the teacher model's body and edges separately to the compact student model. Specifically, we employ two distinct loss functions: (i) edge loss, which aims to distinguish between ambiguous classes at the pixel level in edge regions; (ii) body loss, which utilizes shape constraints and selectively attends to the inner-semantic regions. Our experiments demonstrate that the proposed BPKD method provides extensive refinements and aggregation for edge and body regions. Additionally, the method achieves state-of-the-art distillation performance for semantic segmentation on three popular benchmark datasets, highlighting its effectiveness and generalization ability. BPKD shows consistent improvements across a diverse array of lightweight segmentation structures, including both CNNs and transformers, underscoring its architecture-agnostic adaptability. The code is available at https://github.com/AkideLiu/BPKD.

  • 6 authors
·
Jun 13, 2023

Skill-Targeted Adaptive Training

Language models often show little to no improvement (i.e., "saturation") when trained via vanilla supervised fine-tuning (SFT) on data similar to what they saw in their training set (e.g., MATH). We introduce a new fine-tuning strategy, STAT, to train such a student model by using the metacognition ability of a stronger large language model (LLM) as the teacher. The teacher uses the task dataset to create a list of skills needed for the task, and then labels each data point with its required skills (Didolkar et al., 2024). By monitoring the student's answers, the teacher creates a Missing-Skill-Profile for the student, tracking how often they failed to apply each skill in their responses. We use this idea to build a modified training set in one of two ways. In STAT-Sel, the teacher uses an existing set of training examples but adaptively reweights them according to the Missing-Skill-Profile. In STAT-Syn, the teacher synthesizes additional examples involving missing skills. Across extensive experiments on Llama and Qwen models, our methods yield improvements of up to 7.5% on MATH, whereas SFT provides only limited gains. Furthermore, STAT enhances performance on out-of-distribution benchmarks (e.g., AIME24/25, AMC23, etc.) by an average of 4.6%. Crucially, we find that STAT is complementary to RL via GRPO (Shao et al., 2024): after the model is improved using STAT to address skill gaps, GRPO continues to add further gains. We conclude that skill-targeted adaptive training should broadly improve current training pipelines. Our code is available at: https://github.com/princeton-pli/STAT.

PrincetonUniversity Princeton University
·
Oct 11, 2025 2

OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data

Mathematical reasoning continues to be a critical challenge in large language model (LLM) development with significant interest. However, most of the cutting-edge progress in mathematical reasoning with LLMs has become closed-source due to lack of access to training data. This lack of data access limits researchers from understanding the impact of different choices for synthesizing and utilizing the data. With the goal of creating a high-quality finetuning (SFT) dataset for math reasoning, we conduct careful ablation experiments on data synthesis using the recently released Llama3.1 family of models. Our experiments show that: (a) solution format matters, with excessively verbose solutions proving detrimental to SFT performance, (b) data generated by a strong teacher outperforms on-policy data generated by a weak student model, (c) SFT is robust to low-quality solutions, allowing for imprecise data filtering, and (d) question diversity is crucial for achieving data scaling gains. Based on these insights, we create the OpenMathInstruct-2 dataset, which consists of 14M question-solution pairs (approx 600K unique questions), making it nearly eight times larger than the previous largest open-source math reasoning dataset. Finetuning the Llama-3.1-8B-Base using OpenMathInstruct-2 outperforms Llama3.1-8B-Instruct on MATH by an absolute 15.9\% (51.9\% rightarrow 67.8\%). Finally, to accelerate the open-source efforts, we release the code, the finetuned models, and the OpenMathInstruct-2 dataset under a commercially permissive license.

  • 6 authors
·
Oct 2, 2024

Reverse Thinking Makes LLMs Stronger Reasoners

Reverse thinking plays a crucial role in human reasoning. Humans can reason not only from a problem to a solution but also in reverse, i.e., start from the solution and reason towards the problem. This often enhances overall reasoning performance as it enables consistency checks between their forward and backward thinking. To enable Large Language Models (LLMs) to perform reverse thinking, we introduce Reverse-Enhanced Thinking (RevThink), a framework composed of data augmentation and learning objectives. In RevThink, we augment the dataset by collecting structured forward-backward reasoning from a teacher model, consisting of: (1) the original question, (2) forward reasoning, (3) backward question, and (4) backward reasoning. We then employ three objectives to train a smaller student model in a multi-task learning fashion: (a) generate forward reasoning from a question, (b) generate a backward question from a question, and (c) generate backward reasoning from the backward question. Experiments across 12 datasets covering commonsense, math, and logical reasoning show an average 13.53% improvement over the student model's zero-shot performance and a 6.84% improvement over the strongest knowledge distillation baselines. Moreover, our method demonstrates sample efficiency -- using only 10% of the correct forward reasoning from the training data, it outperforms a standard fine-tuning method trained on 10x more forward reasoning. RevThink also exhibits strong generalization to out-of-distribution held-out datasets.

