Simiao Zuo

Chen Liang, Simiao Zuo, Qingru Zhang et al. · gatech, microsoft-research

Layer-wise distillation is a powerful tool to compress large models (i.e. teacher models) into small ones (i.e., student models). The student distills knowledge from the teacher by mimicking the hidden representations of the teacher at every intermediate layer. However, layer-wise distillation is difficult. Since the student has a smaller model capacity than the teacher, it is often under-fitted. Furthermore, the hidden representations of the teacher contain redundant information that the student does not necessarily need for the target task's learning. To address these challenges, we propose a novel Task-aware layEr-wise Distillation (TED). TED designs task-aware filters to align the hidden representations of the student and the teacher at each layer. The filters select the knowledge that is useful for the target task from the hidden representations. As such, TED reduces the knowledge gap between the two models and helps the student to fit better on the target task. We evaluate TED in two scenarios: continual pre-training and fine-tuning. TED demonstrates significant and consistent improvements over existing distillation methods in both scenarios. Code is available at https://github.com/cliang1453/task-aware-distillation.

Qingru Zhang, Simiao Zuo, Chen Liang et al. · gatech, microsoft-research

Large Transformer-based models have exhibited superior performance in various natural language processing and computer vision tasks. However, these models contain enormous amounts of parameters, which restrict their deployment to real-world applications. To reduce the model size, researchers prune these models based on the weights' importance scores. However, such scores are usually estimated on mini-batches during training, which incurs large variability/uncertainty due to mini-batch sampling and complicated training dynamics. As a result, some crucial weights could be pruned by commonly used pruning methods because of such uncertainty, which makes training unstable and hurts generalization. To resolve this issue, we propose PLATON, which captures the uncertainty of importance scores by upper confidence bound (UCB) of importance estimation. In particular, for the weights with low importance scores but high uncertainty, PLATON tends to retain them and explores their capacity. We conduct extensive experiments with several Transformer-based models on natural language understanding, question answering and image classification to validate the effectiveness of PLATON. Results demonstrate that PLATON manifests notable improvement under different sparsity levels. Our code is publicly available at https://github.com/QingruZhang/PLATON.

Simiao Zuo, Qingru Zhang, Chen Liang et al. · gatech, microsoft-research

Pre-trained language models have demonstrated superior performance in various natural language processing tasks. However, these models usually contain hundreds of millions of parameters, which limits their practicality because of latency requirements in real-world applications. Existing methods train small compressed models via knowledge distillation. However, performance of these small models drops significantly compared with the pre-trained models due to their reduced model capacity. We propose MoEBERT, which uses a Mixture-of-Experts structure to increase model capacity and inference speed. We initialize MoEBERT by adapting the feed-forward neural networks in a pre-trained model into multiple experts. As such, representation power of the pre-trained model is largely retained. During inference, only one of the experts is activated, such that speed can be improved. We also propose a layer-wise distillation method to train MoEBERT. We validate the efficiency and effectiveness of MoEBERT on natural language understanding and question answering tasks. Results show that the proposed method outperforms existing task-specific distillation algorithms. For example, our method outperforms previous approaches by over 2% on the MNLI (mismatched) dataset. Our code is publicly available at https://github.com/SimiaoZuo/MoEBERT.

Alexander Bukharin, Tianyi Liu, Shengjie Wang et al. · stanford

Machine learning force fields (MLFF) have been proposed to accelerate molecular dynamics (MD) simulation, which finds widespread applications in chemistry and biomedical research. Even for the most data-efficient MLFFs, reaching chemical accuracy can require hundreds of frames of force and energy labels generated by expensive quantum mechanical algorithms, which may scale as $O(n^3)$ to $O(n^7)$, with $n$ proportional to the number of basis functions. To address this issue, we propose a multi-stage computational framework -- ASTEROID, which lowers the data cost of MLFFs by leveraging a combination of cheap inaccurate data and expensive accurate data. The motivation behind ASTEROID is that inaccurate data, though incurring large bias, can help capture the sophisticated structures of the underlying force field. Therefore, we first train a MLFF model on a large amount of inaccurate training data, employing a bias-aware loss function to prevent the model from overfitting tahe potential bias of this data. We then fine-tune the obtained model using a small amount of accurate training data, which preserves the knowledge learned from the inaccurate training data while significantly improving the model's accuracy. Moreover, we propose a variant of ASTEROID based on score matching for the setting where the inaccurate training data are unlabeled. Extensive experiments on MD datasets and downstream tasks validate the efficacy of ASTEROID. Our code and data are available at https://github.com/abukharin3/asteroid.

