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Trajectory data is fundamental to modern urban intelligence, yet its sensitivity raises significant privacy concerns. Generative models such as Generative Adversarial Networks, Variational Autoencoders, and Diffusion Models have been developed to generate realistic synthetic trajectory data by capturing underlying spatiotemporal distributions and mobility patterns. Although these models are often assumed to preserve privacy due to their generative nature, this assumption does not necessarily hold. In this work, we investigate the intersection of generative trajectory modeling and privacy evaluation. By identifying applicable empirical methods for assessing privacy preservation in trajectory generation tasks, we demonstrate a significant gap in the evaluation of privacy for generative trajectory models. Motivated by this gap, we implement Membership Inference Attacks against representative models, demonstrating the feasibility of using such empirical privacy evaluation methods and showing that their generative nature does not eliminate privacy risks.

We consider a partition of the projective space PG(m + n - 1, K), with K any (commutative) field, into one space of dimension m - 1 while all other spaces of the partition have dimension n - 1. Characterizations of particular partitions of this type are given. This research is motivated by some interesting problems on translation generalized quadrangles. In the paper we apply our results to generalized ovoids and generalized quadrangles. Finally we give some ideas for further research.

The use of discriminators to train or fine-tune generative models has proven to be a rather successful framework. A notable example is Generative Adversarial Networks (GANs) that minimize a loss incurred by training discriminators along with other paradigms that boost generative models via discriminators that satisfy weak learner constraints. More recently, even diffusion models have shown advantages with some kind of discriminator guidance. In this work, we extend a strong-duality result related to $f$-divergences which gives rise to a discriminator-guided recipe that allows us to \textit{refine} any generative model. We then show that the refined generative models provably improve generalization, compared to its non-refined counterpart. In particular, our analysis reveals that the gap in generalization is improved based on the Rademacher complexity of the discriminator set used for refinement. Our recipe subsumes a recently introduced score-based diffusion approach (Kim et al., 2022) that has shown great empirical success, however allows us to shed light on the generalization guarantees of this method by virtue of our analysis. Thus, our work provides a theoretical validation for

Generative art merges creativity with computation, using algorithms to produce aesthetic works. This paper introduces Samila, a Python-based generative art library that employs mathematical functions and randomness to create visually compelling compositions. The system allows users to control the generation process through random seeds, function selections, and projection modes, enabling the exploration of randomness and artistic expression. By adjusting these parameters, artists can create diverse compositions that reflect intentionality and unpredictability. We demonstrate that Samila's outputs are uniquely determined by two random generation seeds, making regeneration nearly impossible without both. Additionally, altering the point generation functions while preserving the seed produces artworks with distinct graphical characteristics, forming a visual family. Samila serves as both a creative tool for artists and an educational resource for teaching mathematical and programming concepts. It also provides a platform for research in generative design and computational aesthetics. Future developments could include AI-driven generation and aesthetic evaluation metrics to enhance cre

Recent progress in Multimodal Large Language Models (MLLMs) demonstrates that Chain-of-Thought (CoT) reasoning enables systematic solutions to complex understanding tasks. However, its extension to generation tasks remains nascent and limited by scenario-specific mechanisms that hinder generalization and adaptation. In this work, we present ThinkGen, the first think-driven visual generation framework that explicitly leverages MLLM's CoT reasoning in various generation scenarios. ThinkGen employs a decoupled architecture comprising a pretrained MLLM and a Diffusion Transformer (DiT), wherein the MLLM generates tailored instructions based on user intent, and DiT produces high-quality images guided by these instructions. We further propose a separable GRPO-based training paradigm (SepGRPO), alternating reinforcement learning between the MLLM and DiT modules. This flexible design enables joint training across diverse datasets, facilitating effective CoT reasoning for a wide range of generative scenarios. Extensive experiments demonstrate that ThinkGen achieves robust, state-of-the-art performance across multiple generation benchmarks. Code is available: https://github.com/jiaosiyuu/Thi

We investigate the capabilities of Quantum Generative Adversarial Networks (QGANs) in image generations tasks. Our analysis centers on fully quantum implementations of both the generator and discriminator. Through extensive numerical testing of current main architectures, we find that QGANs struggle to generalize across datasets, converging on merely the average representation of the training data. When the output of the generator is a pure-state, we analytically derive a lower bound for the discriminator quality given by the fidelity between the pure-state output of the generator and the target data distribution, thereby providing a theoretical explanation for the limitations observed in current models. Our findings reveal fundamental challenges in the generalization capabilities of existing quantum generative models. While our analysis focuses on QGANs, the results carry broader implications for the performance of related quantum generative models.