  • 11 authors
·
Nov 29, 2024 2

Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation

On-policy distillation (OPD), which aligns the student with the teacher's logit distribution on student-generated trajectories, has demonstrated strong empirical gains in improving student performance and often outperforms off-policy distillation and reinforcement learning (RL) paradigms. In this work, we first theoretically show that OPD is a special case of dense KL-constrained RL where the reward function and the KL regularization are always weighted equally and the reference model can by any model. Then, we propose the Generalized On-Policy Distillation (G-OPD) framework, which extends the standard OPD objective by introducing a flexible reference model and a reward scaling factor that controls the relative weight of the reward term against the KL regularization. Through comprehensive experiments on math reasoning and code generation tasks, we derive two novel insights: (1) Setting the reward scaling factor to be greater than 1 (i.e., reward extrapolation), which we term ExOPD, consistently improves over standard OPD across a range of teacher-student size pairings. In particular, in the setting where we merge the knowledge from different domain experts, obtained by applying domain-specific RL to the same student model, back into the original student, ExOPD enables the student to even surpass the teacher's performance boundary and outperform the domain teachers. (2) Building on ExOPD, we further find that in the strong-to-weak distillation setting (i.e., distilling a smaller student from a larger teacher), performing reward correction by choosing the reference model as the teacher's base model before RL yields a more accurate reward signal and further improves distillation performance. However, this choice assumes access to the teacher's pre-RL variant and incurs more computational overhead. We hope our work offers new insights for future research on OPD.

Can LLMs Model Incorrect Student Reasoning? A Case Study on Distractor Generation

Modeling plausible student misconceptions is critical for AI in education. In this work, we examine how large language models (LLMs) reason about misconceptions when generating multiple-choice distractors, a task that requires modeling incorrect yet plausible answers by coordinating solution knowledge, simulating student misconceptions, and evaluating plausibility. We introduce a taxonomy for analyzing the strategies used by state-of-the-art LLMs, examining their reasoning procedures and comparing them to established best practices in the learning sciences. Our structured analysis reveals a surprising alignment between their processes and best practices: the models typically solve the problem correctly first, then articulate and simulate multiple potential misconceptions, and finally select a set of distractors. An analysis of failure modes reveals that errors arise primarily from failures in recovering the correct solution and selecting among response candidates, rather than simulating errors or structuring the process. Consistent with these results, we find that providing the correct solution in the prompt improves alignment with human-authored distractors by 8%, highlighting the critical role of anchoring to the correct solution when generating plausible incorrect student reasoning. Overall, our analysis offers a structured and interpretable lens into LLMs' ability to model incorrect student reasoning and produce high-quality distractors.

  • 6 authors
·
Mar 15

Aligning Teacher with Student Preferences for Tailored Training Data Generation

Large Language Models (LLMs) have shown significant promise as copilots in various tasks. Local deployment of LLMs on edge devices is necessary when handling privacy-sensitive data or latency-sensitive tasks. The computational constraints of such devices make direct deployment of powerful large-scale LLMs impractical, necessitating the Knowledge Distillation from large-scale models to lightweight models. Lots of work has been done to elicit diversity and quality training examples from LLMs, but little attention has been paid to aligning teacher instructional content based on student preferences, akin to "responsive teaching" in pedagogy. Thus, we propose ARTE, dubbed Aligning TeacheR with StudenT PreferencEs, a framework that aligns the teacher model with student preferences to generate tailored training examples for Knowledge Distillation. Specifically, we elicit draft questions and rationales from the teacher model, then collect student preferences on these questions and rationales using students' performance with in-context learning as a proxy, and finally align the teacher model with student preferences. In the end, we repeat the first step with the aligned teacher model to elicit tailored training examples for the student model on the target task. Extensive experiments on academic benchmarks demonstrate the superiority of ARTE over existing instruction-tuning datasets distilled from powerful LLMs. Moreover, we thoroughly investigate the generalization of ARTE, including the generalization of fine-tuned student models in reasoning ability and the generalization of aligned teacher models to generate tailored training data across tasks and students. In summary, our contributions lie in proposing a novel framework for tailored training example generation, demonstrating its efficacy in experiments, and investigating the generalization of both student & aligned teacher models in ARTE.

  • 6 authors
·
Jun 27, 2024 2

Stare at What You See: Masked Image Modeling without Reconstruction

Masked Autoencoders (MAE) have been prevailing paradigms for large-scale vision representation pre-training. By reconstructing masked image patches from a small portion of visible image regions, MAE forces the model to infer semantic correlation within an image. Recently, some approaches apply semantic-rich teacher models to extract image features as the reconstruction target, leading to better performance. However, unlike the low-level features such as pixel values, we argue the features extracted by powerful teacher models already encode rich semantic correlation across regions in an intact image.This raises one question: is reconstruction necessary in Masked Image Modeling (MIM) with a teacher model? In this paper, we propose an efficient MIM paradigm named MaskAlign. MaskAlign simply learns the consistency of visible patch features extracted by the student model and intact image features extracted by the teacher model. To further advance the performance and tackle the problem of input inconsistency between the student and teacher model, we propose a Dynamic Alignment (DA) module to apply learnable alignment. Our experimental results demonstrate that masked modeling does not lose effectiveness even without reconstruction on masked regions. Combined with Dynamic Alignment, MaskAlign can achieve state-of-the-art performance with much higher efficiency. Code and models will be available at https://github.com/OpenPerceptionX/maskalign.

  • 7 authors
·
Nov 16, 2022

LLM Teacher-Student Framework for Text Classification With No Manually Annotated Data: A Case Study in IPTC News Topic Classification

With the ever-increasing number of news stories available online, classifying them by topic, regardless of the language they are written in, has become crucial for enhancing readers' access to relevant content. To address this challenge, we propose a teacher-student framework based on large language models (LLMs) for developing multilingual news classification models of reasonable size with no need for manual data annotation. The framework employs a Generative Pretrained Transformer (GPT) model as the teacher model to develop an IPTC Media Topic training dataset through automatic annotation of news articles in Slovenian, Croatian, Greek, and Catalan. The teacher model exhibits a high zero-shot performance on all four languages. Its agreement with human annotators is comparable to that between the human annotators themselves. To mitigate the computational limitations associated with the requirement of processing millions of texts daily, smaller BERT-like student models are fine-tuned on the GPT-annotated dataset. These student models achieve high performance comparable to the teacher model. Furthermore, we explore the impact of the training data size on the performance of the student models and investigate their monolingual, multilingual and zero-shot cross-lingual capabilities. The findings indicate that student models can achieve high performance with a relatively small number of training instances, and demonstrate strong zero-shot cross-lingual abilities. Finally, we publish the best-performing news topic classifier, enabling multilingual classification with the top-level categories of the IPTC Media Topic schema.

