In standard autoregressive generation, an LLM predicts the next-token distribution, samples a discrete token, and then discards the distribution, passing only the sampled token as new input. To preserve this distribution's rich information, we propose Mixture of Inputs (MoI), a training-free method for autoregressive generation. After generating a token following the standard paradigm, we construct a new input that blends the generated discrete token with the previously discarded token distribution. Specifically, we employ a Bayesian estimation method that treats the token distribution as the prior, the sampled token as the observation, and replaces the conventional one-hot vector with the continuous posterior expectation as the new model input. MoI allows the model to maintain a richer internal representation throughout the generation process, resulting in improved text quality and reasoning capabilities. On mathematical reasoning, code generation, and PhD-level QA tasks, MoI consistently improves performance across multiple models including QwQ-32B, Nemotron-Super-49B, Gemma-3-27B, and DAPO-Qwen-32B, with no additional training and negligible computational overhead.

The matrix normal model, i.e., the family of Gaussian matrix-variate distributions whose covariance matrices are the Kronecker product of two lower dimensional factors, is frequently used to model matrix-variate data. The tensor normal model generalizes this family to Kronecker products of three or more factors. We study the estimation of the Kronecker factors of the covariance matrix in the matrix and tensor normal models. For the above models, we show that the maximum likelihood estimator (MLE) achieves nearly optimal nonasymptotic sample complexity and nearly tight error rates in the Fisher-Rao and Thompson metrics. In contrast to prior work, our results do not rely on the factors being well-conditioned or sparse, nor do we need to assume an accurate enough initial guess. For the matrix normal model, all our bounds are minimax optimal up to logarithmic factors, and for the tensor normal model our bounds for the largest factor and for overall covariance matrix are minimax optimal up to constant factors provided there are enough samples for any estimator to obtain constant Frobenius error. In the same regimes as our sample complexity bounds, we show that the flip-flop algorithm, a practical and widely used iterative procedure to compute the MLE, converges linearly with high probability. Our main technical insight is that, given enough samples, the negative log-likelihood function is strongly geodesically convex in the geometry on positive-definite matrices induced by the Fisher information metric. This strong convexity is determined by the expansion of certain random quantum channels.

Breast cancer is considered the most critical and frequently diagnosed cancer in women worldwide, leading to an increase in cancer-related mortality. Early and accurate detection is crucial as it can help mitigate possible threats while improving survival rates. In terms of prediction, conventional diagnostic methods are often limited by variability, cost, and, most importantly, risk of misdiagnosis. To address these challenges, machine learning (ML) has emerged as a powerful tool for computer-aided diagnosis, with feature selection playing a vital role in improving model performance and interpretability. This research study proposes an integrated framework that incorporates customized Particle Swarm Optimization (PSO) for feature selection. This framework has been evaluated on a comprehensive set of 29 different models, spanning classical classifiers, ensemble techniques, neural networks, probabilistic algorithms, and instance-based algorithms. To ensure interpretability and clinical relevance, the study uses cross-validation in conjunction with explainable AI methods. Experimental evaluation showed that the proposed approach achieved a superior score of 99.1\% across all performance metrics, including accuracy and precision, while effectively reducing dimensionality and providing transparent, model-agnostic explanations. The results highlight the potential of combining swarm intelligence with explainable ML for robust, trustworthy, and clinically meaningful breast cancer diagnosis.

Knowledge graph alignment is the task of matching equivalent entities (that is, instances and classes) and relations across two knowledge graphs. Most existing methods focus on pure entity-level alignment, computing the similarity of entities in some embedding space. They lack interpretable reasoning and need training data to work. In this paper, we propose FLORA, a simple yet effective method that (1) is unsupervised, i.e., does not require training data, (2) provides a holistic alignment for entities and relations iteratively, (3) is based on fuzzy logic and thus delivers interpretable results, (4) provably converges, (5) allows dangling entities, i.e., entities without a counterpart in the other KG, and (6) achieves state-of-the-art results on major benchmarks.

This paper presents the FuzzyDistillViT-MobileNet model, a novel approach for lung cancer (LC) classification, leveraging dynamic fuzzy logic-driven knowledge distillation (KD) to address uncertainty and complexity in disease diagnosis. Unlike traditional models that rely on static KD with fixed weights, our method dynamically adjusts the distillation weight using fuzzy logic, enabling the student model to focus on high-confidence regions while reducing attention to ambiguous areas. This dynamic adjustment improves the model ability to handle varying uncertainty levels across different regions of LC images. We employ the Vision Transformer (ViT-B32) as the instructor model, which effectively transfers knowledge to the student model, MobileNet, enhancing the student generalization capabilities. The training process is further optimized using a dynamic wait adjustment mechanism that adapts the training procedure for improved convergence and performance. To enhance image quality, we introduce pixel-level image fusion improvement techniques such as Gamma correction and Histogram Equalization. The processed images (Pix1 and Pix2) are fused using a wavelet-based fusion method to improve image resolution and feature preservation. This fusion method uses the wavedec2 function to standardize images to a 224x224 resolution, decompose them into multi-scale frequency components, and recursively average coefficients at each level for better feature representation. To address computational efficiency, Genetic Algorithm (GA) is used to select the most suitable pre-trained student model from a pool of 12 candidates, balancing model performance with computational cost. The model is evaluated on two datasets, including LC25000 histopathological images (99.16% accuracy) and IQOTH/NCCD CT-scan images (99.54% accuracy), demonstrating robustness across different imaging domains.

