Many security applications require unsupervised anomaly detection, as malicious data are extremely rare and often only unlabeled normal data are available for training (i.e., zero-positive). However, security operators are concerned about the high stakes of trusting black-box models due to their lack of interpretability. In this paper, we propose a post-hoc method to globally explain a black-box unsupervised anomaly detection model via rule extraction.First, we propose the concept of distribution decomposition rules that decompose the complex distribution of normal data into multiple compositional distributions. To find such rules, we design an unsupervised Interior Clustering Tree that incorporates the model prediction into the splitting criteria. Then, we propose the Compositional Boundary Exploration (CBE) algorithm to obtain the boundary inference rules that estimate the decision boundary of the original model on each compositional distribution. By merging these two types of rules into a rule set, we can present the inferential process of the unsupervised black-box model in a human-understandable way, and build a surrogate rule-based model for online deployment at the same time. We conduct comprehensive experiments on the explanation of four distinct unsupervised anomaly detection models on various real-world datasets. The evaluation shows that our method outperforms existing methods in terms of diverse metrics including fidelity, correctness and robustness.

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.

We present the Multi-value Rule Set (MRS) for interpretable classification with feature efficient presentations. Compared to rule sets built from single-value rules, MRS adopts a more generalized form of association rules that allows multiple values in a condition. Rules of this form are more concise than classical single-value rules in capturing and describing patterns in data. Our formulation also pursues a higher efficiency of feature utilization, which reduces possible cost in data collection and storage. We propose a Bayesian framework for formulating an MRS model and develop an efficient inference method for learning a maximum a posteriori, incorporating theoretically grounded bounds to iteratively reduce the search space and improve the search efficiency. Experiments on synthetic and real-world data demonstrate that MRS models have significantly smaller complexity and fewer features than baseline models while being competitive in predictive accuracy.

Learning rule-based systems plays a pivotal role in knowledge graph completion (KGC). Existing rule-based systems restrict the input of the system to structural knowledge only, which may omit some useful knowledge for reasoning, e.g., textual knowledge. In this paper, we propose a two-stage framework that imposes both structural and textual knowledge to learn rule-based systems. In the first stage, we compute a set of triples with confidence scores (called \emph{soft triples}) from a text corpus by distant supervision, where a textual entailment model with multi-instance learning is exploited to estimate whether a given triple is entailed by a set of sentences. In the second stage, these soft triples are used to learn a rule-based model for KGC.

Rule sets are highly interpretable logical models in which the predicates for decision are expressed in disjunctive normal form (DNF, OR-of-ANDs), or, equivalently, the overall model comprises an unordered collection of if-then decision rules. In this paper, we consider a submodular optimization based approach for learning rule sets. The learning problem is framed as a subset selection task in which a subset of all possible rules needs to be selected to form an accurate and interpretable rule set. We employ an objective function that exhibits submodularity and thus is amenable to submodular optimization techniques. To overcome the difficulty arose from dealing with the exponential-sized ground set of rules, the subproblem of searching a rule is casted as another subset selection task that asks for a subset of features. We show it is possible to write the induced objective function for the subproblem as a difference of two submodular (DS) functions to make it approximately solvable by DS optimization algorithms. Overall, the proposed approach is simple, scalable, and likely to be benefited from further research on submodular optimization. Experiments on real datasets demonstrate the effectiveness of our method.

Knowledge graph reasoning, which aims at predicting missing facts through reasoning with observed facts, is critical for many applications. Such a problem has been widely explored by traditional logic rule-based approaches and recent knowledge graph embedding methods. A principled logic rule-based approach is the Markov Logic Network (MLN), which is able to leverage domain knowledge with first-order logic and meanwhile handle uncertainty. However, the inference in MLNs is usually very difficult due to the complicated graph structures.

