Semi-supervised classification, where unlabeled data are massive but labeled data are limited, often arises in machine learning applications. We address this challenge under high-dimensional data by leveraging the manifold and cluster assumptions. Based on the Fermat distance, a density-sensitive metric that naturally encodes the cluster assumption, we propose the weighted $k$-nearest neighbors (NN) classifier and multidimensional scaling (MDS)-induced classifiers. The use of MDS with a large target dimension allows the effective application of linear classifiers to complex manifold data. Theoretically, we derive a sharp lower bound for the expected excess risk within clusters and prove that the weighted $k$-NN classifier utilizing the true Fermat distance is minimax optimal. Furthermore, we explicitly quantify the utility of unlabeled data by showing that the error arising from estimating the Fermat distance decays exponentially with the pooled sample size. Such a rate is much faster than the related rates in the literature. Extensive experiments on synthetic and real datasets demonstrate competitive or superior performance of our approaches compared to state-of-the-art graph-based semi-supervised classifiers.

In order to emulate the local connectivity constraints of the retina, we would like neighboring pixels in 2D image-space tomap toneighboring pixels in1D vector-space.

Inference in semi-supervised (SS) settings has gained substantial attention in recent years due to increased relevance in modern big-data problems. In a typical SS setting, there is a much larger-sized unlabeled data, containing only observations of predictors, and a moderately sized labeled data containing observations for both an outcome and the set of predictors. Such data naturally arises when the outcome, unlike the predictors, is costly or difficult to obtain. One of the primary statistical objectives in SS settings is to explore whether parameter estimation can be improved by exploiting the unlabeled data. We propose a novel Bayesian method for estimating the population mean in SS settings. The approach yields estimators that are both efficient and optimal for estimation and inference. The method itself has several interesting artifacts. The central idea behind the method is to model certain summary statistics of the data in a targeted manner, rather than the entire raw data itself, along with a novel Bayesian notion of debiasing. Specifying appropriate summary statistics crucially relies on a debiased representation of the population mean that incorporates unlabeled data through a flexible nuisance function while also learning its estimation bias. Combined with careful usage of sample splitting, this debiasing approach mitigates the effect of bias due to slow rates or misspecification of the nuisance parameter from the posterior of the final parameter of interest, ensuring its robustness and efficiency. Concrete theoretical results, via Bernstein--von Mises theorems, are established, validating all claims, and are further supported through extensive numerical studies. To our knowledge, this is possibly the first work on Bayesian inference in SS settings, and its central ideas also apply more broadly to other Bayesian semi-parametric inference problems.

Understanding and controlling the informational complexity of neural networks is a central challenge in machine learning, with implications for generalization, optimization, and model capacity. While most approaches rely on entropy-based loss functions and statistical metrics, these measures often fail to capture deeper, causally relevant algorithmic regularities embedded in network structure. We propose a shift toward algorithmic information theory, using Binarized Neural Networks (BNNs) as a first proxy. Grounded in algorithmic probability (AP) and the universal distribution it defines, our approach characterizes learning dynamics through a formal, causally grounded lens. We apply the Block Decomposition Method (BDM) -- a scalable approximation of algorithmic complexity based on AP -- and demonstrate that it more closely tracks structural changes during training than entropy, consistently exhibiting stronger correlations with training loss across varying model sizes and randomized training runs. These results support the view of training as a process of algorithmic compression, where learning corresponds to the progressive internalization of structured regularities. In doing so, our work offers a principled estimate of learning progression and suggests a framework for complexity-aware learning and regularization, grounded in first principles from information theory, complexity, and computability.

We introduce an open-ended test grounded in algorithmic probability that can avoid benchmark contamination in the quantitative evaluation of frontier models in the context of their Artificial General Intelligence (AGI) and Superintelligence (ASI) claims. Unlike other tests, this test does not rely on statistical compression methods (such as GZIP or LZW), which are more closely related to Shannon entropy than to Kolmogorov complexity. The test challenges aspects related to features of intelligence of fundamental nature such as synthesis and model creation in the context of inverse problems (generating new knowledge from observation). We argue that metrics based on model abstraction and optimal Bayesian inference for planning can provide a robust framework for testing intelligence, including natural intelligence (human and animal), narrow AI, AGI, and ASI. Our results show no clear evidence of LLM convergence towards a defined level of intelligence, particularly AGI or ASI. We found that LLM model versions tend to be fragile and incremental, as new versions may perform worse than older ones, with progress largely driven by the size of training data. The results were compared with a hybrid neurosymbolic approach that theoretically guarantees model convergence from optimal inference based on the principles of algorithmic probability and Kolmogorov complexity. The method outperforms LLMs in a proof-of-concept on short binary sequences. Our findings confirm suspicions regarding the fundamental limitations of LLMs, exposing them as systems optimised for the perception of mastery over human language. Progress among different LLM versions from the same developers was found to be inconsistent and limited, particularly in the absence of a solid symbolic counterpart.

