The growing presence of mobile and IoT devices has led to massive decentralized and evolving data, driving the rise of Federated Learning (FL) to enable collaborative training without data sharing. However, traditional FL assumes static data distributions, which is unrealistic for dynamic real-world environments. To address this challenge, Federated Class-Incremental Learning (FCIL) has emerged as a promising framework that enables flexible adaptation to newly introduced classes over time. Existing FCIL methods typically integrate old knowledge preservation into local client training. However, these methods cannot avoid spatial-temporal client drift caused by data heterogeneity and often incur significant computational and communication overhead, limiting practical deployment. To address these challenges simultaneously, we propose a novel approach, Spatial-Temporal Statistics Aggregation (STSA), which provides a unified framework to aggregate feature statistics both spatially (across clients) and temporally (across stages). The aggregated feature statistics are unaffected by data heterogeneity and can be used to update the classifier in closed form at each stage. Additionally, we introduce STSA-E, a communication-efficient variant that enables the server to approximate global second-order feature statistics using first-order statistics uploaded from clients. Theoretical analysis shows that it achieves similar performance to STSA with much lower communication overhead. Extensive experiments on three widely used FCIL datasets, with varying degrees of data heterogeneity, show that our method outperforms state-of-the-art FCIL methods in terms of performance, flexibility, and both communication and computation efficiency. The code is available at https://github.com/Yuqin-G/STSA.
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Deep neural networks often rely on spurious correlations, i.e., superficial associations between non-causal features and prediction targets. While yielding high overall accuracy during training, such reliance degrades generalization on minority groups where these correlations break down. Existing methods mitigate this issue by using external group annotations or auxiliary deterministic models, but group annotations are costly to obtain and deterministic auxiliaries may fail to capture the full spectrum of biases learned by the model. We propose Evidential Alignment, a framework that leverages uncertainty quantification to identify and suppress spurious correlations without requiring group annotations. By transforming a biased ERM model from first-order to second-order risk minimization with a Dirichlet distribution and applying an evidential calibration step that reweighs samples by their epistemic uncertainty, Evidential Alignment debiases the model while preserving core features. We provide theoretical guarantees and demonstrate strong worst-group accuracy across diverse architectures and modalities.
Riemannian optimization has attracted increasing attention recently as it is related to a variety of machine learning problems, including principal component analysis, dictionary learning, and mixture modeling. To tackle modern large-scale machine learning tasks, distributed learning is usually considered as an effective solution that trains a global model over multiple worker nodes collaboratively to enhance the computational power. Centralized learning and decentralized learning are two types of distributed learning. Centralized learning employs a central parameter server to coordinate the training process while in decentralized learning, each worker only communicates with its peer neighbors. In this paper, we propose accelerated distributed Riemannian stochastic gradient descent algorithms with random shuffling in the cases of both centralized and decentralized learning. We improve the stochastic first-order oracle complexity of the Riemannian SGD from to where is the size of training data. We conduct an experiment of the leading eigenvector problem under the condition of centralized learning and decentralized learning to validate the performance of our methods.
Dynamic systems in AI are often complex and heterogeneous, so that an internal specification is not accessible and hence verification techniques like model checking are not applicable. Monitoring is in such cases an attractive alternative, as it deals with the observation of desirable properties along traces generated by an unknown dynamic system. In this work, we consider anticipatory monitoring of linear-time properties enriched with an arbitrary SMT theory over finite traces (data-LTLf). Anticipatory monitoring in this setting is a highly challenging problem and undecidable in general, as the monitoring state depends on both the trace prefix seen so far and all its possible finite continuations. Under reasonable assumptions on the background theory, we present and formally prove the correctness of a novel foundational framework for monitoring data-LTLf properties. The framework combines automata-theoretic methods to handle the temporal aspects of reasoning with automated reasoning techniques to address the first-order dimension. Moreover, we identify for the first time decidable fragments of this monitoring problem that are practically relevant as they combine linear arithmetic with uninterpreted functions, which covers e.g. data-aware business processes and dynamic systems operating over a database. Feasibility is witnessed by a prototype implementation and preliminary evaluation.
