Density Functional Theory (DFT) is a widely used computational method for estimating the energy and behavior of molecules. Machine Learning Interatomic Potentials (MLIPs) are models trained to approximate DFT-level energies and forces at dramatically lower computational cost. Many modern MLIPs rely on a scalar regression formulation; given information about a molecule, they predict a single energy value and corresponding forces while minimizing absolute error with DFT's calculations. In this work, we explore a multi-class classification formulation that predicts a categorical distribution over energy/force values, providing richer supervision through multiple targets. Most importantly, this approach offers a principled way to quantify model uncertainty. In particular, our method predicts a histogram of the energy/force distribution, converts scalar targets into histograms, and trains the model using cross-entropy loss. Our results demonstrate that this categorical formulation can achieve absolute error performance comparable to regression baselines. Furthermore, this representation enables the quantification of epistemic uncertainty through the entropy of the predicted distribution, offering a measure of model confidence absent in scalar regression approaches.

Predictive maintenance in manufacturing environments presents a challenging optimization problem characterized by extreme cost asymmetry, where missed failures incur costs roughly fifty times higher than false alarms. Conventional machine learning approaches typically optimize statistical accuracy metrics that do not reflect this operational reality and cannot reliably distinguish causal relationships from spurious correlations. This study evaluates eight predictive models, ranging from baseline statistical approaches to formal causal inference methods, on a dataset of 10,000 CNC machines with a 3.3 percent failure prevalence. The formal causal inference model (L5) achieved estimated annual cost savings of 1.16 million USD (a 70.2 percent reduction), outperforming the best correlation-based decision tree model (L3) by approximately 80,000 USD per year. The causal model matched the highest observed recall (87.9 percent) while reducing false alarms by 97 percent (from 165 to 5) and attained a precision of 92.1 percent, with a train-test performance gap of only 2.6 percentage points. These results indicate that causal AI methods, when combined with domain knowledge, can yield superior financial outcomes and more interpretable predictions compared to correlation-based approaches in predictive maintenance applications.

Algorithmic reasoning -- the ability to perform step-by-step logical inference -- has become a core benchmark for evaluating reasoning in graph neural networks (GNNs) and large language models (LLMs). Ideally, one would like to design a single model capable of performing well on multiple algorithmic reasoning tasks simultaneously. However, this is challenging when the execution steps of algorithms differ from one another, causing negative interference when they are trained together. We propose branching neural networks, a principled architecture for multitask algorithmic reasoning. Searching for the optimal $k$-ary tree with $L$ layers over $n$ algorithmic tasks is combinatorial, requiring exploration of up to $k^{nL}$ possible structures. We develop AutoBRANE, an efficient algorithm that reduces this search to $O(nL)$ time by solving a convex relaxation at each layer to approximate an optimal task partition. The method clusters tasks using gradient-based affinity scores and can be used on top of any base model, including GNNs and LLMs. We validate AutoBRANE on a broad suite of graph-algorithmic and text-based reasoning benchmarks. We show that gradient features estimate true task performance within 5% error across four GNNs and four LLMs (up to 34B parameters). On the CLRS benchmark, it outperforms the strongest single multitask GNN by 3.7% and the best baseline by 1.2%, while reducing runtime by 48% and memory usage by 26%. The learned branching structures reveal an intuitively reasonable hierarchical clustering of related algorithms. On three text-based graph reasoning benchmarks, AutoBRANE improves over the best non-branching multitask baseline by 3.2%. Finally, on a large graph dataset with 21M edges and 500 tasks, AutoBRANE achieves a 28% accuracy gain over existing multitask and branching architectures, along with a 4.5$\times$ reduction in runtime.