Simiao Zuo, Xiaodong Liu, Jian Jiao et al. · microsoft-research

Transformer models have achieved superior performance in various natural language processing tasks. However, the quadratic computational cost of the attention mechanism limits its practicality for long sequences. There are existing attention variants that improve the computational efficiency, but they have limited ability to effectively compute global information. In parallel to Transformer models, state space models (SSMs) are tailored for long sequences, but they are not flexible enough to capture complicated local information. We propose SPADE, short for $\underline{\textbf{S}}$tate s$\underline{\textbf{P}}$ace $\underline{\textbf{A}}$ugmente$\underline{\textbf{D}}$ Transform$\underline{\textbf{E}}$r. Specifically, we augment a SSM into the bottom layer of SPADE, and we employ efficient local attention methods for the other layers. The SSM augments global information, which complements the lack of long-range dependency issue in local attention methods. Experimental results on the Long Range Arena benchmark and language modeling tasks demonstrate the effectiveness of the proposed method. To further demonstrate the scalability of SPADE, we pre-train large encoder-decoder models and present fine-tuning results on natural language understanding and natural language generation tasks.

Alexander Bukharin, Yan Li, Yue Yu et al. · gatech

Multi-Agent Reinforcement Learning (MARL) has shown promising results across several domains. Despite this promise, MARL policies often lack robustness and are therefore sensitive to small changes in their environment. This presents a serious concern for the real world deployment of MARL algorithms, where the testing environment may slightly differ from the training environment. In this work we show that we can gain robustness by controlling a policy's Lipschitz constant, and under mild conditions, establish the existence of a Lipschitz and close-to-optimal policy. Based on these insights, we propose a new robust MARL framework, ERNIE, that promotes the Lipschitz continuity of the policies with respect to the state observations and actions by adversarial regularization. The ERNIE framework provides robustness against noisy observations, changing transition dynamics, and malicious actions of agents. However, ERNIE's adversarial regularization may introduce some training instability. To reduce this instability, we reformulate adversarial regularization as a Stackelberg game. We demonstrate the effectiveness of the proposed framework with extensive experiments in traffic light control and particle environments. In addition, we extend ERNIE to mean-field MARL with a formulation based on distributionally robust optimization that outperforms its non-robust counterpart and is of independent interest. Our code is available at https://github.com/abukharin3/ERNIE.

Zichong Li, Yanbo Xu, Simiao Zuo et al.

Transformer Hawkes process models have shown to be successful in modeling event sequence data. However, most of the existing training methods rely on maximizing the likelihood of event sequences, which involves calculating some intractable integral. Moreover, the existing methods fail to provide uncertainty quantification for model predictions, e.g., confidence intervals for the predicted event's arrival time. To address these issues, we propose SMURF-THP, a score-based method for learning Transformer Hawkes process and quantifying prediction uncertainty. Specifically, SMURF-THP learns the score function of events' arrival time based on a score-matching objective that avoids the intractable computation. With such a learned score function, we can sample arrival time of events from the predictive distribution. This naturally allows for the quantification of uncertainty by computing confidence intervals over the generated samples. We conduct extensive experiments in both event type prediction and uncertainty quantification of arrival time. In all the experiments, SMURF-THP outperforms existing likelihood-based methods in confidence calibration while exhibiting comparable prediction accuracy.

Simiao Zuo, Tianyi Liu, Tuo Zhao et al.

Point process models are of great importance in real world applications. In certain critical applications, estimation of point process models involves large amounts of sensitive personal data from users. Privacy concerns naturally arise which have not been addressed in the existing literature. To bridge this glaring gap, we propose the first general differentially private estimation procedure for point process models. Specifically, we take the Hawkes process as an example, and introduce a rigorous definition of differential privacy for event stream data based on a discretized representation of the Hawkes process. We then propose two differentially private optimization algorithms, which can efficiently estimate Hawkes process models with the desired privacy and utility guarantees under two different settings. Experiments are provided to back up our theoretical analysis.

Simiao Zuo, Qingyu Yin, Haoming Jiang et al.