Skeleton-based human activity recognition (HAR) has achieved strong empirical performance, yet most existing models remain black boxes and difficult to interpret. In this work, we introduce a neurosymbolic formulation of skeleton-based HAR that reframes action recognition as concept-driven first-order logical reasoning over motion primitives. Our framework bridges representation learning and symbolic inference by grounding first-order logic predicates in learnable spatial and temporal motion concepts. Specifically, we employ a standard spatio-temporal skeleton encoder to extract latent motion representations, which are then mapped to interpretable concept predicates via a spatio-temporal concept decoder that explicitly separates pose-centric and dynamics-centric abstractions. These concept predicates are composed through differentiable first-order logic layers, enabling the model to learn human-readable logical rules that govern action semantics. To impose semantic structure on the learned concepts, we align skeleton representations with LLM-derived descriptions of atomic motion primitives, establishing a shared conceptual space for perception and reasoning. Extensive experiments on NTU RGB+D 60/120 and NW-UCLA demonstrate that our approach achieves competitive recognition performance while providing explicit, interpretable explanations grounded in logical structure. Our results highlight neurosymbolic reasoning as an effective paradigm for interpretable spatio-temporal action understanding.
Progression, the task of updating a knowledge base to reflect action effects, generally requires second-order logic. Identifying first-order special cases, by restricting either the knowledge base or action effects, has long been a central topic in reasoning about actions. It is known that local-effect, normal, and acyclic actions, three increasingly expressive classes, admit first-order progression. However, a systematic analysis of the size of such progressions, crucial for practical applications, has been missing. In this paper, using the framework of Situation Calculus, we show that under reasonable assumptions, first-order progression for these action classes grows only polynomially. Moreover, we show that when the KB belongs to decidable fragments such as two-variable first-order logic or universal theories with constants, the progression remains within the same fragment, ensuring decidability and practical applicability.
Multi-channel data fusion is essential for capturing comprehensive representations in complex systems. While graph convolutional networks have demonstrated remarkable efficacy, existing fusion paradigms primarily rely on discrete architectures governed by first-order propagation. These models are typically confined to discrete message-passing mechanisms, which makes it difficult to characterize the continuous evolution of underlying system dynamics. To address these limitations, we propose a multi-channel Graph Continuous Network (mcGCN), a novel framework for multi-channel data fusion. By formulating the information propagation as a second-order partial differential equation on graphs, mcGCN transitions from discrete layer-wise updates to a continuous dynamical system. Specifically, mcGCN integrates a multi-channel encoding module with continuous feature dynamics to initialize and evolve the latent node representations over static graph topologies. This physical analogy enables more robust information flow and effectively mitigates the performance degradation typically associated with deep graph architectures. Extensive experiments on diverse benchmark datasets demonstrate that our method outperforms state-of-the-art baselines, validating its effectiveness and robustness.
In emerging clinical applications such as ultrasound-based burn assessment, the lack of domain-specific data presents a significant challenge for developing robust AI systems. Vision-language models (VLMs) have shown strong performance in general computer vision tasks, yet their application to medical imaging remains limited, particularly due to insufficient reasoning capabilities and the scarcity of high-quality training data. We introduce AURA (Automated Unified Reasoning for Burn Assessment), a multi-modal approach that integrates pre-trained VLMs with symbolic first-order logic (FOL) reasoning to improve diagnostic accuracy and interpretability in this data-limited setting. For this study, we collected real-patient data over a one-year period at a U.S. burn center, performing all experiments in a real clinical setting to ensure practical relevance. The dataset includes both conventional B-Mode ultrasound and Tissue Doppler Imaging (TDI), with TDI introduced here for the first time in burn assessment, underscoring the emerging nature of this work. Beyond burn severity classification, we assess the system’s ability to produce expert-level surgical insight directly from imaging data. On the retrospective dataset, it achieves up to 93% accuracy in surgical classification and 87% in fine-grained burn depth prediction, comparable to expert-informed predictions and substantially exceeding the 70% accuracy of traditional visual inspection by human experts. These results, obtained from a novel multi-modal dataset collected in a real clinical burn center setting, highlight the potential of this approach to improve decision-making in burn care. To further support future deployment, we demonstrate a prototype integration with an Electronic Medical Record (EMR) system that aligns with clinical workflows and supports scalable, real-world implementation.
