Entity alignment (EA) aims to merge two knowledge graphs (KGs) by identifying equivalent entity pairs. Existing methods can be categorized into symbolic and neural models. Symbolic models, while precise, struggle with substructure heterogeneity and sparsity, whereas neural models, although effective, generally lack interpretability and cannot handle uncertainty. We propose NeuSymEA, a unified neuro-symbolic reasoning framework that combines the strengths of both methods to fully exploit the cross-KG structural pattern for robust entity alignment. NeuSymEA models the joint probability of all possible pairs' truth scores in a Markov random field, regulated by a set of rules, and optimizes it with the variational EM algorithm.

Offline Learning from Observations (LfO) focuses on enabling agents to imitate expert behavior using datasets that contain only expert state trajectories and separate transition data with suboptimal actions. This setting is both practical and critical in real-world scenarios where direct environment interaction or access to expert action labels is costly, risky, or infeasible. Most existing LfO methods attempt to solve this problem through state or state-action occupancy matching. They typically rely on pretraining a discriminator to differentiate between expert and non-expert states, which could introduce errors and instability--especially when the discriminator is poorly trained. While recent discriminator-free methods have emerged, they generally require substantially more data, limiting their practicality in low-data regimes.

Deep learning models for time series classification (TSC) have achieved impressive performance, but explaining their decisions remains a significant challenge. Existing post-hoc explanation methods typically operate solely in the time domain and from a single-view perspective, limiting both faithfulness and robustness. In this work, we propose MIX (Multi-view Time-Frequency Interactive EXplanation Framework), a novel framework that helps to explain deep learning models in a multi-view setting by leveraging multi-resolution, time-frequency views constructed using the Haar Discrete Wavelet Transform (DWT). MIX introduces an interactive cross-view refinement scheme, where explanation's information from one view is propagated across views to enhance overall interpretability. To align with user-preferred perspectives, we propose a greedy selection strategy that traverses the multi-view space to identify the most informative features. Additionally, we present OSIGV, a user-aligned segment-level attribution mechanism based on overlapping windows for each view, and introduce keystone-first IG, a method that refines explanations in each view using additional information from another view. Extensive experiments across multiple TSC benchmarks and model architectures demonstrate that MIX significantly outperforms state-of-the-art (SOTA) methods in terms of explanation faithfulness and robustness.

Biological sensorimotor systems process information through spatially organized, functionally specialized modules. A canonical example is the rodent barrel cortex, in which each vibrissa (whisker) projects to a dedicated cortical column, forming a precise somatotopic map. This anatomical organization stands in stark contrast to the architectures of most artificial neural networks, which are typically monolithic or rely on globally routed mixture-of-experts (MoE) mechanisms. In this work, we introduce a brain-inspired modular architecture that treats the barrel cortex as a biologically constrained instantiation of an expert system. Each module (or "expert") corresponds to a cortical column composed of multiple neuron subtypes spanning vertical cortical layers.

Considering local and bounded-size neighborhoods of knowledge bases renders logical inference and learning tractable, mitigates the problem of overfitting, and facilitates weight sharing.

Neural Information Processing Systems http://nips.cc/

We introduce deep neural networks for end-to-end differentiable theorem proving that operate on dense vector representations of symbols. These neural networks are recursively constructed by following the backward chaining algorithm as used in Prolog. Specifically, we replace symbolic unification with a differentiable computation on vector representations of symbols using a radial basis function kernel, thereby combining symbolic reasoning with learning subsymbolic vector representations. The resulting neural network can be trained to infer facts from a given incomplete knowledge base using gradient descent. By doing so, it learns to (i) place representations of similar symbols in close proximity in a vector space, (ii) make use of such similarities to prove facts, (iii) induce logical rules, and (iv) it can use provided and induced logical rules for complex multi-hop reasoning. On four benchmark knowledge bases we demonstrate that this architecture outperforms ComplEx, a state-of-the-art neural link prediction model, while at the same time inducing interpretable function-free first-order logic rules.

This paper considers the learning of Boolean rules in either disjunctive normal form (DNF, OR-of-ANDs, equivalent to decision rule sets) or conjunctive normal form (CNF, AND-of-ORs) as an interpretable model for classification. An integer program is formulated to optimally trade classification accuracy for rule simplicity. Column generation (CG) is used to efficiently search over an exponential number of candidate clauses (conjunctions or disjunctions) without the need for heuristic rule mining. This approach also bounds the gap between the selected rule set and the best possible rule set on the training data. To handle large datasets, we propose an approximate CG algorithm using randomization. Compared to three recently proposed alternatives, the CG algorithm dominates the accuracy-simplicity trade-off in 8 out of 16 datasets. When maximized for accuracy, CG is competitive with rule learners designed for this purpose, sometimes finding significantly simpler solutions that are no less accurate.