E-commerce queries are often short and ambiguous. Consequently, query understanding often uses query rewriting to disambiguate user-input queries. While using e-commerce search tools, users tend to enter multiple searches, which we call context, before purchasing. These history searches contain contextual insights about users' true shopping intents. Therefore, modeling such contextual information is critical to a better query rewriting model. However, existing query rewriting models ignore users' history behaviors and consider only the instant search query, which is often a short string offering limited information about the true shopping intent. We propose an end-to-end context-aware query rewriting model to bridge this gap, which takes the search context into account. Specifically, our model builds a session graph using the history search queries and their contained words. We then employ a graph attention mechanism that models cross-query relations and computes contextual information of the session. The model subsequently calculates session representations by combining the contextual information with the instant search query using an aggregation network. The session representations are then decoded to generate rewritten queries. Empirically, we demonstrate the superiority of our method to state-of-the-art approaches under various metrics. On in-house data from an online shopping platform, by introducing contextual information, our model achieves 11.6% improvement under the MRR (Mean Reciprocal Rank) metric and 20.1% improvement under the HIT@16 metric (a hit rate metric), in comparison with the best baseline method (Transformer-based model).

Xinyu Hu, Pengfei Tang, Simiao Zuo et al.

Large language models (LLMs) have made impressive progress in natural language processing. These models rely on proper human instructions (or prompts) to generate suitable responses. However, the potential of LLMs are not fully harnessed by commonly-used prompting methods: many human-in-the-loop algorithms employ ad-hoc procedures for prompt selection; while auto prompt generation approaches are essentially searching all possible prompts randomly and inefficiently. We propose Evoke, an automatic prompt refinement framework. In Evoke, there are two instances of a same LLM: one as a reviewer (LLM-Reviewer), it scores the current prompt; the other as an author (LLM-Author), it edits the prompt by considering the edit history and the reviewer's feedback. Such an author-reviewer feedback loop ensures that the prompt is refined in each iteration. We further aggregate a data selection approach to Evoke, where only the hard samples are exposed to the LLM. The hard samples are more important because the LLM can develop deeper understanding of the tasks out of them, while the model may already know how to solve the easier cases. Experimental results show that Evoke significantly outperforms existing methods. For instance, in the challenging task of logical fallacy detection, Evoke scores above 80, while all other baseline methods struggle to reach 20.

Simiao Zuo, Haoming Jiang, Qingyu Yin et al.

Graph neural network (GNN) pre-training methods have been proposed to enhance the power of GNNs. Specifically, a GNN is first pre-trained on a large-scale unlabeled graph and then fine-tuned on a separate small labeled graph for downstream applications, such as node classification. One popular pre-training method is to mask out a proportion of the edges, and a GNN is trained to recover them. However, such a generative method suffers from graph mismatch. That is, the masked graph inputted to the GNN deviates from the original graph. To alleviate this issue, we propose DiP-GNN (Discriminative Pre-training of Graph Neural Networks). Specifically, we train a generator to recover identities of the masked edges, and simultaneously, we train a discriminator to distinguish the generated edges from the original graph's edges. In our framework, the graph seen by the discriminator better matches the original graph because the generator can recover a proportion of the masked edges. Extensive experiments on large-scale homogeneous and heterogeneous graphs demonstrate the effectiveness of the proposed framework.

Yaoxiang Wang, Simiao Zuo, Qingguo Hu et al.

Embedding models are pivotal in industrial information retrieval systems like search and advertising. However, existing pretrained models often exhibit fixed architectures and embedding dimensionalities, posing significant challenges when adapting them to diverse deployment scenarios with varying business-driven constraints. A common practice involves fine-tuning with partial parameter initialization from larger pretrained models for resource-constrained tasks. This method is often suboptimal as the misalignment between pretraining and downstream usage prevents full realization of pretraining benefits. To address this limitation, we introduce m3BERT: a Modern, Multi-lingual, Matryoshka Bidirectional Encoder, which features a novel pretraining strategy that jointly optimizes representations across both transformer layers and multiple embedding dimensions. This enables a single model to be tailored to varied resource and accuracy targets while maintaining consistency with pretraining. Incorporating recent architectural improvements, m3BERT uses a three-stage pretraining: monolingual pretraining, multilingual adaptation to serve diverse user bases, and crucial continual pretraining on a massive web domain corpus to enhance utility in commercial retrieval. m3BERT significantly outperforms state-of-the-art embedding models in Bing-Click, a large-scale industrial retrieval dataset, showcasing its practical versatility as an efficient foundation for resource-aware industrial retrieval systems. Further experiments on public datasets also confirm the general effectiveness of our multigranular Matryoshka pretraining strategy.