Black-box algorithms aim to optimize functions without access to their analytical structure or gradient information, making them essential when gradients are unavailable or computationally expensive to obtain. Traditional methods for black-box optimization (BBO) primarily utilize non-parametric models, but these approaches often struggle to scale effectively in large input spaces. Conversely, parametric approaches, which rely on neural estimators and gradient signals via backpropagation, frequently encounter substantial gradient estimation errors, limiting their reliability. Explicit Gradient Learning (EGL), a recent advancement, directly learns gradients using a first-order Taylor approximation and has demonstrated superior performance compared to both parametric and non-parametric methods. However, EGL inherently remains local and myopic, often faltering on highly non-convex optimization landscapes. In this work, we address this limitation by integrating global statistical insights from the evolutionary algorithm CMA-ES into the gradient learning framework, effectively biasing gradient estimates towards regions with higher optimization potential. Moreover, we enhance the gradient learning process by estimating the Hessian matrix, allowing us to correct the second-order residual of the Taylor series approximation. Our proposed algorithm, EvoGrad2 (Evolutionary Gradient Learning with second-order approximation), achieves state-of-the-art results on the synthetic COCO test suite, exhibiting significant advantages in high-dimensional optimization problems. We further demonstrate EvoGrad2's effectiveness on challenging real-world machine learning tasks, including adversarial training and code generation, highlighting its ability to produce more robust, high-quality solutions. Our results underscore EvoGrad2's potential as a powerful tool for researchers and practitioners facing complex, high-dimensional, and non-linear optimization problems.
First-order relational languages have been used in MDP planning and reinforcement learning (RL) for two main purposes: specifying MDPs in compact form, and representing and learning policies that are general and not tied to specific instances or state spaces. In this work, we instead consider the use of first-order languages in goal-conditioned RL and generalized planning. The question is how to learn goal-conditioned and general policies when the training instances are large and the goal cannot be reached by random exploration alone. The technique of Hindsight Experience Replay (HER) provides an answer to this question: it relabels unsuccessful trajectories as successful ones by replacing the original goal with one that was actually achieved. If the target policy must generalize across states and goals, trajectories that do not reach the original goal states can enable more data- and time-efficient learning. In this work, we show that further performance gains can be achieved when states and goals are represented by sets of atoms. We consider three versions: goals as full states, goals as subsets of the original goals, and goals as lifted versions of these subgoals. The result is that the latter two successfully learn general policies on large planning instances with sparse rewards by automatically creating a curriculum of easier goals of increasing complexity. The experiments illustrate the computational gains of these versions, their limitations, and opportunities for addressing them.
Constrained and Robust Policy Synthesis with Satisfiability-Modulo-Probabilistic-Model-Checking
PDF ↗The ability to compute reward-optimal policies for given and known finite Markov decision processes (MDPs) underpins a variety of applications across planning, controller synthesis, and verification. However, we often want policies (1) to be robust, i.e., they perform well on perturbations of the MDP and (2) to satisfy additional structural constraints regarding, e.g., their representation or implementation cost. Computing such robust and constrained policies is indeed computationally more challenging. This paper contributes the first approach to effectively compute robust policies subject to arbitrary structural constraints using a flexible and efficient framework. We achieve flexibility by allowing to express our constraints in a first-order theory over a set of MDPs, while the root for our efficiency lies in the tight integration of satisfiability solvers to handle the combinatorial nature of the problem and probabilistic model checking algorithms to handle the analysis of MDPs. Experiments on a few hundred benchmarks demonstrate the feasibility for constrained and robust policy synthesis and the competitiveness with state-of-the-art methods for various fragments of the problem.
