Knowledge Graph (KG) reasoning has received significant attention in the fields of artificial intelligence and knowledge engineering, owing to its ability to autonomously deduce new knowledge and consequently enhance the availability and precision of downstream applications. However, current methods predominantly concentrate on a single form of neural or symbolic reasoning, failing to effectively integrate the inherent strengths of both approaches. Furthermore, the current prevalent methods primarily focus on addressing a single reasoning scenario, presenting limitations in meeting the diverse demands of real-world reasoning tasks. Unifying the neural and symbolic methods, as well as diverse reasoning scenarios in one model is challenging as there is a natural representation gap between symbolic rules and neural networks, and diverse scenarios exhibit distinct knowledge structures and specific reasoning objectives. To address these issues, we propose a unified neurosymbolic reasoning framework, namely Tunsr, for KG reasoning. Tunsr first introduces a consistent structure of reasoning graph that starts from the query entity and constantly expands subsequent nodes by iteratively searching posterior neighbors. Based on it, a forward logic message-passing mechanism is proposed to update both the propositional representations and attentions, as well as first-order logic (FOL) representations and attentions of each node. In this way, Tunsr conducts the transformation of merging multiple rules by merging possible relations at each step. Finally, the FARI algorithm is proposed to induce FOL rules by constantly performing attention calculations over the reasoning graph. Extensive experimental results on 19 datasets of four reasoning scenarios (transductive, inductive, interpolation, and extrapolation) demonstrate the effectiveness of Tunsr.

Federated learning with differential privacy suffers from two major costs: each client must transmit $d$-dimensional gradients every round, and the magnitude of DP noise grows with $d$. Yet empirical studies show that gradient updates exhibit strong temporal correlations and lie in a $k$-dimensional subspace with $k \ll d$. Motivated by this, we introduce DOME, a decentralized DP optimization framework in which each client maintains a compact sketch to project gradients into $\mathbb{R}^k$ before privatization and Secure Aggregation. This reduces per-round communication from order $d$ to order $k$ and moves towards a gradient approximation mean-squared error of $σ^2 k$. To allow the sketch to span new directions and prevent it from collapsing onto historical gradients, we augment it with random probes orthogonal to historical directions. We prove that our overall protocol satisfies $(ε,δ)$-Differential Privacy.

This article introduces semantically meaningful causal language modeling (SMCLM), a selfsupervised method of training autoregressive models to generate semantically equivalent text. Our approach involves using semantically meaningful text representation as an initial embedding in the autoregressive training and generation processes. The extensive empirical study demonstrates that the SMCLM approach makes autoregressive models capable of learning robust and high-quality paraphrase generation. The proposed method is competitive with the supervised method and achieves state-of-the-art results in unsupervised approaches. This article also presents a comprehensive set of automatic metrics that cover a wide range of autogenerated paraphrase evaluation aspects. Simultaneously, this article highlights the low reliability of the metrics that are widely used in paraphrase generation evaluation, including BLEU, ROUGE, and BERTScore.

Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common linguistic usage and its extension into the broader practice of natural language plus "grassroots mathematics". We begin with a brief review of first-order logic with counting operators and cardinality comparisons. This system is known to be of high complexity, and drowns out finer aspects of the combination of logic and counting. We move to a small fragment that can represent numerical syllogisms and basic reasoning about comparative size: monadic first-order logic with counting. We provide normal forms that allow for axiomatization, determine which arithmetical notions can be defined on finite and on infinite models, and conversely, we discuss which logical notions can be defined out of purely arithmetical ones, and what sort of (non-)classical logics can be induced. Next, we investigate a series of strengthenings, again using normal form methods. The monadic second-order version is close, in a precise sense, to additive Presburger Arithmetic, while versions with the natural device of tuple counting take us to Diophantine equations, making the logic undecidable. We also define a system that combines basic modal logic over binary accessibility relations with counting, needed to formulate ubiquitous reasoning patterns such as the Pigeonhole Principle. We return to our starting point in natural language, confronting the architecture of our formal systems with linguistic quantifier vocabulary and syntax. We conclude with some general thoughts on yet further entanglements of logic and counting in formal systems, on rethinking the qualitative/quantitative divide, and on connecting our analysis to empirical findings in cognitive science.

Self Supervised Learning(SSL) has emerged as a prominent paradigm for label-efficient learning, and has been widely utilized by remote sensing foundation models(RSFMs). Recent RSFMs including SatMAE, DoFA, primarily rely on masked autoencoding(MAE), contrastive learning or some combination of them. However, these pretext tasks often overlook the unique temporal characteristics of agricultural landscape, namely nature's cycle. Motivated by this gap, we propose three novel agriculture-specific pretext tasks, namely Time-Difference Prediction(TD), Temporal Frequency Prediction(FP), and Future-Frame Prediction(FF). Comprehensive evaluation on SICKLE dataset shows FF achieves 69.6% IoU on crop mapping and FP reduces yield prediction error to 30.7% MAPE, outperforming all baselines, and TD remains competitive on most tasks.