Federated learning must address heterogeneity, strict communication and computation limits, and privacy while ensuring performance. We propose an operator-theoretic framework that maps the $L^2$-optimal solution into a reproducing kernel Hilbert space (RKHS) via a forward operator, approximates it using available data, and maps back with the inverse operator, yielding a gradient-free scheme. Finite-sample bounds are derived using concentration inequalities over operator norms, and the framework identifies a data-dependent hypothesis space with guarantees on risk, error, robustness, and approximation. Within this space we design efficient kernel machines leveraging the space folding property of Kernel Affine Hull Machines. Clients transfer knowledge via a scalar space folding measure, reducing communication and enabling a simple differentially private protocol: summaries are computed from noise-perturbed data matrices in one step, avoiding per-round clipping and privacy accounting. The induced global rule requires only integer minimum and equality-comparison operations per test point, making it compatible with fully homomorphic encryption (FHE). Across four benchmarks, the gradient-free FL method with fixed encoder embeddings matches or outperforms strong gradient-based fine-tuning, with gains up to 23.7 points. In differentially private experiments, kernel smoothing mitigates accuracy loss in high-privacy regimes. The global rule admits an FHE realization using $Q \times C$ encrypted minimum and $C$ equality-comparison operations per test point, with operation-level benchmarks showing practical latencies. Overall, the framework provides provable guarantees with low communication, supports private knowledge transfer via scalar summaries, and yields an FHE-compatible prediction rule offering a mathematically grounded alternative to gradient-based federated learning under heterogeneity.

Organisms constantly pivot between tasks such as evading predators, foraging, traversing rugged terrain, and socializing, often within milliseconds. Remarkably, they preserve knowledge of once-learned environments sans catastrophic forgetting, a phenomenon neuroscientists hypothesize, is due to a singular neural circuitry dynamically overlayed by neuromodulatory agents such as dopamine and acetylcholine. In parallel, deep learning research addresses analogous challenges via domain generalization (DG) and continual learning (CL), yet these methods remain siloed, despite the brains ability to perform them seamlessly. In particular, prior work has not explored architectures involving associative memories (AMs), which are an integral part of biological systems, to jointly address these tasks. We propose Memory-Integrated Reconfigurable Adapters (MIRA), a unified framework that integrates Hopfield-style associative memory modules atop a shared backbone. Associative memory keys are learned post-hoc to index and retrieve an affine combination of stored adapter updates for any given task or domain on a per-sample basis. By varying only the task-specific objectives, we demonstrate that MIRA seamlessly accommodates domain shifts and sequential task exposures under one roof. Empirical evaluations on standard benchmarks confirm that our AM-augmented architecture significantly enhances adaptability and retention: in DG, MIRA achieves SoTA out-of-distribution accuracy, and in incremental learning settings, it outperforms architectures explicitly designed to handle catastrophic forgetting using generic CL algorithms. By unifying adapter-based modulation with biologically inspired associative memory, MIRA delivers rapid task switching and enduring knowledge retention in a single extensible architecture, charting a path toward more versatile and memory-augmented AI systems.

Embedding spaces are fundamental to modern AI, translating raw data into high-dimensional vectors that encode rich semantic relationships. Y et, their internal structures remain opaque, with existing approaches often sacrificing semantic coherence for structural regularity or incurring high computational overhead to improve interpretability. To address these challenges, we introduce the Semantic Field Subspace (SFS), a geometry-preserving, context-aware representation that captures local semantic neighborhoods within the embedding space. We also propose SAF ARI (SemAntic Field subspAce deteRmInation), an unsupervised, modality-agnostic algorithm that uncovers hierarchical semantic structures using a novel metric called Semantic Shift, which quantifies how semantics evolve as SFSes evolve. To ensure scalability, we develop an efficient approximation of Semantic Shift that replaces costly SVD computations, achieving a 15 30 speedup with average errors below 0.01. Extensive evaluations across six real-world text and image datasets show that SFSes outperform standard classifiers not only in classification but also in nuanced tasks such as political bias detection, while SAF ARI consistently reveals interpretable and generalizable semantic hierarchies. This work presents a unified framework for structuring, analyzing, and scaling semantic understanding in embedding spaces.