  • 2 authors
·
Nov 29, 2024 2

Motion Consistency Model: Accelerating Video Diffusion with Disentangled Motion-Appearance Distillation

Image diffusion distillation achieves high-fidelity generation with very few sampling steps. However, applying these techniques directly to video diffusion often results in unsatisfactory frame quality due to the limited visual quality in public video datasets. This affects the performance of both teacher and student video diffusion models. Our study aims to improve video diffusion distillation while improving frame appearance using abundant high-quality image data. We propose motion consistency model (MCM), a single-stage video diffusion distillation method that disentangles motion and appearance learning. Specifically, MCM includes a video consistency model that distills motion from the video teacher model, and an image discriminator that enhances frame appearance to match high-quality image data. This combination presents two challenges: (1) conflicting frame learning objectives, as video distillation learns from low-quality video frames while the image discriminator targets high-quality images; and (2) training-inference discrepancies due to the differing quality of video samples used during training and inference. To address these challenges, we introduce disentangled motion distillation and mixed trajectory distillation. The former applies the distillation objective solely to the motion representation, while the latter mitigates training-inference discrepancies by mixing distillation trajectories from both the low- and high-quality video domains. Extensive experiments show that our MCM achieves the state-of-the-art video diffusion distillation performance. Additionally, our method can enhance frame quality in video diffusion models, producing frames with high aesthetic scores or specific styles without corresponding video data.

  • 9 authors
·
Jun 10, 2024

Distilling Large Vision-Language Model with Out-of-Distribution Generalizability

Large vision-language models have achieved outstanding performance, but their size and computational requirements make their deployment on resource-constrained devices and time-sensitive tasks impractical. Model distillation, the process of creating smaller, faster models that maintain the performance of larger models, is a promising direction towards the solution. This paper investigates the distillation of visual representations in large teacher vision-language models into lightweight student models using a small- or mid-scale dataset. Notably, this study focuses on open-vocabulary out-of-distribution (OOD) generalization, a challenging problem that has been overlooked in previous model distillation literature. We propose two principles from vision and language modality perspectives to enhance student's OOD generalization: (1) by better imitating teacher's visual representation space, and carefully promoting better coherence in vision-language alignment with the teacher; (2) by enriching the teacher's language representations with informative and finegrained semantic attributes to effectively distinguish between different labels. We propose several metrics and conduct extensive experiments to investigate their techniques. The results demonstrate significant improvements in zero-shot and few-shot student performance on open-vocabulary out-of-distribution classification, highlighting the effectiveness of our proposed approaches. Code released at https://github.com/xuanlinli17/large_vlm_distillation_ood

  • 6 authors
·
Jul 6, 2023

Self-supervised Audio Teacher-Student Transformer for Both Clip-level and Frame-level Tasks

Self-supervised learning (SSL) has emerged as a popular approach for learning audio representations. One goal of audio self-supervised pre-training is to transfer knowledge to downstream audio tasks, generally including clip-level and frame-level tasks. While frame-level tasks are important for fine-grained acoustic scene/event understanding, prior studies primarily evaluate on clip-level downstream tasks. In order to tackle both clip-level and frame-level tasks, this paper proposes Audio Teacher-Student Transformer (ATST), with a clip-level version (named ATST-Clip) and a frame-level version (named ATST-Frame), responsible for learning clip-level and frame-level representations, respectively. Both methods use a Transformer encoder and a teacher-student training scheme. We have carefully designed the view creation strategy for ATST-Clip and ATST-Frame. Specifically, ATST-Clip uses segment-wise data augmentations, and ATST-Frame integrates frame-wise data augmentations and masking. Experimental results show that our ATST-Frame model obtains state-of-the-art (SOTA) performances on most of the clip-level and frame-level downstream tasks. Especially, it outperforms other models by a large margin on the frame-level sound event detection task. In addition, the performance can be further improved by combining the two models through knowledge distillation. Our code is available online.

  • 3 authors
·
Jun 7, 2023

DisWOT: Student Architecture Search for Distillation WithOut Training

Knowledge distillation (KD) is an effective training strategy to improve the lightweight student models under the guidance of cumbersome teachers. However, the large architecture difference across the teacher-student pairs limits the distillation gains. In contrast to previous adaptive distillation methods to reduce the teacher-student gap, we explore a novel training-free framework to search for the best student architectures for a given teacher. Our work first empirically show that the optimal model under vanilla training cannot be the winner in distillation. Secondly, we find that the similarity of feature semantics and sample relations between random-initialized teacher-student networks have good correlations with final distillation performances. Thus, we efficiently measure similarity matrixs conditioned on the semantic activation maps to select the optimal student via an evolutionary algorithm without any training. In this way, our student architecture search for Distillation WithOut Training (DisWOT) significantly improves the performance of the model in the distillation stage with at least 180times training acceleration. Additionally, we extend similarity metrics in DisWOT as new distillers and KD-based zero-proxies. Our experiments on CIFAR, ImageNet and NAS-Bench-201 demonstrate that our technique achieves state-of-the-art results on different search spaces. Our project and code are available at https://lilujunai.github.io/DisWOT-CVPR2023/.

