We propose SAINT+, a successor of SAINT which is a Transformer based knowledge tracing model that separately processes exercise information and student response information. Following the architecture of SAINT, SAINT+ has an encoder-decoder structure where the encoder applies self-attention layers to a stream of exercise embeddings, and the decoder alternately applies self-attention layers and encoder-decoder attention layers to streams of response embeddings and encoder output. Moreover, SAINT+ incorporates two temporal feature embeddings into the response embeddings: elapsed time, the time taken for a student to answer, and lag time, the time interval between adjacent learning activities. We empirically evaluate the effectiveness of SAINT+ on EdNet, the largest publicly available benchmark dataset in the education domain. Experimental results show that SAINT+ achieves state-of-the-art performance in knowledge tracing with an improvement of 1.25% in area under receiver operating characteristic curve compared to SAINT, the current state-of-the-art model in EdNet dataset. CCS CONCEPTS• Computing methodologies → Artificial intelligence; Neural networks; • Applied computing → Interactive learning environments; • Social and professional topics → Student assessment.
Probabilistic programming is the idea of writing models from statistics and machine learning using program notations and reasoning about these models using generic inference engines. Recently its combination with deep learning has been explored intensely, which led to the development of so called deep probabilistic programming languages, such as Pyro, Edward and ProbTorch. At the core of this development lie inference engines based on stochastic variational inference algorithms. When asked to find information about the posterior distribution of a model written in such a language, these algorithms convert this posterior-inference query into an optimisation problem and solve it approximately by a form of gradient ascent or descent. In this paper, we analyse one of the most fundamental and versatile variational inference algorithms, called score estimator or REINFORCE, using tools from denotational semantics and program analysis. We formally express what this algorithm does on models denoted by programs, and expose implicit assumptions made by the algorithm on the models. The violation of these assumptions may lead to an undefined optimisation objective or the loss of convergence guarantee of the optimisation process. We then describe rules for proving these assumptions, which can be automated by static program analyses. Some of our rules use nontrivial facts from continuous mathematics, and let us replace requirements about integrals in the assumptions, such as integrability of functions defined in terms of programs' denotations, by conditions involving differentiation or boundedness, which are much easier to prove automatically (and manually). Following our general methodology, we have developed a static program analysis for the Pyro programming language that aims at discharging the assumption about what we call model-guide support match. Our analysis is applied to the eight representative model-guide pairs from the Pyro webpage, which include sophisticated neural network models such as AIR. It finds a bug in two of these cases, and shows that the assumptions are met in the others.In this paper, we consider inference engines that lie at the core of so called deep probabilistic programming languages, such as Pyro [Bingham et al. 2019], Edward [Tran et al. 2018, 2016 and ProbTorch [Siddharth et al. 2017]. These languages let their users freely mix deep neural networks with constructs from probabilistic programming, in particular, those for writing Bayesian probabilistic models. In so doing, they facilitate the development of probabilistic deep-network models that may address the problem of measuring the uncertainty in current non-Bayesian deepnetwork models; a non-Bayesian model may predict that the price of energy goes up and that of a house goes down, but it cannot express, for instance, that the model is very confident with the first prediction but not the second.The primary inference engines for these deep probabilistic programming languages implement stochastic variational inference algorithms. Converting infer...
Differentiation lies at the core of many machine-learning algorithms, and is wellsupported by popular autodiff systems, such as TensorFlow and PyTorch. Originally, these systems have been developed to compute derivatives of differentiable functions, but in practice, they are commonly applied to functions with non-differentiabilities. For instance, neural networks using ReLU define nondifferentiable functions in general, but the gradients of losses involving those functions are computed using autodiff systems in practice. This status quo raises a natural question: are autodiff systems correct in any formal sense when they are applied to such non-differentiable functions? In this paper, we provide a positive answer to this question. Using counterexamples, we first point out flaws in oftenused informal arguments, such as: non-differentiabilities arising in deep learning do not cause any issues because they form a measure-zero set. We then investigate a class of functions, called PAP functions, that includes nearly all (possibly nondifferentiable) functions in deep learning nowadays. For these PAP functions, we propose a new type of derivatives, called intensional derivatives, and prove that these derivatives always exist and coincide with standard derivatives for almost all inputs. We also show that these intensional derivatives are what most autodiff systems compute or try to compute essentially. In this way, we formally establish the correctness of autodiff systems applied to non-differentiable functions.Preprint. Under review.
Annotating task-oriented dialogues is notorious for the expensive and difficult data collection process. Few-shot dialogue state tracking (DST) is a realistic solution to this problem. In this paper, we hypothesize that dialogue summaries are essentially unstructured dialogue states; hence, we propose to reformulate dialogue state tracking as a dialogue summarization problem. To elaborate, we train a text-totext language model with synthetic templatebased dialogue summaries, generated by a set of rules. Then, the dialogue states can be recovered by inversely applying the summary generation rules. We empirically show that our method DS2 outperforms previous works on few-shot DST in MultiWoZ 2.0 and 2.1, in both cross-domain and multi-domain settings. Our method 1 also exhibits vast speedup during both training and inference as it can generate all states at once. Finally, based on our analysis, we discover that the naturalness of the summary templates plays a key role for successful training.
The automatic generation of Multiple Choice Questions (MCQ) has the potential to reduce the time educators spend on student assessment significantly. However, existing evaluation metrics for MCQ generation, such as BLEU, ROUGE, and METEOR, focus on the n-gram based similarity of the generated MCQ to the gold sample in the dataset and disregard their educational value. They fail to evaluate the MCQ's ability to assess the student's knowledge of the corresponding target fact. To tackle this issue, we propose a novel automatic evaluation metric, coined Knowledge Dependent Answerability (KDA), which measures the MCQ's answerability given knowledge of the target fact. Specifically, we first show how to measure KDA based on student responses from a human survey. Then, we propose two automatic evaluation metrics, KDA disc and KDA cont , that approximate KDA by leveraging pre-trained language models to imitate students' problem-solving behavior. Through our human studies, we show that KDA disc and KDA cont have strong correlations with both (1) KDA and (2) usability in an actual classroom setting, labeled by experts. Furthermore, when combined with ngram based similarity metrics, KDA disc and KDA cont are shown to have a strong predictive power for various expert-labeled MCQ quality measures. 1
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