We present gg-bench, a collection of game environments designed to evaluate general reasoning capabilities in language models. Unlike most static benchmarks, gg-bench is a data generating process where new evaluation instances can be generated at will. In particular, gg-bench is synthetically generated by (1) using a large language model (LLM) to generate natural language descriptions of novel games, (2) using the LLM to implement each game in code as a Gym environment, and (3) training reinforcement learning (RL) agents via self-play on the generated games. We evaluate language models by their winrate against these RL agents by prompting models with the game description, current board state, and a list of valid moves, after which models output the moves they wish to take. gg-bench is challenging: state-of-the-art LLMs such as GPT-4o and Claude 3.7 Sonnet achieve winrates of 7-9% on gg-bench using in-context learning, while reasoning models such as o1, o3-mini and DeepSeek-R1 achieve average winrates of 31-36%. We release the generated games, data generation process, and evaluation code in order to support future modeling work and expansion of our benchmark.

Parallel LLM inference scaling involves sampling a set of $N>1$ responses for a single input prompt. However, these $N$ parallel responses tend to be generated independently from each other, partitioning compute resources and leaving potentially useful information in one generation untapped by others. This is in contrast to response length scaling where past computation is used in all future steps. For higher quality responses and response sets, we propose Bridge to generate interdependent responses in parallel by rethinking batched LLM hidden states as holistic tensors rather than independent slices. With only a small amount (2.8%-5.1%) of new parameters, Bridge improves the relative mean accuracy gains from reinforcement learning with verifiable rewards by up to 39% and boosts consistency of correct responses. Trained once, Bridge scales to any generation width, all with greater performance than independent generations, unlocking a more general mode of parallel scaling that effectively leverages information between sequences, compatible with any post-generation aggregation technique.

Let $R$ be a ring with identity, $(S,\leq)$ an ordered monoid, $ω:S \to End(R)$ a monoid homomorphism, and $A= R\left[\left[S,ω\right]\right]$ the ring of skew generalized power series. The concepts of generalized Baer and generalized quasi-Baer rings are generalization of Baer and quasi-Baer rings, respectively. A ring $R$ is called generalized right Baer (generalized right quasi-Baer) if for any non-empty subset $S$ (right ideal $I$) of $R$, the right annihilator of $S^n \space{0.1cm}(I^n)$ is generated by an idempotent for some positive integer $n$. Left cases may be defined analogously. A ring $R$ is called generalized Baer (generalized quasi-Baer) if it is both generalized right and left Baer (generalized right and left quasi-Baer) ring. In this paper, we examine the behavior of a skew generalized power series ring over a generalized right Baer (generalized right quasi-Baer) ring and prove that, under specific conditions, the ring $A$ is generalized right Baer (generalized right quasi-Baer) if and only if $R$ is a generalized right Baer (generalized right quasi-Baer) ring.

Generative Models (GMs), particularly Large Language Models (LLMs), have garnered significant attention in machine learning and artificial intelligence for their ability to generate new data by learning the statistical properties of training data and creating data that resemble the original. This capability offers a wide range of applications across various domains. However, the complex structures and numerous model parameters of GMs make the input-output processes opaque, complicating the understanding and control of outputs. Moreover, the purely data-driven learning mechanism limits GM's ability to acquire broader knowledge. There remains substantial potential for enhancing the robustness and generalization capabilities of GMs. In this work, we introduce the fuzzy system, a classical modeling method that combines data and knowledge-driven mechanisms, to generative tasks. We propose a novel Generative Fuzzy System framework, named GenFS, which integrates the deep learning capabilities of GM with the interpretability and dual-driven mechanisms of fuzzy systems. Specifically, we propose an end-to-end GenFS-based model for sequence generation, called FuzzyS2S. A series of experimenta

This paper presents an algorithmic method for generating random orthogonal matrices \(A\) that satisfy the property \(A^t S A = S\), where \(S\) is a fixed real invertible symmetric or skew-symmetric matrix. This method is significant as it generalizes the procedures for generating orthogonal matrices that fix a general fixed symmetric or skew-symmetric bilinear form. These include orthogonal matrices that fall to groups such as the symplectic group, Lorentz group, Poincaré group, and more generally the indefinite orthogonal group, to name a few. These classes of matrices play crucial roles in diverse fields such as theoretical physics, where they are used to describe symmetries and conservation laws, as well as in computational geometry, numerical analysis, and number theory, where they are integral to the study of quadratic forms and modular forms. The implementation of our algorithms can be accomplished using standard linear algebra libraries.