Generalised planning (GP) refers to the task of synthesising programs that solve families of related planning problems. We introduce a novel, yet simple method for GP: given a set of training problems, for each problem, compute an optimal plan for each goal atom in some order, perform goal regression on the resulting plans, and lift the corresponding outputs to obtain a set of first-order Condition → Actions rules. The rules collectively constitute a generalised plan that can be executed as is or alternatively be used to prune the planning search space. We formalise and prove the conditions under which our method is guaranteed to learn valid generalised plans and state space pruning axioms for search. Experiments demonstrate significant improvements over state-of-the-art (generalised) planners with respect to the 3 metrics of synthesis cost, planning coverage, and solution quality on various classical and numeric planning domains.
Zero-shot stance detection (ZSSD) seeks to determine the stance of text toward previously unseen targets, a task critical for analyzing dynamic and polarized online discourse with limited labeled data. While large language models (LLMs) offer zero-shot capabilities, prompting-based approaches often fall short in handling complex reasoning and lack robust generalization to novel targets. Meanwhile, LLM-enhanced methods still require substantial labeled data and struggle to move beyond instance-level patterns, limiting their interpretability and adaptability. Inspired by cognitive science, we propose the Cognitive Inductive Reasoning Framework (CIRF), a schema-driven method that bridges linguistic inputs and abstract reasoning via automatic induction and application of cognitive reasoning schemas. CIRF abstracts first-order logic patterns from raw text into multi-relational schema graphs in an unsupervised manner, and leverages a schema-enhanced graph kernel model to align input structures with schema templates for robust, interpretable zero-shot inference. Extensive experiments on SemEval-2016, VAST, and COVID-19-Stance benchmarks demonstrate that CIRF not only establishes new state-of-the-art results, but also achieves comparable performance with just 30% of the labeled data, demonstrating its strong generalization and efficiency in low-resource settings.
Information retrieval (IR) systems play a critical role in navigating information overload across various applications. Existing IR benchmarks primarily focus on simple queries that are semantically analogous to single- and multi-hop relations, overlooking complex logical queries involving first-order logic operations such as conjunction (∧), disjunction (∨), and negation (¬). Thus, these benchmarks can not be used to sufficiently evaluate the performance of IR models on complex queries in real-world scenarios. To address this problem, we propose a novel method leveraging large language models (LLMs) to construct a new IR dataset ComLQ for Complex Logical Queries, which comprises 2,909 queries and 11,251 candidate passages. A key challenge in constructing the dataset lies in capturing the underlying logical structures within unstructured text. Therefore, by designing the subgraph-guided prompt with the subgraph indicator, an LLM (such as GPT-4o) is guided to generate queries with specific logical structures based on selected passages. All query-passage pairs in ComLQ are ensured structure conformity and evidence distribution through expert annotation. To better evaluate whether retrievers can handle queries with negation, we further propose a new evaluation metric, Log-Scaled Negation Consistency (LSNC@K). As a supplement to standard relevance-based metrics (such as nDCG and mAP), LSNC@K measures whether top-K retrieved passages violate negation conditions in queries. Our experimental results under zero-shot settings demonstrate existing retrieval models' limited performance on complex logical queries, especially on queries with negation, exposing their inferior capabilities of modeling exclusion. In summary, our ComLQ offers a comprehensive and fine-grained exploration, paving the way for future research on complex logical queries in IR.