  • 3 authors
·
Mar 27, 2023

Distiller: A Systematic Study of Model Distillation Methods in Natural Language Processing

We aim to identify how different components in the KD pipeline affect the resulting performance and how much the optimal KD pipeline varies across different datasets/tasks, such as the data augmentation policy, the loss function, and the intermediate representation for transferring the knowledge between teacher and student. To tease apart their effects, we propose Distiller, a meta KD framework that systematically combines a broad range of techniques across different stages of the KD pipeline, which enables us to quantify each component's contribution. Within Distiller, we unify commonly used objectives for distillation of intermediate representations under a universal mutual information (MI) objective and propose a class of MI-alpha objective functions with better bias/variance trade-off for estimating the MI between the teacher and the student. On a diverse set of NLP datasets, the best Distiller configurations are identified via large-scale hyperparameter optimization. Our experiments reveal the following: 1) the approach used to distill the intermediate representations is the most important factor in KD performance, 2) among different objectives for intermediate distillation, MI-alpha performs the best, and 3) data augmentation provides a large boost for small training datasets or small student networks. Moreover, we find that different datasets/tasks prefer different KD algorithms, and thus propose a simple AutoDistiller algorithm that can recommend a good KD pipeline for a new dataset.

  • 6 authors
·
Sep 22, 2021

Deliberative Alignment is Deep, but Uncertainty Remains: Inference time safety improvement in reasoning via attribution of unsafe behavior to base model

While the wide adoption of refusal training in large language models (LLMs) has showcased improvements in model safety, recent works have highlighted shortcomings due to the shallow nature of these alignment methods. To this end, the work on Deliberative alignment proposed distilling reasoning capabilities from stronger reasoning models, thereby instilling deeper safety in LLMs. In this work, we study the impact of deliberative alignment in language models. First, we show that despite being larger in model size and stronger in safety capability, there exists an alignment gap between teacher and student language models, which affects both the safety and general utility of the student model. Furthermore, we show that models aligned through deliberative alignment can retain unsafe behaviors from the base model despite learning the reasoning patterns of larger reasoning models. Building upon this observation, we propose a BoN sampling method that attributes the unsafe behavior back to the base LLMs in the latent space, thereby down-ranking unsafe responses to gain a meaningful improvement in model safety across multiple safety benchmarks with minimal loss in utility. In particular, across 7 teacher models and 6 student models of different classes and sizes, we show an average attack success rate (ASR) reduction of 28.2% in DAN, 31.3% in WildJailbreak and 35.4 % in StrongREJECT benchmarks. We further show that these safety gains prevail post RL training, thus highlighting the uncertainty in safety reasoning and it's explicit attribution to the base model.

  • 2 authors
·
Mar 31

Distribution-Aligned Sequence Distillation for Superior Long-CoT Reasoning

In this report, we introduce DASD-4B-Thinking, a lightweight yet highly capable, fully open-source reasoning model. It achieves SOTA performance among open-source models of comparable scale across challenging benchmarks in mathematics, scientific reasoning, and code generation -- even outperforming several larger models. We begin by critically reexamining a widely adopted distillation paradigm in the community: SFT on teacher-generated responses, also known as sequence-level distillation. Although a series of recent works following this scheme have demonstrated remarkable efficiency and strong empirical performance, they are primarily grounded in the SFT perspective. Consequently, these approaches focus predominantly on designing heuristic rules for SFT data filtering, while largely overlooking the core principle of distillation itself -- enabling the student model to learn the teacher's full output distribution so as to inherit its generalization capability. Specifically, we identify three critical limitations in current practice: i) Inadequate representation of the teacher's sequence-level distribution; ii) Misalignment between the teacher's output distribution and the student's learning capacity; and iii) Exposure bias arising from teacher-forced training versus autoregressive inference. In summary, these shortcomings reflect a systemic absence of explicit teacher-student interaction throughout the distillation process, leaving the essence of distillation underexploited. To address these issues, we propose several methodological innovations that collectively form an enhanced sequence-level distillation training pipeline. Remarkably, DASD-4B-Thinking obtains competitive results using only 448K training samples -- an order of magnitude fewer than those employed by most existing open-source efforts. To support community research, we publicly release our models and the training dataset.

LLM2LLM: Boosting LLMs with Novel Iterative Data Enhancement

Pretrained large language models (LLMs) are currently state-of-the-art for solving the vast majority of natural language processing tasks. While many real-world applications still require fine-tuning to reach satisfactory levels of performance, many of them are in the low-data regime, making fine-tuning challenging. To address this, we propose LLM2LLM, a targeted and iterative data augmentation strategy that uses a teacher LLM to enhance a small seed dataset by augmenting additional data that can be used for fine-tuning on a specific task. LLM2LLM (1) fine-tunes a baseline student LLM on the initial seed data, (2) evaluates and extracts data points that the model gets wrong, and (3) uses a teacher LLM to generate synthetic data based on these incorrect data points, which are then added back into the training data. This approach amplifies the signal from incorrectly predicted data points by the LLM during training and reintegrates them into the dataset to focus on more challenging examples for the LLM. Our results show that LLM2LLM significantly enhances the performance of LLMs in the low-data regime, outperforming both traditional fine-tuning and other data augmentation baselines. LLM2LLM reduces the dependence on labor-intensive data curation and paves the way for more scalable and performant LLM solutions, allowing us to tackle data-constrained domains and tasks. We achieve improvements up to 24.2% on the GSM8K dataset, 32.6% on CaseHOLD, 32.0% on SNIPS, 52.6% on TREC and 39.8% on SST-2 over regular fine-tuning in the low-data regime using a LLaMA2-7B student model.

