Issues of inequity in U.S. high schools' course scheduling did not previously exist. However, in recent years, with the increase in student population and course variety, students perceive that the course scheduling method is unfair. Current integer programming (IP) methods to the high school scheduling problem (HSSP) fall short in addressing these fairness concerns. The purpose of this research is to develop a solution methodology that generates feasible and fair course schedules using student preferences. Utilizing principles of fairness, which have been well studied in market design, we define the fair high school scheduling problem (FHSSP), a novel extension to the HSSP, and devise a corresponding algorithm based on integer programming to solve the FHSSP. We test our approach on a real course request dataset from a high school in California, USA. Results show that our algorithm can generate schedules that are both feasible and fair. In this paper, we demonstrate that our IP algorithm not only solves the HSSP and FHSSP in the United States but has the potential to be applied to various real-world scheduling problems. Additionally, we show the feasibility of integrating human emotions into mathematical modeling.

We address a persistent challenge in text-to-image models: accurately generating a specified number of objects. Current models, which learn from image-text pairs, inherently struggle with counting, as training data cannot depict every possible number of objects for any given object. To solve this, we propose optimizing the generated image based on a counting loss derived from a counting model that aggregates an object\'s potential. Employing an out-of-the-box counting model is challenging for two reasons: first, the model requires a scaling hyperparameter for the potential aggregation that varies depending on the viewpoint of the objects, and second, classifier guidance techniques require modified models that operate on noisy intermediate diffusion steps. To address these challenges, we propose an iterated online training mode that improves the accuracy of inferred images while altering the text conditioning embedding and dynamically adjusting hyperparameters. Our method offers three key advantages: (i) it can consider non-derivable counting techniques based on detection models, (ii) it is a zero-shot plug-and-play solution facilitating rapid changes to the counting techniques and image generation methods, and (iii) the optimized counting token can be reused to generate accurate images without additional optimization. We evaluate the generation of various objects and show significant improvements in accuracy. The project page is available at https://ozzafar.github.io/count_token.

Can AI be used ethically for school work? It depends upon who you ask -- quite literally. That's because less than two years after ChatGPT was originally released in November 2022, the attitudes towards AI in the classroom still vary widely. High schools have viewed AI as a crutch at best, and at worst as a tool for cheating. But several universities leave generative AI use entirely up to the discretion of the person teaching the course.

In this study, we investigate whether non-English-centric LLMs, despite their strong performance, `think' in their respective dominant language: more precisely, `think' refers to how the representations of intermediate layers, when un-embedded into the vocabulary space, exhibit higher probabilities for certain dominant languages during generation. We term such languages as internal $\textbf{latent languages}$. We examine the latent language of three typical categories of models for Japanese processing: Llama2, an English-centric model; Swallow, an English-centric model with continued pre-training in Japanese; and LLM-jp, a model pre-trained on balanced English and Japanese corpora. Our empirical findings reveal that, unlike Llama2 which relies exclusively on English as the internal latent language, Japanese-specific Swallow and LLM-jp employ both Japanese and English, exhibiting dual internal latent languages. For any given target language, the model preferentially activates the latent language most closely related to it. In addition, we explore how intermediate layers respond to questions involving cultural conflicts between latent internal and target output languages. We further explore how the language identity shifts across layers while keeping consistent semantic meaning reflected in the intermediate layer representations. This study deepens the understanding of non-English-centric large language models, highlighting the intricate dynamics of language representation within their intermediate layers.

Gloss-free Sign Language Translation (SLT) converts sign videos directly into spoken language sentences without relying on glosses. Recently, Large Language Models (LLMs) have shown remarkable translation performance in gloss-free methods by harnessing their powerful natural language generation capabilities. However, these methods often rely on domain-specific fine-tuning of visual encoders to achieve optimal results. By contrast, this paper emphasizes the importance of capturing the spatial configurations and motion dynamics inherent in sign language. With this in mind, we introduce Spatial and Motion-based Sign Language Translation (SpaMo), a novel LLM-based SLT framework. The core idea of SpaMo is simple yet effective. We first extract spatial and motion features using off-the-shelf visual encoders and then input these features into an LLM with a language prompt. Additionally, we employ a visual-text alignment process as a warm-up before the SLT supervision. Our experiments demonstrate that SpaMo achieves state-of-the-art performance on two popular datasets, PHOENIX14T and How2Sign.