Clustering non-independent and identically distributed (non-IID) data under local differential privacy (LDP) in federated settings presents a critical challenge: preserving privacy while maintaining accuracy without iterative communication. Existing one-shot methods rely on unstable pairwise centroid distances or neighborhood rankings, degrading severely under strong LDP noise and data heterogeneity. We present Gravitational Federated Clustering (GFC), a novel approach to privacy-preserving federated clustering that overcomes the limitations of distance-based methods under varying LDP. Addressing the critical challenge of clustering non-IID data with diverse privacy guarantees, GFC transforms privatized client centroids into a global gravitational potential field where true cluster centers emerge as topologically persistent singularities. Our framework introduces two key innovations: (1) a client-side compactness-aware perturbation mechanism that encodes local cluster geometry as "mass" values, and (2) a server-side topological aggregation phase that extracts stable centroids through persistent homology analysis of the potential field's superlevel sets. Theoretically, we establish a closed-form bound between the privacy budget $ε$ and centroid estimation error, proving the potential field's Lipschitz smoothing properties exponentially suppress noise in high-density regions. Empirically, GFC outperforms state-of-the-art methods on ten benchmarks, especially under strong LDP constraints ($ε< 1$), while maintaining comparable performance at lower privacy budgets. By reformulating federated clustering as a topological persistence problem in a synthetic physics-inspired space, GFC achieves unprecedented privacy-accuracy trade-offs without iterative communication, providing a new perspective for privacy-preserving distributed learning.

Federated learning (FL) enables collaborative training over distributed multimedia data but suffers acutely from statistical heterogeneity and communication constraints, especially when clients deploy large models. Classic parameter-averaging methods such as FedAvg transmit full model weights and can diverge under nonindependent and identically distributed (non-IID) data. We propose KTA v2, a prediction-space knowledge trading market for FL. Each round, clients locally train on their private data, then share only logits on a small public reference set. The server constructs a client-client similarity graph in prediction space, combines it with reference-set accuracy to form per-client teacher ensembles, and sends back personalized soft targets for a second-stage distillation update. This two-stage procedure can be interpreted as approximate block-coordinate descent on a unified objective with prediction-space regularization. Experiments on FEMNIST, CIFAR-10 and AG News show that, under comparable or much lower communication budgets, KTA v2 consistently outperforms a local-only baseline and strong parameter-based methods (FedAvg, FedProx), and substantially improves over a FedMD-style global teacher. On CIFAR-10 with ResNet-18, KTA v2 reaches 57.7% test accuracy using approximately 1/1100 of FedAvg's communication, while on AG News it attains 89.3% accuracy with approximately 1/300 of FedAvg's traffic.

Iteration 1 uses a broad, data-driven prior; subsequent iterations exploit memory to execute focused, theory-driven repairs, steadily converging on a causally defensible graph. This iterative loop is made explicit in Algorithm 1, while the statistics used during Evaluate are summarised in Table 2 and computed procedurally in Algorithm 2. 3.1. Causal Assumptions Every proposed DAG must explicitly address the four core assumptions required for causal identification. First, regarding unobserved confounding, the agent must state which latent factors remain and how observed variables serve as proxies for these unobserved influences. Second, the positivity assumption requires that the agent argue no sub-population is locked into or out of the treatment, often demonstrated by reporting overlap in the propensity-score distribution across treatment groups.

Quantifying uncertainty in deep regression models is important both for understanding the confidence of the model and for safe decision-making in high-risk domains. Existing approaches that yield prediction intervals overlook distributional information, neglecting the effect of multimodal or asymmetric distributions on decision-making. Similarly, full or approximated Bayesian methods, while yielding the predictive posterior density, demand major modifications to the model architecture and retraining. We introduce MCNF, a novel post hoc uncertainty quantification method that produces both prediction intervals and the full conditioned predictive distribution. MCNF operates on top of the underlying trained predictive model; thus, no predictive model retraining is needed. We provide experimental evidence that the MCNF-based uncertainty estimate is well calibrated, is competitive with state-of-the-art uncertainty quantification methods, and provides richer information for downstream decision-making tasks.