Yanda Chen, Chandan Singh, Xiaodong Liu et al.

Large language models (LLMs) often generate convincing, fluent explanations. However, different from humans, they often generate inconsistent explanations on different inputs. For example, an LLM may generate the explanation "all birds can fly" when answering the question "Can sparrows fly?" but meanwhile answer "no" to the related question "Can penguins fly?". Explanations should be consistent across related examples so that they allow a human to simulate the LLM's decision process on multiple examples. We propose explanation-consistency finetuning (EC-finetuning), a method that adapts LLMs to generate more consistent natural-language explanations on related examples. EC-finetuning involves finetuning LLMs on synthetic data that is carefully constructed to contain consistent explanations. Across a variety of question-answering datasets in various domains, EC-finetuning yields a 10.0% relative explanation consistency improvement on four finetuning datasets, and generalizes to seven out-of-distribution datasets not seen during finetuning (+4.5% relative). Code is available at https://github.com/yandachen/explanation-consistency-finetuning .

Simiao Zuo, Xiaodong Liu, Jian Jiao et al.

Sparsely activated models (SAMs), such as Mixture-of-Experts (MoE), can easily scale to have outrageously large amounts of parameters without significant increase in computational cost. However, SAMs are reported to be parameter inefficient such that larger models do not always lead to better performance. While most on-going research focuses on improving SAMs models by exploring methods of routing inputs to experts, our analysis reveals that such research might not lead to the solution we expect, i.e., the commonly-used routing methods based on gating mechanisms do not work better than randomly routing inputs to experts. In this paper, we propose a new expert-based model, THOR (Transformer witH StOchastic ExpeRts). Unlike classic expert-based models, such as the Switch Transformer, experts in THOR are randomly activated for each input during training and inference. THOR models are trained using a consistency regularized loss, where experts learn not only from training data but also from other experts as teachers, such that all the experts make consistent predictions. We validate the effectiveness of THOR on machine translation tasks. Results show that THOR models are more parameter efficient in that they significantly outperform the Transformer and MoE models across various settings. For example, in multilingual translation, THOR outperforms the Switch Transformer by 2 BLEU scores, and obtains the same BLEU score as that of a state-of-the-art MoE model that is 18 times larger. Our code is publicly available at: https://github.com/microsoft/Stochastic-Mixture-of-Experts.

Simiao Zuo, Chen Liang, Haoming Jiang et al.

Adversarial regularization can improve model generalization in many natural language processing tasks. However, conventional approaches are computationally expensive since they need to generate a perturbation for each sample in each epoch. We propose a new adversarial regularization method ARCH (adversarial regularization with caching), where perturbations are generated and cached once every several epochs. As caching all the perturbations imposes memory usage concerns, we adopt a K-nearest neighbors-based strategy to tackle this issue. The strategy only requires caching a small amount of perturbations, without introducing additional training time. We evaluate our proposed method on a set of neural machine translation and natural language understanding tasks. We observe that ARCH significantly eases the computational burden (saves up to 70% of computational time in comparison with conventional approaches). More surprisingly, by reducing the variance of stochastic gradients, ARCH produces a notably better (in most of the tasks) or comparable model generalization. Our code is available at https://github.com/SimiaoZuo/Caching-Adv.

Simiao Zuo, Chen Liang, Haoming Jiang et al.

Adversarial regularization has been shown to improve the generalization performance of deep learning models in various natural language processing tasks. Existing works usually formulate the method as a zero-sum game, which is solved by alternating gradient descent/ascent algorithms. Such a formulation treats the adversarial and the defending players equally, which is undesirable because only the defending player contributes to the generalization performance. To address this issue, we propose Stackelberg Adversarial Regularization (SALT), which formulates adversarial regularization as a Stackelberg game. This formulation induces a competition between a leader and a follower, where the follower generates perturbations, and the leader trains the model subject to the perturbations. Different from conventional approaches, in SALT, the leader is in an advantageous position. When the leader moves, it recognizes the strategy of the follower and takes the anticipated follower's outcomes into consideration. Such a leader's advantage enables us to improve the model fitting to the unperturbed data. The leader's strategic information is captured by the Stackelberg gradient, which is obtained using an unrolling algorithm. Our experimental results on a set of machine translation and natural language understanding tasks show that SALT outperforms existing adversarial regularization baselines across all tasks. Our code is available at https://github.com/SimiaoZuo/Stackelberg-Adv.