Large Vision-Language Models (LVLMs) have shown significant capability in vision-language understanding. However, one critical issue that persists in these models is sycophancy, which means models are unduly influenced by leading or deceptive prompts, resulting in biased outputs and hallucinations. Despite the progress in LVLMs, evaluating and mitigating sycophancy is yet much under-explored. In this work, we fill this gap by systematically analyzing sycophancy on various VL benchmarks with curated leading queries and further proposing a text contrastive decoding method for mitigation. While the specific sycophantic behavior varies significantly among models, our analysis reveals the severe deficiency of all LVLMs in resilience of sycophancy across various tasks. For improvement, we propose Leading Query Contrastive Decoding (LQCD), a model-agnostic method focusing on calibrating the LVLMs' over-reliance on leading cues by identifying and suppressing the probabilities of sycophancy tokens at the decoding stage. Extensive experiments show that LQCD effectively mitigate sycophancy, outperforming both prompt engineering methods and common methods for hallucination mitigation. We further demonstrate that LQCD does not hurt but even slightly improves LVLMs' responses to neutral queries, suggesting it being a more effective strategy for general-purpose decoding but not limited to sycophancy.

This work builds off the manifold-constrained Gaussian process inference (MAGI) method for Bayesian parameter inference and trajectory reconstruction of ODE-based dynamical systems, focusing primarily on sparse and noisy data conditions. First, we introduce Pilot MAGI (pMAGI), a novel methodological upgrade on the base MAGI method that confers significantly-improved numerical stability, parameter inference, and trajectory reconstruction. Second, we demonstrate, for the first time to our knowledge, how one can combine MAGI-based methods with dynamical systems theory to provide probabilistic classifications of whether a system is stable or chaotic. Third, we demonstrate how pMAGI performs favorably in many settings against much more computationally-expensive and overparameterized methods. Fourth, we introduce Pilot MAGI Sequential Prediction (PMSP), a novel method building upon pMAGI that allows one to predict the trajectory of ODE-based dynamical systems multiple time steps into the future, given only sparse and noisy observations. We show that PMSP can output accurate future predictions even on chaotic dynamical systems and significantly outperform PINN-based methods. Overall, we contribute to the literature two novel methods, pMAGI and PMSP, that serve as Bayesian, uncertainty-quantified competitors to the Physics-Informed Neural Network.

Active learning (AL) has shown promise for being a particularly data-efficient machine learning approach. Yet, its performance depends on the application and it is not clear when AL practitioners can expect computational savings. Here, we carry out a systematic AL performance assessment for three diverse molecular datasets and two common scientific tasks: compiling compact, informative datasets and targeted molecular searches. We implemented AL with Gaussian processes (GP) and used the many-body tensor as molecular representation. For the first task, we tested different data acquisition strategies, batch sizes and GP noise settings. AL was insensitive to the acquisition batch size and we observed the best AL performance for the acquisition strategy that combines uncertainty reduction with clustering to promote diversity. However, for optimal GP noise settings, AL did not outperform randomized selection of data points. Conversely, for targeted searches, AL outperformed random sampling and achieved data savings up to 64%. Our analysis provides insight into this task-specific performance difference in terms of target distributions and data collection strategies. We established that the performance of AL depends on the relative distribution of the target molecules in comparison to the total dataset distribution, with the largest computational savings achieved when their overlap is minimal.

The loss functions of many learning problems contain multiple additive terms that can disagree and yield conflicting update directions. For Physics-Informed Neural Networks (PINNs), loss terms on initial/boundary conditions and physics equations are particularly interesting as they are well-established as highly difficult tasks. To improve learning the challenging multi-objective task posed by PINNs, we propose the ConFIG method, which provides conflict-free updates by ensuring a positive dot product between the final update and each loss-specific gradient. It also maintains consistent optimization rates for all loss terms and dynamically adjusts gradient magnitudes based on conflict levels. We additionally leverage momentum to accelerate optimizations by alternating the back-propagation of different loss terms. The proposed method is evaluated across a range of challenging PINN scenarios, consistently showing superior performance and runtime compared to baseline methods. We also test the proposed method in a classic multi-task benchmark, where the ConFIG method likewise exhibits a highly promising performance. Source code is available at \url{https://tum-pbs.github.io/ConFIG}.

Teachers are important to imparting knowledge and guiding learners, and the role of large language models (LLMs) as potential educators is emerging as an important area of study. Recognizing LLMs' capability to generate educational content can lead to advances in automated and personalized learning. While LLMs have been tested for their comprehension and problem-solving skills, their capability in teaching remains largely unexplored. In teaching, questioning is a key skill that guides students to analyze, evaluate, and synthesize core concepts and principles. Therefore, our research introduces a benchmark to evaluate the questioning capability in education as a teacher of LLMs through evaluating their generated educational questions, utilizing Anderson and Krathwohl's taxonomy across general, monodisciplinary, and interdisciplinary domains. We shift the focus from LLMs as learners to LLMs as educators, assessing their teaching capability through guiding them to generate questions. We apply four metrics, including relevance, coverage, representativeness, and consistency, to evaluate the educational quality of LLMs' outputs. Our results indicate that GPT-4 demonstrates significant potential in teaching general, humanities, and science courses; Claude2 appears more apt as an interdisciplinary teacher. Furthermore, the automatic scores align with human perspectives.