  • 9 authors
·
Mar 22, 2024 2

Incentivizing Strong Reasoning from Weak Supervision

Large language models (LLMs) have demonstrated impressive performance on reasoning-intensive tasks, but enhancing their reasoning abilities typically relies on either reinforcement learning (RL) with verifiable signals or supervised fine-tuning (SFT) with high-quality long chain-of-thought (CoT) demonstrations, both of which are expensive. In this paper, we study a novel problem of incentivizing the reasoning capacity of LLMs without expensive high-quality demonstrations and reinforcement learning. We investigate whether the reasoning capabilities of LLMs can be effectively incentivized via supervision from significantly weaker models. We further analyze when and why such weak supervision succeeds in eliciting reasoning abilities in stronger models. Our findings show that supervision from significantly weaker reasoners can substantially improve student reasoning performance, recovering close to 94% of the gains of expensive RL at a fraction of the cost. Experiments across diverse benchmarks and model architectures demonstrate that weak reasoners can effectively incentivize reasoning in stronger student models, consistently improving performance across a wide range of reasoning tasks. Our results suggest that this simple weak-to-strong paradigm is a promising and generalizable alternative to costly methods for incentivizing strong reasoning capabilities at inference-time in LLMs. The code is publicly available at https://github.com/yuanyige/w2sr.

  • 7 authors
·
May 26, 2025

Can Language Models Teach Weaker Agents? Teacher Explanations Improve Students via Theory of Mind

Large Language Models (LLMs) perform complex reasoning by generating explanations for their predictions. However, a complementary goal of explanations is to also communicate useful knowledge that improves weaker agents. Hence, we investigate whether LLMs also make good teachers for weaker agents. In particular, we consider a student-teacher framework between two LLM agents and study if, when, and how the teacher should intervene with natural language explanations to improve the student's performance. Since communication is expensive, we define a budget such that the teacher only communicates explanations for a fraction of the data, after which the student should perform well on its own. We decompose the teaching problem along four axes: (1) if teacher's test time intervention improve student predictions, (2) when it is worth explaining a data point, (3) how the teacher should personalize explanations to better teach the student, and (4) if teacher explanations also improve student performance on future unexplained data. We first show that teacher LLMs can indeed intervene on student reasoning to improve their performance. Next, we propose a Theory of Mind approach, in which the teacher builds two few-shot mental models of the student. The first model defines an Intervention Function that simulates the utility of an intervention, allowing the teacher to intervene when this utility is the highest and improving student performance at lower budgets. The second model enables the teacher to personalize explanations for a particular student and outperform unpersonalized teachers. We also demonstrate that in multi-turn interactions, teacher explanations generalize and learning from explained data improves student performance on future unexplained data. Finally, we also verify that misaligned teachers can lower student performance to random chance by intentionally misleading them.

  • 3 authors
·
Jun 15, 2023

Deep Knowledge Tracing with Learning Curves

Knowledge tracing (KT) has recently been an active research area of computational pedagogy. The task is to model students' mastery level of knowledge concepts based on their responses to the questions in the past, as well as predict the probabilities that they correctly answer subsequent questions in the future. KT tasks were historically solved using statistical modeling methods such as Bayesian inference and factor analysis, but recent advances in deep learning have led to the successive proposals that leverage deep neural networks, including long short-term memory networks, memory-augmented networks and self-attention networks. While those deep models demonstrate superior performance over the traditional approaches, they all neglect the explicit modeling of the learning curve theory, which generally says that more practice on the same knowledge concept enhances one's mastery level of the concept. Based on this theory, we propose a Convolution-Augmented Knowledge Tracing (CAKT) model in this paper. The model employs three-dimensional convolutional neural networks to explicitly learn a student's recent experience on applying the same knowledge concept with that in the next question, and fuses the learnt feature with the feature representing her overall latent knowledge state obtained using a classic LSTM network. The fused feature is then fed into a second LSTM network to predict the student's response to the next question. Experimental results show that CAKT achieves the new state-of-the-art performance in predicting students' responses compared with existing models. We also conduct extensive sensitivity analysis and ablation study to show the stability of the results and justify the particular architecture of CAKT, respectively.

  • 3 authors
·
Jul 26, 2020

TeLL-Drive: Enhancing Autonomous Driving with Teacher LLM-Guided Deep Reinforcement Learning

Although Deep Reinforcement Learning (DRL) and Large Language Models (LLMs) each show promise in addressing decision-making challenges in autonomous driving, DRL often suffers from high sample complexity, while LLMs have difficulty ensuring real-time decision making. To address these limitations, we propose TeLL-Drive, a hybrid framework that integrates a Teacher LLM to guide an attention-based Student DRL policy. By incorporating risk metrics, historical scenario retrieval, and domain heuristics into context-rich prompts, the LLM produces high-level driving strategies through chain-of-thought reasoning. A self-attention mechanism then fuses these strategies with the DRL agent's exploration, accelerating policy convergence and boosting robustness across diverse driving conditions. The experimental results, evaluated across multiple traffic scenarios, show that TeLL-Drive outperforms existing baseline methods, including other LLM-based approaches, in terms of success rates, average returns, and real-time feasibility. Ablation studies underscore the importance of each model component, especially the synergy between the attention mechanism and LLM-driven guidance. Finally, we build a virtual-real fusion experimental platform to verify the real-time performance, robustness, and reliability of the algorithm running on real vehicles through vehicle-in-loop experiments.