Federated Learning (FL) aims to train a global inference model from remotely distributed clients, gaining popularity due to its benefit of improving data privacy. However, traditional FL often faces challenges in practical applications, including model overfitting and divergent local models due to limited and non-IID data among clients. To address these issues, we introduce a novel Bayesian meta-learning approach called meta-variational dropout (MetaVD). MetaVD learns to predict client-dependent dropout rates via a shared hypernetwork, enabling effective model personalization of FL algorithms in limited non-IID data settings. We also emphasize the posterior adaptation view of meta-learning and the posterior aggregation view of Bayesian FL via the conditional dropout posterior. We conducted extensive experiments on various sparse and non-IID FL datasets. MetaVD demonstrated excellent classification accuracy and uncertainty calibration performance, especially for out-of-distribution (OOD) clients. MetaVD compresses the local model parameters needed for each client, mitigating model overfitting and reducing communication costs. Code is available at https://github.com/insujeon/MetaVD.

Although quantum systems are generally described by quantum state vectors, we show that in certain cases their measurement processes can be reformulated as probabilistic equations expressed in terms of probabilistic state vectors. These probabilistic representations can, in turn, be approximated by the neural network dynamics of the Tensor Brain (TB) model. The Tensor Brain is a recently proposed framework for modeling perception and memory in the brain, providing a biologically inspired mechanism for efficiently integrating generated symbolic representations into reasoning processes.

Dynamic treatment regimes are sequential decision rules that adapt treatment according to individual time-varying characteristics and outcomes to achieve optimal effects, with applications in precision medicine, personalized recommendations, and dynamic marketing. Estimating optimal dynamic treatment regimes via sequential randomized trials might face costly and ethical hurdles, often necessitating the use of historical observational data. In this work, we utilize proximal causal inference framework for learning optimal dynamic treatment regimes when the unconfoundedness assumption fails. Our contributions are four-fold: (i) we propose three nonparametric identification methods for optimal dynamic treatment regimes; (ii) we establish the semiparametric efficiency bound for the value function of a given regime; (iii) we propose a (K+1)-robust method for learning optimal dynamic treatment regimes, where K is the number of stages; (iv) as a by-product for marginal structural models, we establish identification and estimation of counterfactual means under a static regime. Numerical experiments validate the efficiency and multiple robustness of our proposed methods.

Masked diffusion models (MDM) are powerful generative models for discrete data that generate samples by progressively unmasking tokens in a sequence. Each token can take one of two states: masked or unmasked. We observe that token sequences often remain unchanged between consecutive sampling steps; consequently, the model repeatedly processes identical inputs, leading to redundant computation. To address this inefficiency, we propose the Partial masking scheme (Prime), which augments MDM by allowing tokens to take intermediate states interpolated between the masked and unmasked states. This design enables the model to make predictions based on partially observed token information, and facilitates a fine-grained denoising process. We derive a variational training objective and introduce a simple architectural design to accommodate intermediate-state inputs. Our method demonstrates superior performance across a diverse set of generative modeling tasks. On text data, it achieves a perplexity of 15.36 on OpenWebText, outperforming previous MDM (21.52), autoregressive models (17.54), and their hybrid variants (17.58), without relying on an autoregressive formulation. On image data, it attains competitive FID scores of 3.26 on CIFAR-10 and 6.98 on ImageNet-32, comparable to leading continuous generative models.

Learning to infer the conditional posterior model is a key step for robust meta-learning. This paper presents a new Bayesian meta-learning approach called Neural Variational Dropout Processes (NVDPs). NVDPs model the conditional posterior distribution based on a task-specific dropout; a low-rank product of Bernoulli experts meta-model is utilized for a memory-efficient mapping of dropout rates from a few observed contexts. It allows for a quick reconfiguration of a globally learned and shared neural network for new tasks in multi-task few-shot learning. In addition, NVDPs utilize a novel prior conditioned on the whole task data to optimize the conditional \textit{dropout} posterior in the amortized variational inference. Surprisingly, this enables the robust approximation of task-specific dropout rates that can deal with a wide range of functional ambiguities and uncertainties. We compared the proposed method with other meta-learning approaches in the few-shot learning tasks such as 1D stochastic regression, image inpainting, and classification. The results show the excellent performance of NVDPs.