Curved Boolean Logic (CBL) generalizes propositional logic by allowing local truth assignments that do not extend to a single global valuation, analogous to curvature in geometry. We give equivalent sheaf and exclusivity-graph semantics and a context-aware proof calculus that is conservative in the flat limit. We formalize CBL-SAT and basic complexity (NP-complete in general) and present operational operators (CBL-AC and CBL-CONS) that prune contradictions earlier on classical hardware. We model noise with iid, AR(1)-correlated, and adversarial bounded perturbations and provide permutation-based significance with Benjamini-Hochberg FDR control. A Colab-ready notebook (ancillary files) regenerates all figures and statistics. We position CBL relative to KCBS, CSW, and sheaf frameworks and outline links to SAT/CSP and robustness/adapter stability in large language models.

Concept Bottleneck Models (CBMs) provide interpretable prediction by introducing an intermediate Concept Bottleneck Layer (CBL), which encodes human-understandable concepts to explain models' decision.

We introduce the Concept Bottleneck Large Language Model (CB-LLM), a pioneering approach to creating inherently interpretable Large Language Models (LLMs). Unlike traditional black-box LLMs that rely on post-hoc interpretation methods with limited neuron function insights, CB-LLM sets a new standard with its built-in interpretability, scalability, and ability to provide clear, accurate explanations. We investigate two essential tasks in the NLP domain: text classification and text generation. In text classification, CB-LLM narrows the performance gap with traditional black-box models and provides clear interpretability. In text generation, we show how interpretable neurons in CB-LLM can be used for concept detection and steering text generation. Our CB-LLMs enable greater interaction between humans and LLMs across a variety of tasks -- a feature notably absent in existing LLMs. Large Language Models (LLMs) have become instrumental in advancing Natural Language Processing (NLP) tasks.

Background. Federated learning (FL) has gained wide popularity as a collaborative learning paradigm enabling collaborative AI in sensitive healthcare applications. Nevertheless, the practical implementation of FL presents technical and organizational challenges, as it generally requires complex communication infrastructures. In this context, consensus-based learning (CBL) may represent a promising collaborative learning alternative, thanks to the ability of combining local knowledge into a federated decision system, while potentially reducing deployment overhead. Methods. In this work we propose an extensive benchmark of the accuracy and cost-effectiveness of a panel of FL and CBL methods in a wide range of collaborative medical data analysis scenarios. The benchmark includes 7 different medical datasets, encompassing 3 machine learning tasks, 8 different data modalities, and multi-centric settings involving 3 to 23 clients. Findings. Our results reveal that CBL is a cost-effective alternative to FL. When compared across the panel of medical dataset in the considered benchmark, CBL methods provide equivalent accuracy to the one achieved by FL.Nonetheless, CBL significantly reduces training time and communication cost (resp. 15 fold and 60 fold decrease) (p < 0.05). Interpretation. This study opens a novel perspective on the deployment of collaborative AI in real-world applications, whereas the adoption of cost-effective methods is instrumental to achieve sustainability and democratisation of AI by alleviating the need for extensive computational resources.

We study a collaborative learning problem where $m$ agents estimate a vector $\mu\in\mathbb{R}^d$ by collecting samples from normal distributions, with each agent $i$ incurring a cost $c_{i,k} \in (0, \infty]$ to sample from the $k^{\text{th}}$ distribution $\mathcal{N}(\mu_k, \sigma^2)$. Instead of working on their own, agents can collect data that is cheap to them, and share it with others in exchange for data that is expensive or even inaccessible to them, thereby simultaneously reducing data collection costs and estimation error. However, when agents have different collection costs, we need to first decide how to fairly divide the work of data collection so as to benefit all agents. Moreover, in naive sharing protocols, strategic agents may under-collect and/or fabricate data, leading to socially undesirable outcomes. Our mechanism addresses these challenges by combining ideas from cooperative and non-cooperative game theory. We use ideas from axiomatic bargaining to divide the cost of data collection. Given such a solution, we develop a Nash incentive-compatible (NIC) mechanism to enforce truthful reporting. We achieve a $\mathcal{O}(\sqrt{m})$ approximation to the minimum social penalty (sum of agent estimation errors and data collection costs) in the worst case, and a $\mathcal{O}(1)$ approximation under favorable conditions. We complement this with a hardness result, showing that $\Omega(\sqrt{m})$ is unavoidable in any NIC mechanism.