Xiao Liang, Xinyu Hu, Simiao Zuo et al.

Large Language Models (LLMs) have shown superior performance in various applications and fields. To achieve better performance on specialized domains such as law and advertisement, LLMs are often continue pre-trained on in-domain data. However, existing approaches suffer from two major issues. First, in-domain data are scarce compared with general domain-agnostic data. Second, data used for continual pre-training are not task-aware, such that they may not be helpful to downstream applications. We propose TRAIT, a task-oriented in-domain data augmentation framework. Our framework is divided into two parts: in-domain data selection and task-oriented synthetic passage generation. The data selection strategy identifies and selects a large amount of in-domain data from general corpora, and thus significantly enriches domain knowledge in the continual pre-training data. The synthetic passages contain guidance on how to use domain knowledge to answer questions about downstream tasks. By training on such passages, the model aligns with the need of downstream applications. We adapt LLMs to two domains: advertisement and math. On average, TRAIT improves LLM performance by 8% in the advertisement domain and 7.5% in the math domain.

Chen Liang, Haoming Jiang, Simiao Zuo et al.

Recent research has shown the existence of significant redundancy in large Transformer models. One can prune the redundant parameters without significantly sacrificing the generalization performance. However, we question whether the redundant parameters could have contributed more if they were properly trained. To answer this question, we propose a novel training strategy that encourages all parameters to be trained sufficiently. Specifically, we adaptively adjust the learning rate for each parameter according to its sensitivity, a robust gradient-based measure reflecting this parameter's contribution to the model performance. A parameter with low sensitivity is redundant, and we improve its fitting by increasing its learning rate. In contrast, a parameter with high sensitivity is well-trained, and we regularize it by decreasing its learning rate to prevent further overfitting. We conduct extensive experiments on natural language understanding, neural machine translation, and image classification to demonstrate the effectiveness of the proposed schedule. Analysis shows that the proposed schedule indeed reduces the redundancy and improves generalization performance.

Zhigen Zhao, Simiao Zuo, Tuo Zhao et al.

Recent advancement in combining trajectory optimization with function approximation (especially neural networks) shows promise in learning complex control policies for diverse tasks in robot systems. Despite their great flexibility, the large neural networks for parameterizing control policies impose significant challenges. The learned neural control policies are often overcomplex and non-smooth, which can easily cause unexpected or diverging robot motions. Therefore, they often yield poor generalization performance in practice. To address this issue, we propose adVErsarially Regularized pOlicy learNIng guided by trajeCtory optimizAtion (VERONICA) for learning smooth control policies. Specifically, our proposed approach controls the smoothness (local Lipschitz continuity) of the neural control policies by stabilizing the output control with respect to the worst-case perturbation to the input state. Our experiments on robot manipulation show that our proposed approach not only improves the sample efficiency of neural policy learning but also enhances the robustness of the policy against various types of disturbances, including sensor noise, environmental uncertainty, and model mismatch.

Simiao Zuo, Yue Yu, Chen Liang et al.

Self-training achieves enormous success in various semi-supervised and weakly-supervised learning tasks. The method can be interpreted as a teacher-student framework, where the teacher generates pseudo-labels, and the student makes predictions. The two models are updated alternatingly. However, such a straightforward alternating update rule leads to training instability. This is because a small change in the teacher may result in a significant change in the student. To address this issue, we propose DRIFT, short for differentiable self-training, that treats teacher-student as a Stackelberg game. In this game, a leader is always in a more advantageous position than a follower. In self-training, the student contributes to the prediction performance, and the teacher controls the training process by generating pseudo-labels. Therefore, we treat the student as the leader and the teacher as the follower. The leader procures its advantage by acknowledging the follower's strategy, which involves differentiable pseudo-labels and differentiable sample weights. Consequently, the leader-follower interaction can be effectively captured via Stackelberg gradient, obtained by differentiating the follower's strategy. Experimental results on semi- and weakly-supervised classification and named entity recognition tasks show that our model outperforms existing approaches by large margins.

Chen Liang, Simiao Zuo, Minshuo Chen et al.