From Hypothesis to Premises: LLM-based Backward Logical Reasoning with Selective Symbolic Translation
PDF ↗Logical reasoning is a core challenge in natural language understanding and a fundamental capability of artificial intelligence, underpinning scientific discovery, mathematical theorem proving, and complex decision-making. Despite the remarkable progress of large language models (LLMs), most current approaches still rely on forward reasoning paradigms, generating step-by-step rationales from premises to conclusions. However, such methods often suffer from redundant inference paths, hallucinated steps, and semantic drift, resulting in inefficient and unreliable reasoning. In this paper, we propose a novel framework, Hypothesis-driven Backward Logical Reasoning (HBLR). The core idea is to integrate confidence-aware symbolic translation with hypothesis-driven backward reasoning. In the translation phase, only high-confidence spans are converted into logical form, such as first-order logic (FOL), while uncertain content remains in natural language. A translation reflection module further ensures semantic fidelity by evaluating symbolic outputs and reverting lossy ones back to text when necessary. In the reasoning phase, HBLR simulates human deductive thinking by assuming the conclusion is true and recursively verifying its premises. A reasoning reflection module further identifies and corrects flawed inference steps, enhancing logical coherence. Extensive experiments on five reasoning benchmarks demonstrate that HBLR consistently outperforms strong baselines in both accuracy and efficiency.
Do LLMs Really Struggle at NL-FOL Translation? Revealing Their Strengths via a Novel Benchmarking Strategy
PDF ↗Due to its expressiveness and unambiguous nature, First-Order Logic (FOL) is a powerful formalism for representing concepts expressed in natural language (NL). This is useful, e.g., for specifying and verifying desired system properties. While translating FOL into human-readable English is relatively straightforward, the inverse problem, converting NL to FOL (NL-FOL translation), has remained a longstanding challenge, for both humans and machines. Although the emergence of Large Language Models (LLMs) promised a breakthrough, recent literature provides contrasting results on their ability to perform NL-FOL translation. In this work, we provide a threefold contribution. First, we critically examine existing datasets and protocols for evaluating NL-FOL translation performance, revealing key limitations that may cause a misrepresentation of LLMs' actual capabilities. Second, to overcome these shortcomings, we propose a novel evaluation protocol explicitly designed to distinguish genuine semantic-level logical understanding from superficial pattern recognition, memorization, and dataset contamination. Third, using this new approach, we show that state-of-the-art, dialogue-oriented LLMs demonstrate strong NL-FOL translation skills and a genuine grasp of sentence-level logic, whereas embedding-centric models perform markedly worse.
Modern vision-language models (VLMs) deliver impressive predictive accuracy yet offer little insight into 'why' a decision is reached, frequently hallucinating facts, particularly when encountering out-of-distribution data. Neurosymbolic frameworks address this by pairing black-box perception with interpretable symbolic reasoning, but current methods extract their symbols solely from task labels, leaving them weakly grounded in the underlying visual data. In this paper, we introduce a multi-agent system - Concept-RuleNet that reinstates visual grounding while retaining transparent reasoning. Specifically, a multimodal concept generator first mines discriminative visual concepts directly from a representative subset of training images. Next, these visual concepts are utilized to condition symbol discovery, anchoring the generations in real image statistics and mitigating label bias. Subsequently, symbols are composed into executable first-order rules by a large language model reasoner agent - yielding interpretable neurosymbolic rules. Finally, during inference, a vision verifier agent quantifies the degree of presence of each symbol and triggers rule execution in tandem with outputs of black-box neural models, predictions with explicit reasoning pathways. Experiments on five benchmarks, including two challenging medical-imaging tasks and three underrepresented natural-image datasets, show that our system augments state-of-the-art neurosymbolic baselines by an average of 5% while also reducing the occurrence of hallucinated symbols in rules by up to 50%.