Generating fake data is an essential dimension of modern software testing, as demonstrated by the number and significance of data faking libraries. Yet, developers of faking libraries cannot keep up with the wide range of data to be generated for different natural languages and domains. In this paper, we assess the ability of generative AI for generating test data in different domains. We design three types of prompts for Large Language Models (LLMs), which perform test data generation tasks at different levels of integrability: 1) raw test data generation, 2) synthesizing programs in a specific language that generate useful test data, and 3) producing programs that use state-of-the-art faker libraries. We evaluate our approach by prompting LLMs to generate test data for 11 domains. The results show that LLMs can successfully generate realistic test data generators in a wide range of domains at all three levels of integrability.

Generative Flow Networks (GFlowNets) have emerged as an innovative learning paradigm designed to address the challenge of sampling from an unnormalized probability distribution, called the reward function. This framework learns a policy on a constructed graph, which enables sampling from an approximation of the target probability distribution through successive steps of sampling from the learned policy. To achieve this, GFlowNets can be trained with various objectives, each of which can lead to the model s ultimate goal. The aspirational strength of GFlowNets lies in their potential to discern intricate patterns within the reward function and their capacity to generalize effectively to novel, unseen parts of the reward function. This paper attempts to formalize generalization in the context of GFlowNets, to link generalization with stability, and also to design experiments that assess the capacity of these models to uncover unseen parts of the reward function. The experiments will focus on length generalization meaning generalization to states that can be constructed only by longer trajectories than those seen in training.

We introduce Generator Matching, a modality-agnostic framework for generative modeling using arbitrary Markov processes. Generators characterize the infinitesimal evolution of a Markov process, which we leverage for generative modeling in a similar vein to flow matching: we construct conditional generators which generate single data points, then learn to approximate the marginal generator which generates the full data distribution. We show that Generator Matching unifies various generative modeling methods, including diffusion models, flow matching and discrete diffusion models. Furthermore, it expands the design space to new and unexplored Markov processes such as jump processes. Finally, Generator Matching enables the construction of superpositions of Markov generative models and enables the construction of multimodal models in a rigorous manner. We empirically validate our method on image and multimodal generation, e.g. showing that superposition with a jump process improves performance.

Pre-training backbone networks on a general annotated dataset (e.g., ImageNet) that comprises numerous manually collected images with category annotations has proven to be indispensable for enhancing the generalization capacity of downstream visual tasks. However, those manually collected images often exhibit bias, which is non-transferable across either categories or domains, thus causing the model's generalization capacity degeneration. To mitigate this problem, we present a low-biased general annotated dataset generation framework (lbGen). Instead of expensive manual collection, we aim at directly generating low-biased images with category annotations. To achieve this goal, we propose to leverage the advantage of a multimodal foundation model (e.g., CLIP), in terms of aligning images in a low-biased semantic space defined by language. Specifically, we develop a bi-level semantic alignment loss, which not only forces all generated images to be consistent with the semantic distribution of all categories belonging to the target dataset in an adversarial learning manner, but also requires each generated image to match the semantic description of its category name. In addition, we fu

We construct generalized symmetries for linearized Einstein gravity in arbitrary dimensions. First-principle considerations in QFT force generalized symmetries to appear in dual pairs. Verifying this prediction helps us find the full set of non-trivial conserved charges -- associated, in equal parts, with 2-form and $(D-2)$-form currents. Their total number is $D(D+1)$. We compute the quantum commutators of pairs of dual charges, showing that they are non-vanishing for regions whose boundaries are non-trivially linked with each other and zero otherwise, as expected on general grounds. We also consider general linearized higher-curvature gravities. These propagate, in addition to the usual graviton, a spin-0 mode as well as a massive ghost-like spin-2 one. When the latter is absent, the theory is unitary and the dual-pairs principle is respected. In particular, we find that the number and types of charges remain the same as for Einstein gravity, and that they correspond to continuous generalizations of the Einsteinian ones.