The Lottery Ticket Hypothesis suggests that an over-parametrized network consists of ``lottery tickets'', and training a certain collection of them (i.e., a subnetwork) can match the performance of the full model. In this paper, we study such a collection of tickets, which is referred to as ``winning tickets'', in extremely over-parametrized models, e.g., pre-trained language models. We observe that at certain compression ratios, the generalization performance of the winning tickets can not only match but also exceed that of the full model. In particular, we observe a phase transition phenomenon: As the compression ratio increases, generalization performance of the winning tickets first improves then deteriorates after a certain threshold. We refer to the tickets on the threshold as ``super tickets''. We further show that the phase transition is task and model dependent -- as the model size becomes larger and the training data set becomes smaller, the transition becomes more pronounced. Our experiments on the GLUE benchmark show that the super tickets improve single task fine-tuning by $0.9$ points on BERT-base and $1.0$ points on BERT-large, in terms of task-average score. We also demonstrate that adaptively sharing the super tickets across tasks benefits multi-task learning.

Yujia Xie, Yixiu Mao, Simiao Zuo et al.

We consider a variant of regression problem, where the correspondence between input and output data is not available. Such shuffled data is commonly observed in many real world problems. Taking flow cytometry as an example, the measuring instruments may not be able to maintain the correspondence between the samples and the measurements. Due to the combinatorial nature of the problem, most existing methods are only applicable when the sample size is small, and limited to linear regression models. To overcome such bottlenecks, we propose a new computational framework -- ROBOT -- for the shuffled regression problem, which is applicable to large data and complex nonlinear models. Specifically, we reformulate the regression without correspondence as a continuous optimization problem. Then by exploiting the interaction between the regression model and the data correspondence, we develop a hypergradient approach based on differentiable programming techniques. Such a hypergradient approach essentially views the data correspondence as an operator of the regression, and therefore allows us to find a better descent direction for the model parameter by differentiating through the data correspondence. ROBOT can be further extended to the inexact correspondence setting, where there may not be an exact alignment between the input and output data. Thorough numerical experiments show that ROBOT achieves better performance than existing methods in both linear and nonlinear regression tasks, including real-world applications such as flow cytometry and multi-object tracking.

Yue Yu, Simiao Zuo, Haoming Jiang et al.

Fine-tuned pre-trained language models (LMs) have achieved enormous success in many natural language processing (NLP) tasks, but they still require excessive labeled data in the fine-tuning stage. We study the problem of fine-tuning pre-trained LMs using only weak supervision, without any labeled data. This problem is challenging because the high capacity of LMs makes them prone to overfitting the noisy labels generated by weak supervision. To address this problem, we develop a contrastive self-training framework, COSINE, to enable fine-tuning LMs with weak supervision. Underpinned by contrastive regularization and confidence-based reweighting, this contrastive self-training framework can gradually improve model fitting while effectively suppressing error propagation. Experiments on sequence, token, and sentence pair classification tasks show that our model outperforms the strongest baseline by large margins on 7 benchmarks in 6 tasks, and achieves competitive performance with fully-supervised fine-tuning methods.

Simiao Zuo, Haoming Jiang, Zichong Li et al.

Modern data acquisition routinely produce massive amounts of event sequence data in various domains, such as social media, healthcare, and financial markets. These data often exhibit complicated short-term and long-term temporal dependencies. However, most of the existing recurrent neural network based point process models fail to capture such dependencies, and yield unreliable prediction performance. To address this issue, we propose a Transformer Hawkes Process (THP) model, which leverages the self-attention mechanism to capture long-term dependencies and meanwhile enjoys computational efficiency. Numerical experiments on various datasets show that THP outperforms existing models in terms of both likelihood and event prediction accuracy by a notable margin. Moreover, THP is quite general and can incorporate additional structural knowledge. We provide a concrete example, where THP achieves improved prediction performance for learning multiple point processes when incorporating their relational information.

Simiao Zuo, Jialin Wu

There has long been debates on how we could interpret neural networks and understand the decisions our models make. Specifically, why deep neural networks tend to be error-prone when dealing with samples that output low softmax scores. We present an efficient approach to measure the confidence of decision-making steps by statistically investigating each unit's contribution to that decision. Instead of focusing on how the models react on datasets, we study the datasets themselves given a pre-trained model. Our approach is capable of assigning a score to each sample within a dataset that measures the frequency of occurrence of that sample's chain of activation. We demonstrate with experiments that our method could select useful samples to improve deep neural networks in a semi-supervised leaning setting.