Post-training quantization (PTQ) offers an efficient approach to compressing large language models (LLMs), significantly reducing memory access and computational costs. Existing compensation-based weight calibration methods often rely on a second-order Taylor expansion to model quantization error, under the assumption that the first-order term is negligible in well-trained full-precision models. However, we reveal that the progressive compensation process introduces accumulated first-order deviations between latent weights and their full-precision counterparts, making this assumption fundamentally flawed. To address this, we propose FOEM, a novel PTQ method that explicitly incorporates first-order gradient terms to improve quantization error compensation. FOEM approximates gradients by performing a first-order Taylor expansion around the pre-quantization weights. This yields an approximation based on the difference between latent and full-precision weights as well as the Hessian matrix. When substituted into the theoretical solution, the formulation eliminates the need to explicitly compute the Hessian, thereby avoiding the high computational cost and limited generalization of backpropagation-based gradient methods. This design introduces only minimal additional computational overhead. Extensive experiments across a wide range of models and benchmarks demonstrate that FOEM consistently outperforms the classical GPTQ method. In 3-bit weight-only quantization, FOEM reduces the perplexity of Llama3-8B by 17.3% and increases the 5-shot MMLU accuracy from 53.8% achieved by GPTAQ to 56.1%. Moreover, FOEM can be seamlessly combined with advanced techniques such as SpinQuant, delivering additional gains under the challenging W4A4KV4 setting and further narrowing the performance gap with full-precision baselines, surpassing existing state-of-the-art methods.
We study the problem of efficiently estimating policies that simultaneously optimize multiple objectives in reinforcement learning (RL). Given n objectives (or tasks), we seek the optimal partition of these objectives into k groups, which is much smaller than n, where each group comprises related objectives that can be trained together. This problem arises in applications such as robotics, control, and preference optimization in language models, where learning a single policy for all n objectives is suboptimal as n grows. We introduce a two-stage procedure — meta-training followed by fine-tuning — to address this problem. We first learn a meta-policy for all objectives using multitask learning. Then, we adapt the meta-policy to multiple randomly sampled subsets of objectives. The adaptation step leverages a first-order approximation property of well-trained policy networks, which is empirically verified to be accurate within a 2% error margin across various RL environments. The resulting algorithm, PolicyGradEx, efficiently estimates an aggregate task-affinity score matrix given a policy evaluation algorithm. Based on the estimated affinity score matrix, we cluster the n objectives into k groups by maximizing the intra-cluster affinity scores. Experiments on three robotic control and the Meta-World benchmarks demonstrate that our approach outperforms state-of-the-art baselines by 16% on average, while delivering up to 26 times faster speedup relative to performing full training to obtain the clusters. Ablation studies validate each component of our approach. For instance, compared with random grouping and gradient-similarity-based grouping, our loss-based clustering yields an improvement of 19%. Finally, we analyze the generalization error of policy networks by measuring the Hessian trace of the loss surface, which gives non-vacuous measures relative to the observed generalization errors.
Multimodal learning has shown significant superiority on various tasks by integrating multiple modalities. However, the interdependencies among modalities increase the susceptibility of multimodal models to adversarial attacks. Existing methods mainly focus on attacks on specific modalities or indiscriminately attack all modalities. In this paper, we find that these approaches ignore the differences between modalities in their contribution to final robustness, resulting in suboptimal robustness performance. To bridge this gap, we introduce Vulnerability-Aware Robust Multimodal Adversarial Training (VARMAT), a probe-in-training adversarial training method that improves multimodal robustness by identifying the vulnerability of each modality. To be specific, VARMAT first explicitly quantifies the vulnerability of each modality, grounded in a first-order approximation of the attack objective (Probe). Then, we propose a targeted regularization term that penalizes modalities with high vulnerability, guiding robust learning while maintaining task accuracy (Training). We demonstrate the enhanced robustness of our method across multiple multimodal datasets involving diverse modalities. Finally, we achieve {12.73%, 22.21%, 11.19%} robustness improvement on three multimodal datasets, revealing a significant blind spot in multimodal adversarial training.