Advancing LLM reasoning skills has captivated wide interest. However, current post-training techniques rely heavily on supervisory signals, such as outcome supervision or auxiliary reward models, which face the problem of scalability and high annotation costs. This motivates us to enhance LLM reasoning without the need for external supervision. We introduce a generalizable and purely unsupervised self-training framework, named Genius. Without external auxiliary, Genius requires to seek the optimal response sequence in a stepwise manner and optimize the LLM. To explore the potential steps and exploit the optimal ones, Genius introduces a stepwise foresight re-sampling strategy to sample and estimate the step value by simulating future outcomes. Further, we recognize that the unsupervised setting inevitably induces the intrinsic noise and uncertainty. To provide a robust optimization, we propose an advantage-calibrated optimization (ACO) loss function to mitigate estimation inconsistencies. Combining these techniques together, Genius provides an advanced initial step towards self-improve LLM reasoning with general queries and without supervision, revolutionizing reasoning scaling laws given the vast availability of general queries. The code will be released at https://github.com/xufangzhi/Genius.

Large language models appear quite creative, often performing on par with the average human on creative tasks. However, research on LLM creativity has focused solely on \textit{products}, with little attention on the creative \textit{process}. Process analyses of human creativity often require hand-coded categories or exploit response times, which do not apply to LLMs. We provide an automated method to characterise how humans and LLMs explore semantic spaces on the Alternate Uses Task, and contrast with behaviour in a Verbal Fluency Task. We use sentence embeddings to identify response categories and compute semantic similarities, which we use to generate jump profiles. Our results corroborate earlier work in humans reporting both persistent (deep search in few semantic spaces) and flexible (broad search across multiple semantic spaces) pathways to creativity, where both pathways lead to similar creativity scores. LLMs were found to be biased towards either persistent or flexible paths, that varied across tasks. Though LLMs as a population match human profiles, their relationship with creativity is different, where the more flexible models score higher on creativity. Our dataset and scripts are available on \href{https://github.com/surabhisnath/Creative_Process}{GitHub}.

Knowledge tracing (KT) plays a crucial role in computer-aided education and intelligent tutoring systems, aiming to assess students' knowledge proficiency by predicting their future performance on new questions based on their past response records. While existing deep learning knowledge tracing (DLKT) methods have significantly improved prediction accuracy and achieved state-of-the-art results, they often suffer from a lack of interpretability. To address this limitation, current approaches have explored incorporating psychological influences to achieve more explainable predictions, but they tend to overlook the potential influences of historical responses. In fact, understanding how models make predictions based on response influences can enhance the transparency and trustworthiness of the knowledge tracing process, presenting an opportunity for a new paradigm of interpretable KT. However, measuring unobservable response influences is challenging. In this paper, we resort to counterfactual reasoning that intervenes in each response to answer \textit{what if a student had answered a question incorrectly that he/she actually answered correctly, and vice versa}. Based on this, we propose RCKT, a novel response influence-based counterfactual knowledge tracing framework. RCKT generates response influences by comparing prediction outcomes from factual sequences and constructed counterfactual sequences after interventions. Additionally, we introduce maximization and inference techniques to leverage accumulated influences from different past responses, further improving the model's performance and credibility. Extensive experimental results demonstrate that our RCKT method outperforms state-of-the-art knowledge tracing methods on four datasets against six baselines, and provides credible interpretations of response influences.

In several research problems we face probabilistic sequences of inputs (e.g., sequence of stimuli) from which an agent generates a corresponding sequence of responses and it is of interest to model/discover some kind of relation between them. To model such relation in the context of statistical learning in neuroscience, a new class of stochastic process have been introduced [5], namely sequences of random objects driven by context tree models. In this paper we introduce a freely available Matlab toolbox (SeqROCTM) that implements three model selection methods to make inference about the parameters of this kind of stochastic process.

Numerous learning methods for fuzzy cognitive maps (FCMs), such as the Hebbian-based and the population-based learning methods, have been developed for modeling and simulating dynamic systems. However, these methods are faced with several obvious limitations. Most of these models are extremely time consuming when learning the large-scale FCMs with hundreds of nodes. Furthermore, the FCMs learned by those algorithms lack robustness when the experimental data contain noise. In addition, reasonable distribution of the weights is rarely considered in these algorithms, which could result in the reduction of the performance of the resulting FCM. In this article, a straightforward, rapid, and robust learning method is proposed to learn FCMs from noisy data, especially, to learn large-scale FCMs. The crux of the proposed algorithm is to equivalently transform the learning problem of FCMs to a classic-constrained convex optimization problem in which the least-squares term ensures the robustness of the well-learned FCM and the maximum entropy term regularizes the distribution of the weights of the well-learned FCM. A series of experiments covering two frequently used activation functions (the sigmoid and hyperbolic tangent functions) are performed on both synthetic datasets with noise and real-world datasets. The experimental results show that the proposed method is rapid and robust against data containing noise and that the well-learned weights have better distribution. In addition, the FCMs learned by the proposed method also exhibit superior performance in comparison with the existing methods. Index Terms-Fuzzy cognitive maps (FCMs), maximum entropy, noisy data, rapid and robust learning.