  • 7 authors
·
Feb 3, 2025

FastLightGen: Fast and Light Video Generation with Fewer Steps and Parameters

The recent advent of powerful video generation models, such as Hunyuan, WanX, Veo3, and Kling, has inaugurated a new era in the field. However, the practical deployment of these models is severely impeded by their substantial computational overhead, which stems from enormous parameter counts and the iterative, multi-step sampling process required during inference. Prior research on accelerating generative models has predominantly followed two distinct trajectories: reducing the number of sampling steps (e.g., LCM, DMD, and MagicDistillation) or compressing the model size for more efficient inference (e.g., ICMD). The potential of simultaneously compressing both to create a fast and lightweight model remains an unexplored avenue. In this paper, we propose FastLightGen, an algorithm that transforms large, computationally expensive models into fast, lightweight counterparts. The core idea is to construct an optimal teacher model, one engineered to maximize student performance, within a synergistic framework for distilling both model size and inference steps. Our extensive experiments on HunyuanVideo-ATI2V and WanX-TI2V reveal that a generator using 4-step sampling and 30\% parameter pruning achieves optimal visual quality under a constrained inference budget. Furthermore, FastLightGen consistently outperforms all competing methods, establishing a new state-of-the-art in efficient video generation.

  • 3 authors
·
Mar 2

A Probabilistic Framework for Lifelong Test-Time Adaptation

Test-time adaptation (TTA) is the problem of updating a pre-trained source model at inference time given test input(s) from a different target domain. Most existing TTA approaches assume the setting in which the target domain is stationary, i.e., all the test inputs come from a single target domain. However, in many practical settings, the test input distribution might exhibit a lifelong/continual shift over time. Moreover, existing TTA approaches also lack the ability to provide reliable uncertainty estimates, which is crucial when distribution shifts occur between the source and target domain. To address these issues, we present PETAL (Probabilistic lifElong Test-time Adaptation with seLf-training prior), which solves lifelong TTA using a probabilistic approach, and naturally results in (1) a student-teacher framework, where the teacher model is an exponential moving average of the student model, and (2) regularizing the model updates at inference time using the source model as a regularizer. To prevent model drift in the lifelong/continual TTA setting, we also propose a data-driven parameter restoration technique which contributes to reducing the error accumulation and maintaining the knowledge of recent domains by restoring only the irrelevant parameters. In terms of predictive error rate as well as uncertainty based metrics such as Brier score and negative log-likelihood, our method achieves better results than the current state-of-the-art for online lifelong test-time adaptation across various benchmarks, such as CIFAR-10C, CIFAR-100C, ImageNetC, and ImageNet3DCC datasets. The source code for our approach is accessible at https://github.com/dhanajitb/petal.

  • 2 authors
·
Dec 19, 2022

Distribution Backtracking Builds A Faster Convergence Trajectory for One-step Diffusion Distillation

Accelerating the sampling speed of diffusion models remains a significant challenge. Recent score distillation methods distill a heavy teacher model into an one-step student generator, which is optimized by calculating the difference between the two score functions on the samples generated by the student model. However, there is a score mismatch issue in the early stage of the distillation process, because existing methods mainly focus on using the endpoint of pre-trained diffusion models as teacher models, overlooking the importance of the convergence trajectory between the student generator and the teacher model. To address this issue, we extend the score distillation process by introducing the entire convergence trajectory of teacher models and propose Distribution Backtracking Distillation (DisBack) for distilling student generators. DisBask is composed of two stages: Degradation Recording and Distribution Backtracking. Degradation Recording is designed to obtain the convergence trajectory of teacher models, which records the degradation path from the trained teacher model to the untrained initial student generator. The degradation path implicitly represents the intermediate distributions of teacher models. Then Distribution Backtracking trains a student generator to backtrack the intermediate distributions for approximating the convergence trajectory of teacher models. Extensive experiments show that DisBack achieves faster and better convergence than the existing distillation method and accomplishes comparable generation performance. Notably, DisBack is easy to implement and can be generalized to existing distillation methods to boost performance. Our code is publicly available on https://github.com/SYZhang0805/DisBack.

  • 9 authors
·
Aug 28, 2024 2

MonoTAKD: Teaching Assistant Knowledge Distillation for Monocular 3D Object Detection

Monocular 3D object detection (Mono3D) holds noteworthy promise for autonomous driving applications owing to the cost-effectiveness and rich visual context of monocular camera sensors. However, depth ambiguity poses a significant challenge, as it requires extracting precise 3D scene geometry from a single image, resulting in suboptimal performance when transferring knowledge from a LiDAR-based teacher model to a camera-based student model. To address this issue, we introduce {\em Monocular Teaching Assistant Knowledge Distillation (MonoTAKD)} to enhance 3D perception in Mono3D. Our approach presents a robust camera-based teaching assistant model that effectively bridges the representation gap between different modalities for teacher and student models, addressing the challenge of inaccurate depth estimation. By defining 3D spatial cues as residual features that capture the differences between the teacher and the teaching assistant models, we leverage these cues into the student model, improving its 3D perception capabilities. Experimental results show that our MonoTAKD achieves state-of-the-art performance on the KITTI3D dataset. Additionally, we evaluate the performance on nuScenes and KITTI raw datasets to demonstrate the generalization of our model to multi-view 3D and unsupervised data settings. Our code will be available at https://github.com/hoiliu-0801/MonoTAKD.