Mapping structural brain connectomes for living human brains typically requires expert analysis and rule-based models on diffusion-weighted magnetic resonance imaging. A data-driven approach, however, could overcome limitations in such rule-based approaches and improve precision mappings for individuals. In this work, we explore a framework that facilitates applying learning algorithms to automatically extract brain connectomes. Using a tensor encoding, we design an objective with a group-regularizer that prefers biologically plausible fascicle structure. We show that the objective is convex and has unique solutions, ensuring identifiable connectomes for an individual. We develop an efficient optimization strategy for this extremely high-dimensional sparse problem, by reducing the number of parameters using a greedy algorithm designed specifically for the problem. We show that this greedy algorithm significantly improves on a standard greedy algorithm, called Orthogonal Matching Pursuit. We conclude with an analysis of the solutions found by our method, showing we can accurately reconstruct the diffusion information while maintaining contiguous fascicles with smooth direction changes.

Recent years have seen the rise of statistical program learning based on neural models as an alternative to traditional rule-based systems for programming by example. Rule-based approaches offer correctness guarantees in an unsupervised way as they inherently capture logical rules, while neural models are more realistically scalable to raw, high-dimensional input, and provide resistance to noisy I/O specifications. We introduce PLANS (Program LeArning from Neurally inferred Specifications), a hybrid model for program synthesis from visual observations that gets the best of both worlds, relying on (i) a neural architecture trained to extract abstract, high-level information from each raw individual input (ii) a rule-based system using the extracted information as I/O specifications to synthesize a program capturing the different observations. In order to address the key challenge of making PLANS resistant to noise in the network's output, we introduce a dynamic filtering algorithm for I/O specifications based on selective classification techniques. We obtain state-of-the-art performance at program synthesis from diverse demonstration videos in the Karel and ViZDoom environments, while requiring no ground-truth program for training.

Many aspects of human reasoning, including language, require learning rules from very little data. Humans can do this, often learning systematic rules from very few examples, and combining these rules to form compositional rule-based systems. Current neural architectures, on the other hand, often fail to generalize in a compositional manner, especially when evaluated in ways that vary systematically from training. In this work, we present a neuro-symbolic model which learns entire rule systems from a small set of examples. Instead of directly predicting outputs from inputs, we train our model to induce the explicit system of rules governing a set of previously seen examples, drawing upon techniques from the neural program synthesis literature. Our rule-synthesis approach outperforms neural meta-learning techniques in three domains: an artificial instruction-learning domain used to evaluate human learning, the SCAN challenge datasets, and learning rule-based translations of number words into integers for a wide range of human languages.

Large language models exhibit intelligence without genuine epistemic understanding, exposing a key gap: the absence of epistemic architecture. This paper introduces the Structured Cognitive Loop (SCL) as an executable epistemological framework for emergent intelligence. Unlike traditional AI research asking "what is intelligence?" (ontological), SCL asks "under what conditions does cognition emerge?" (epistemological). Grounded in philosophy of mind and cognitive phenomenology, SCL bridges conceptual philosophy and implementable cognition. Drawing on process philosophy, enactive cognition, and extended mind theory, we define intelligence not as a property but as a performed process -- a continuous loop of judgment, memory, control, action, and regulation. SCL makes three contributions. First, it operationalizes philosophical insights into computationally interpretable structures, enabling "executable epistemology" -- philosophy as structural experiment. Second, it shows that functional separation within cognitive architecture yields more coherent and interpretable behavior than monolithic prompt based systems, supported by agent evaluations. Third, it redefines intelligence: not representational accuracy but the capacity to reconstruct its own epistemic state through intentional understanding. This framework impacts philosophy of mind, epistemology, and AI. For philosophy, it allows theories of cognition to be enacted and tested. For AI, it grounds behavior in epistemic structure rather than statistical regularity. For epistemology, it frames knowledge not as truth possession but as continuous reconstruction within a phenomenologically coherent loop. We situate SCL within debates on cognitive phenomenology, emergence, normativity, and intentionality, arguing that real progress requires not larger models but architectures that realize cognitive principles structurally.