Dataset distillation aims to create a compact dataset that retains essential information while maintaining model performance. Diffusion models (DMs) have shown promise for this task but struggle in low images-per-class (IPC) settings, where generated samples lack diversity. In this paper, we address this issue from an information-theoretic perspective by identifying two key types of information that a distilled dataset must preserve: ($i$) prototype information $\mathrm{I}(X;Y)$, which captures label-relevant features; and ($ii$) contextual information $\mathrm{H}(X | Y)$, which preserves intra-class variability. Here, $(X,Y)$ represents the pair of random variables corresponding to the input data and its ground truth label, respectively. Observing that the required contextual information scales with IPC, we propose maximizing $\mathrm{I}(X;Y) + β\mathrm{H}(X | Y)$ during the DM sampling process, where $β$ is IPC-dependent. Since directly computing $\mathrm{I}(X;Y)$ and $\mathrm{H}(X | Y)$ is intractable, we develop variational estimations to tightly lower-bound these quantities via a data-driven approach. Our approach, information-guided diffusion sampling (IGDS), seamlessly integrates with diffusion models and improves dataset distillation across all IPC settings. Experiments on Tiny ImageNet and ImageNet subsets show that IGDS significantly outperforms existing methods, particularly in low-IPC regimes. The code will be released upon acceptance.

We present any4, a learned 4-bit weight quantization solution for large language models (LLMs) providing arbitrary numeric representations without requiring pre-processing of weights or activations. any4 yields higher accuracy compared to other related 4-bit numeric representation types: int4, fp4 and nf4, as evaluated on a range of model sizes, generations and families (Llama 2, Llama 3, Mistral and Mixtral). While any4 does not require preprocessing of weights or activations, it is also competitive with orthogonal techniques that require such preprocessing (e.g., AWQ and GPTQ). We also experiment with any3 and any2 and show competitiveness at lower bits. Additionally, we show that we can calibrate using a single curated diverse sample rather than hundreds of samples from a dataset as done in most quantization approaches. We also open source tinygemm, a latency optimized GPU matrix multiplication library for LLMs, that implements any4 using a GPU-efficient lookup table strategy along with other common quantization methods. We open source our code at https://github.com/facebookresearch/any4 .

Low-rank recovery builds upon ideas from the theory of compressive sensing, which predicts that sparse signals can be accurately reconstructed from incomplete measurements. Iterative thresholding-type algorithms-particularly the normalized iterative hard thresholding (NIHT) method-have been widely used in compressed sensing (CS) and applied to matrix recovery tasks. In this paper, we propose a tensor extension of NIHT, referred to as TNIHT, for the recovery of low-rank tensors under two widely used tensor decomposition models. This extension enables the effective reconstruction of high-order low-rank tensors from a limited number of linear measurements by leveraging the inherent low-dimensional structure of multi-way data. Specifically, we consider both the CANDECOMP/PARAFAC (CP) rank and the Tucker rank to characterize tensor low-rankness within the TNIHT framework. At the same time, we establish a convergence theorem for the proposed TNIHT method under the tensor restricted isometry property (TRIP), providing theoretical support for its recovery guarantees. Finally, we evaluate the performance of TNIHT through numerical experiments on synthetic, image, and video data, and compare it with several state-of-the-art algorithms.

--With the rise of online learning, the demand for efficient and consistent assessment in mathematics has significantly increased over the past decade. Machine Learning (ML), particularly Natural Language Processing (NLP), has been widely used for autograding student responses, particularly those involving text and/or mathematical expressions. However, there has been limited research on autograding responses involving students' handwritten graphs, despite their prevalence in Science, T echnology, Engineering, and Mathematics (STEM) curricula. In this study, we implement multimodal meta-learning models for autograding images containing students' handwritten graphs and text. We further compare the performance of Vision Large Language Models (VLLMs) with these specially trained meta-learning models. Our results, evaluated on a real-world dataset collected from our institution, show that the best-performing meta-learning models outperform VLLMs in 2-way classification tasks. In contrast, in more complex 3-way classification tasks, the best-performing VLLMs slightly outperform the meta-learning models. While VLLMs show promising results, their reliability and practical applicability remain uncertain and require further investigation. S online education has gained popularity, the need for efficient and scalable methods of automatically grading and assessing student work has become increasingly important. Automated grading offers several advantages, including scalability, time efficiency, grading consistency, and immediate feedback. Early research on automated grading primarily focused on closed-ended questions, such as multiple-choice and fill-in-the-blank questions, where responses could be easily verified using rule-based systems [1], [2].

Understanding human mobility is essential for applications in public health, transportation, and urban planning. However, mobility data often suffers from sparsity due to limitations in data collection methods, such as infrequent GPS sampling or call detail record (CDR) data that only capture locations during communication events. To address this challenge, we propose BERT4Traj, a transformer-based model that reconstructs complete mobility trajectories by predicting hidden visits in sparse movement sequences. Inspired by BERT's masked language modeling objective and self-attention mechanisms, BERT4Traj leverages spatial embeddings, temporal embeddings, and contextual background features such as demographics and anchor points. We evaluate BERT4Traj on real-world CDR and GPS datasets collected in Kampala, Uganda, demonstrating that our approach significantly outperforms traditional models such as Markov Chains, KNN, RNNs, and LSTMs. Our results show that BERT4Traj effectively reconstructs detailed and continuous mobility trajectories, enhancing insights into human movement patterns.