  • 9 authors
·
Apr 7, 2024

MedDet: Generative Adversarial Distillation for Efficient Cervical Disc Herniation Detection

Cervical disc herniation (CDH) is a prevalent musculoskeletal disorder that significantly impacts health and requires labor-intensive analysis from experts. Despite advancements in automated detection of medical imaging, two significant challenges hinder the real-world application of these methods. First, the computational complexity and resource demands present a significant gap for real-time application. Second, noise in MRI reduces the effectiveness of existing methods by distorting feature extraction. To address these challenges, we propose three key contributions: Firstly, we introduced MedDet, which leverages the multi-teacher single-student knowledge distillation for model compression and efficiency, meanwhile integrating generative adversarial training to enhance performance. Additionally, we customize the second-order nmODE to improve the model's resistance to noise in MRI. Lastly, we conducted comprehensive experiments on the CDH-1848 dataset, achieving up to a 5% improvement in mAP compared to previous methods. Our approach also delivers over 5 times faster inference speed, with approximately 67.8% reduction in parameters and 36.9% reduction in FLOPs compared to the teacher model. These advancements significantly enhance the performance and efficiency of automated CDH detection, demonstrating promising potential for future application in clinical practice. See project website https://steve-zeyu-zhang.github.io/MedDet

  • 10 authors
·
Aug 30, 2024

KD-OCT: Efficient Knowledge Distillation for Clinical-Grade Retinal OCT Classification

Age-related macular degeneration (AMD) and choroidal neovascularization (CNV)-related conditions are leading causes of vision loss worldwide, with optical coherence tomography (OCT) serving as a cornerstone for early detection and management. However, deploying state-of-the-art deep learning models like ConvNeXtV2-Large in clinical settings is hindered by their computational demands. Therefore, it is desirable to develop efficient models that maintain high diagnostic performance while enabling real-time deployment. In this study, a novel knowledge distillation framework, termed KD-OCT, is proposed to compress a high-performance ConvNeXtV2-Large teacher model, enhanced with advanced augmentations, stochastic weight averaging, and focal loss, into a lightweight EfficientNet-B2 student for classifying normal, drusen, and CNV cases. KD-OCT employs real-time distillation with a combined loss balancing soft teacher knowledge transfer and hard ground-truth supervision. The effectiveness of the proposed method is evaluated on the Noor Eye Hospital (NEH) dataset using patient-level cross-validation. Experimental results demonstrate that KD-OCT outperforms comparable multi-scale or feature-fusion OCT classifiers in efficiency- accuracy balance, achieving near-teacher performance with substantial reductions in model size and inference time. Despite the compression, the student model exceeds most existing frameworks, facilitating edge deployment for AMD screening. Code is available at https://github.com/erfan-nourbakhsh/KD- OCT.

  • 3 authors
·
Dec 9, 2025 2

Can Large Models Teach Student Models to Solve Mathematical Problems Like Human Beings? A Reasoning Distillation Method via Multi-LoRA Interaction

Recent studies have demonstrated that Large Language Models (LLMs) have strong mathematical reasoning abilities but rely on hundreds of billions of parameters. To tackle the challenge of poor reasoning in Small Language Models (SLMs), existing methods typically leverage LLMs to generate massive amounts of data for cramming training. In psychology, they are akin to System 1 thinking, which resolves reasoning problems rapidly based on experience and intuition. However, human learning also requires System 2 thinking, where knowledge is first acquired and then reinforced through practice. Inspired by such two distinct modes of thinking, we propose a novel method based on the multi-LoRA Interaction for mathematical reasoning Distillation (LoRID). First, we input the question and reasoning of each sample into an LLM to create knowledge-enhanced datasets. Subsequently, we train a LoRA block on the student model as an Intuitive Reasoner (IR), which directly generates Chain-of-Thoughts for problem-solving. Then, to imitate System 2 thinking, we train the Knowledge Generator (KG) and Deep Reasoner (DR), respectively. The former outputs only knowledge after receiving problems, while the latter uses that knowledge to perform reasoning. Finally, to address the randomness in the generation of IR and DR, we evaluate whether their outputs are consistent, and the inference process needs to be iterated if not. This step can enhance the mathematical reasoning ability of SLMs through mutual feedback. Experimental results show that LoRID achieves state-of-the-art performance, especially on the GSM8K dataset, where it outperforms the second-best method by 2.3%, 16.1%, 2.4%, 12.3%, and 1.8% accuracy across the five base models, respectively.

  • 3 authors
·
Aug 18, 2025

POINTS-Reader: Distillation-Free Adaptation of Vision-Language Models for Document Conversion

High-quality labeled data is essential for training accurate document conversion models, particularly in domains with complex formats such as tables, formulas, and multi-column text. However, manual annotation is both costly and time-consuming, while automatic labeling using existing models often lacks accuracy in handling such challenging scenarios. Consequently, training student models by distilling outputs from teacher models can significantly limit their performance in real-world applications. In this paper, we propose a fully automated, distillation-free framework comprising two stages for constructing high-quality document extraction datasets and models capable of handling diverse document formats and layouts. In the first stage, we introduce a method for generating large-scale, diverse synthetic data, which enables a model to extract key elements in a unified format with strong initial performance. In the second stage, we present a self-improvement approach that further adapts the model, initially trained on synthetic data, to real-world documents. Specifically, we first use the fine-tuned model to annotate real documents, then apply a suite of filtering strategies to verify annotation quality, and finally retrain the model on the verified dataset. By iteratively repeating this process, we progressively enhance both the model's conversion capabilities and the quality of the generated data. We train a public POINTS-1.5 model to obtain POINTS-Reader, which surpasses many existing public and proprietary models of comparable or larger size. Our model is available at https://github.com/Tencent/POINTS-Reader.