We introduce Dynamic Information Sub-Selection (DISS), a novel framework of AI assistance designed to enhance the performance of black-box decision-makers by tailoring their information processing on a per-instance basis. Blackbox decision-makers (e.g., humans or real-time systems) often face challenges in processing all possible information at hand (e.g., due to cognitive biases or resource constraints), which can degrade decision efficacy. DISS addresses these challenges through policies that dynamically select the most effective features and options to forward to the black-box decision-maker for prediction. We develop a scalable frequentist data acquisition strategy and a decision-maker mimicking technique for enhanced budget efficiency. We explore several impactful applications of DISS, including biased decision-maker support, expert assignment optimization, large language model decision support, and interpretability. Empirical validation of our proposed DISS methodology shows superior performance to state-of-the-art methods across various applications.

The potential of artificial intelligence in medical education and assessment has been made evident by recent developments in natural language processing and artificial intelligence. Medical questions can now be successfully answered by artificial intelligence algorithms. It can help medical practitioners. This study evaluates the performance of three different artificial intelligence models in answering Turkish medical questions in the 2021 1st Term Medical Specialization Examination (MSE). MSE consists of a total of 240 questions across clinical (CMST) and basic (BMST) medical sciences. According to the results in CMST, it was concluded that Gemini correctly answered 82 questions, ChatGPT-4 answered 105 questions and ChatGPT-4o answered 117 questions. In BMST, Gemini and ChatGPT-4 answered 93 questions and ChatGPT-4o answered 107 questions correctly according to the answer key. ChatGPT-4o outperformed the candidate with the highest scores of 113 and 106 according to CMST and BMST respectively. This study highlights the importance of the potential of artificial intelligence in medical education and assessment. It demonstrates that advanced models can achieve high accuracy and contextual understanding, demonstrating their potential role in medical education and evaluation.

Autonomous Vehicles (AV) and Advanced Driver Assistant Systems (ADAS) prioritize safety over comfort. The intertwining factors of safety and comfort emerge as pivotal elements in ensuring the effectiveness of Autonomous Driving (AD). Users often experience discomfort when AV or ADAS drive the vehicle on their behalf. Providing a personalized human-like AD experience, tailored to match users' unique driving styles while adhering to safety prerequisites, presents a significant opportunity to boost the acceptance of AVs. This paper proposes a novel approach, Neural Driving Style Transfer (NDST), inspired by Neural Style Transfer (NST), to address this issue. NDST integrates a Personalized Block (PB) into the conventional Baseline Driving Model (BDM), allowing for the transfer of a user's unique driving style while adhering to safety parameters. The PB serves as a self-configuring system, learning and adapting to an individual's driving behavior without requiring modifications to the BDM. This approach enables the personalization of AV models, aligning the driving style more closely with user preferences while ensuring baseline safety critical actuation. Two contrasting driving styles (Style A and Style B) were used to validate the proposed NDST methodology, demonstrating its efficacy in transferring personal driving styles to the AV system. Our work highlights the potential of NDST to enhance user comfort in AVs by providing a personalized and familiar driving experience. The findings affirm the feasibility of integrating NDST into existing AV frameworks to bridge the gap between safety and individualized driving styles, promoting wider acceptance and improved user experiences.

Currently, there is a high demand for neural network-based image compression codecs. These codecs employ non-linear transforms to create compact bit representations and facilitate faster coding speeds on devices compared to the hand-crafted transforms used in classical frameworks. The scientific and industrial communities are highly interested in these properties, leading to the standardization effort of JPEG-AI. The JPEG-AI verification model has been released and is currently under development for standardization. Utilizing neural networks, it can outperform the classic codec VVC intra by over 10% BD-rate operating at base operation point. Researchers attribute this success to the flexible bit distribution in the spatial domain, in contrast to VVC intra's anchor that is generated with a constant quality point. However, our study reveals that VVC intra displays a more adaptable bit distribution structure through the implementation of various block sizes. As a result of our observations, we have proposed a spatial bit allocation method to optimize the JPEG-AI verification model's bit distribution and enhance the visual quality. Furthermore, by applying the VVC bit distribution strategy, the objective performance of JPEG-AI verification mode can be further improved, resulting in a maximum gain of 0.45 dB in PSNR-Y.

This study employs machine learning models to predict the failure of Peer-to-Peer (P2P) lending platforms, specifically in China. By employing the filter method and wrapper method with forward selection and backward elimination, we establish a rigorous and practical procedure that ensures the robustness and importance of variables in predicting platform failures. The research identifies a set of robust variables that consistently appear in the feature subsets across different selection methods and models, suggesting their reliability and relevance in predicting platform failures. The study highlights that reducing the number of variables in the feature subset leads to an increase in the false acceptance rate while the performance metrics remain stable, with an AUC value of approximately 0.96 and an F1 score of around 0.88. The findings of this research provide significant practical implications for regulatory authorities and investors operating in the Chinese P2P lending industry.