Concept Bottleneck Models (CBMs) provide interpretable prediction by introducing an intermediate Concept Bottleneck Layer (CBL), which encodes human-understandable concepts to explain models' decision. Recent works proposed to utilize Large Language Models (LLMs) and pre-trained Vision-Language Models (VLMs) to automate the training of CBMs, making it more scalable and automated. However, existing approaches still fall short in two aspects: First, the concepts predicted by CBL often mismatch the input image, raising doubts about the faithfulness of interpretation. Second, it has been shown that concept values encode unintended information: even a set of random concepts could achieve comparable test accuracy to state-of-the-art CBMs. To address these critical limitations, in this work, we propose a novel framework called Vision-Language-Guided Concept Bottleneck Model (VLG-CBM) to enable faithful interpretability with the benefits of boosted performance. Our method leverages off-the-shelf open-domain grounded object detectors to provide visually grounded concept annotation, which largely enhances the faithfulness of concept prediction while further improving the model performance. In addition, we propose a new metric called Number of Effective Concepts (NEC) to control the information leakage and provide better interpretability. Extensive evaluations across five standard benchmarks show that our method, VLG-CBM, outperforms existing methods by at least 4.27% and up to 51.09% on accuracy at NEC=5, and by at least 0.45% and up to 29.78% on average accuracy across different NECs, while preserves both faithfulness and interpretability of the learned concepts as demonstrated in extensive experiments.

We propose a novel architecture and method of explainable classification with Concept Bottleneck Models (CBMs). While SOTA approaches to Image Classification task work as a black box, there is a growing demand for models that would provide interpreted results. Such a models often learn to predict the distribution over class labels using additional description of this target instances, called concepts. However, existing Bottleneck methods have a number of limitations: their accuracy is lower than that of a standard model and CBMs require an additional set of concepts to leverage. We provide a framework for creating Concept Bottleneck Model from pre-trained multi-modal encoder and new CLIP-like architectures. By introducing a new type of layers known as Concept Bottleneck Layers, we outline three methods for training them: with $\ell_1$-loss, contrastive loss and loss function based on Gumbel-Softmax distribution (Sparse-CBM), while final FC layer is still trained with Cross-Entropy. We show a significant increase in accuracy using sparse hidden layers in CLIP-based bottleneck models. Which means that sparse representation of concepts activation vector is meaningful in Concept Bottleneck Models. Moreover, with our Concept Matrix Search algorithm we can improve CLIP predictions on complex datasets without any additional training or fine-tuning. The code is available at: https://github.com/Andron00e/SparseCBM.

Turbulence parametrizations will remain a necessary building block in kilometer-scale Earth system models. In convective boundary layers, where the mean vertical gradients of conserved properties such as potential temperature and moisture are approximately zero, the standard ansatz which relates turbulent fluxes to mean vertical gradients via an eddy diffusivity has to be extended by mass flux parametrizations for the typically asymmetric up- and downdrafts in the atmospheric boundary layer. In this work, we present a parametrization for a dry convective boundary layer based on a generative adversarial network. The model incorporates the physics of self-similar layer growth following from the classical mixed layer theory by Deardorff. This enhances the training data base of the generative machine learning algorithm and thus significantly improves the predicted statistics of the synthetically generated turbulence fields at different heights inside the boundary layer. The algorithm training is based on fully three-dimensional direct numerical simulation data. Differently to stochastic parametrizations, our model is able to predict the highly non-Gaussian transient statistics of buoyancy fluctuations, vertical velocity, and buoyancy flux at different heights thus also capturing the fastest thermals penetrating into the stabilized top region. The results of our generative algorithm agree with standard two-equation or multi-plume stochastic mass-flux schemes. The present parametrization provides additionally the granule-type horizontal organization of the turbulent convection which cannot be obtained in any of the other model closures. Our work paves the way to efficient data-driven convective parametrizations in other natural flows, such as moist convection, upper ocean mixing, or convection in stellar interiors.

In this study, we consider classification problems based on neural networks in a data-imbalanced environment. Learning from an imbalanced dataset is one of the most important and practical problems in the field of machine learning. A weighted loss function (WLF) based on a cost-sensitive approach is a well-known and effective method for imbalanced datasets. We consider a combination of WLF and batch normalization (BN) in this study. BN is considered as a powerful standard technique in the recent developments in deep learning. A simple combination of both methods leads to a size-inconsistency problem due to a mismatch between the interpretations of the effective size of the dataset in both methods. We propose a simple modification to BN, called weighted batch normalization (WBN), to correct the size-mismatch. The idea of WBN is simple and natural. Using numerical experiments, we demonstrate that our method is effective in a data-imbalanced environment.