tencent Tencent
·
Sep 1, 2025 4

When Reasoning Meets Compression: Benchmarking Compressed Large Reasoning Models on Complex Reasoning Tasks

Recent open-source large reasoning models (LRMs) exhibit strong performance on complex reasoning tasks, but their large parameter count makes them prohibitively expensive for individuals. The compression of large language models (LLMs) offers an effective solution to reduce cost of computational resources. However, systematic studies on the performance of compressed LLMs in complex reasoning tasks, especially for LRMs, are lacking. Most works on quantization and pruning focus on preserving language modeling performance, while existing distillation works do not comprehensively benchmark student models based on reasoning difficulty or compression impact on knowledge and reasoning. In this paper, we benchmark compressed DeepSeek-R1 models on four different reasoning datasets (AIME 2024, FOLIO, Temporal Sequences of BIG-Bench Hard, and MuSiQue), ranging from mathematical to multihop reasoning, using quantization, distillation, and pruning methods. We benchmark 2.51-, 1.73-, and 1.58-bit R1 models that adopt dynamic quantization. We also benchmark distilled R1 models that are based on LLaMA or Qwen and run SparseGPT on them to obtain various sparsity levels. Studying the performance and behavior of compressed LRMs, we report their performance scores and test-time compute (number of tokens spent on each question). Notably, using MuSiQue, we find that parameter count has a much greater impact on LRMs' knowledge memorization than on their reasoning capability, which can inform the choice of compression techniques. Through our empirical analysis of test-time compute, we find that shorter model outputs generally achieve better performance than longer ones across several benchmarks for both R1 and its compressed variants, highlighting the need for more concise reasoning chains.

  • 4 authors
·
Apr 2, 2025

Unlock the Power: Competitive Distillation for Multi-Modal Large Language Models

Recently, multi-modal content generation has attracted lots of attention from researchers by investigating the utilization of visual instruction tuning based on large language models (LLMs). To enhance the performance and generalization ability of such LLMs, the practice of distilling knowledge from pretrained multi-modal models (a.k.a. teachers) to more compact multi-modal LLMs (students) has gained considerable interest. However, the prevailing paradigm of instructiontuning in multi-modal LLMs knowledge distillation is resource-intensive and unidirectional, neglecting the potential for mutual feedback between the student and teacher models. Thus, we propose an innovative Competitive Multi-modal Distillation framework (CoMD), which captures bidirectional feedback between teacher and student models and continually updates the multi-modal capabilities that the student model has learned. It comprises two stages: multi-modal pre-training and multi-modal competitive distillation. The first stage pre-trains the student model on a large number of filtered multi-modal datasets. The second stage facilitates a bidirectional knowledge transfer between the student and teacher models. Our experimental analysis of diverse datasets shows that our knowledge transfer method consistently improves the capabilities of the student model. Finally, the 7B-sized student model after four distillations surpassed the current state-of-the-art model LLaVA-13B on the ScienceQA and LLaVA Test dataset, also outperforms other strong baselines in the zero-shot setting.

  • 4 authors
·
Nov 14, 2023

Which Reasoning Trajectories Teach Students to Reason Better? A Simple Metric of Informative Alignment

Long chain-of-thought (CoT) trajectories provide rich supervision signals for distilling reasoning from teacher to student LLMs. However, both prior work and our experiments show that trajectories from stronger teachers do not necessarily yield better students, highlighting the importance of data-student suitability in distillation. Existing methods assess suitability primarily through student likelihood, favoring trajectories that closely align with the model's current behavior but overlooking more informative ones. Addressing this, we propose Rank-Surprisal Ratio (RSR), a simple metric that captures both alignment and informativeness to assess the suitability of a reasoning trajectory. RSR is motivated by the observation that effective trajectories typically combine low absolute probability with relatively high-ranked tokens under the student model, balancing learning signal strength and behavioral alignment. Concretely, RSR is defined as the ratio of a trajectory's average token-wise rank to its average negative log-likelihood, and is straightforward to compute and interpret. Across five student models and reasoning trajectories from 11 diverse teachers, RSR strongly correlates with post-training performance (average Spearman 0.86), outperforming existing metrics. We further demonstrate its practical utility in both trajectory selection and teacher selection.

Mamba base PKD for efficient knowledge compression

Deep neural networks (DNNs) have remarkably succeeded in various image processing tasks. However, their large size and computational complexity present significant challenges for deploying them in resource-constrained environments. This paper presents an innovative approach for integrating Mamba Architecture within a Progressive Knowledge Distillation (PKD) process to address the challenge of reducing model complexity while maintaining accuracy in image classification tasks. The proposed framework distills a large teacher model into progressively smaller student models, designed using Mamba blocks. Each student model is trained using Selective-State-Space Models (S-SSM) within the Mamba blocks, focusing on important input aspects while reducing computational complexity. The work's preliminary experiments use MNIST and CIFAR-10 as datasets to demonstrate the effectiveness of this approach. For MNIST, the teacher model achieves 98% accuracy. A set of seven student models as a group retained 63% of the teacher's FLOPs, approximating the teacher's performance with 98% accuracy. The weak student used only 1% of the teacher's FLOPs and maintained 72% accuracy. Similarly, for CIFAR-10, the students achieved 1% less accuracy compared to the teacher, with the small student retaining 5% of the teacher's FLOPs to achieve 50% accuracy. These results confirm the flexibility and scalability of Mamba Architecture, which can be integrated into PKD, succeeding in the process of finding students as weak learners. The framework provides a solution for deploying complex neural networks in real-time applications with a reduction in computational cost.

  • 4 authors
·
Mar 3, 2025