Synthetic Data

Plasticity—a neural network's ability to adapt to new tasks—is critical for continual and transfer learning. Existing measures, such as effective rank, dead neuron fraction, and weight norm, lack theoretical grounding and correlate poorly with performance on new tasks. We introduce *local redundancy*, an information-theoretic measure derived from universal compression theory. We define local redundancy as the worst-case redundancy of a local model family—parameters in an infinitesimal neighborhood along gradient directions—and show this is a principled measure of plasticity. Although local redundancy is intractable to compute exactly, we prove that the expected squared gradient norm on a synthetic memorization task provides an efficiently computable lower bound. Experiments on continual image classification and time series transfer learning demonstrate that local redundancy predicts downstream performance better than existing measures and enables pretraining checkpoint selection where validation loss plateaus.

In this work, we aim to develop effective data synthesis techniques that autonomously synthesize multimodal training data for enhancing MLLMs in solving complex real-world tasks. To this end, we propose Collective Adversarial Data Synthesis (CADS), a novel and general approach to synthesize high-quality, diverse and challenging multimodal data for MLLMs. The core idea of CADS is to leverage collective intelligence to ensure high-quality and diverse generation, while exploring adversarial learning to synthesize challenging samples for effectively driving model improvement. Specifically, CADS operates with two cyclic phases, i.e., Collective Adversarial Data Generation (CAD-Generate) and Collective Adversarial Data Judgment (CAD-Judge). CAD-Generate leverages collective knowledge to jointly generate new and diverse multimodal data, while CAD-Judge collaboratively assesses the quality of synthesized data. In addition, CADS introduces an Adversarial Context Optimization mechanism to optimize the generation context to encourage challenging and high-value data generation. With CADS, we construct MMSynthetic-20K and train our model R1-SyntheticVL, which demonstrates superior performance on various benchmarks.

Text-guided texture editing aims to modify object appearance while preserving the underlying geometric structure. However, our empirical analysis reveals that even SOTA editing models frequently struggle to maintain structural consistency during texture editing, despite the intended changes being purely appearance-related. Motivated by this observation, we jointly enhance structure preservation from both data and training perspectives, and build TexEditor, a dedicated texture editing model based on Qwen-Image-Edit-2509. Firstly, we construct BlenderTex, a high-quality SFT dataset generated with Blender, which provides strong structural priors for a cold start. Secondly, we introduce StructureNFT, a RL–based approach that integrates structure-preserving losses to transfer the structural priors learned during SFT to real-world scenes. Moreover, due to the limited realism and evaluation coverage of existing benchmarks, we introduce TexBench, a general-purpose real-world benchmark for text-guided texture editing. Extensive experiments on existing Blender-based texture benchmarks and our TexBench show that TexEditor consistently outperforms strong baselines such as Nano Banana Pro. In addition, we assess TexEditor on the general-purpose benchmark ImgEdit to validate its generalization.

Relational Databases (RDBs) are the backbone of modern business, yet they lack foundation models comparable to those in text or vision. A key obstacle is that high-quality RDBs are private, scarce, and structurally heterogeneous, making internet-scale pre-training infeasible. To overcome this data scarcity, we introduce RDB-PFN, the first relational foundation model trained purely via synthetic data. Inspired by Prior-Data Fitted Networks (PFNs), where synthetic data generated from Structural Causal Models (SCMs) enables reasoning on single tables, we design a Relational Prior Generator to create an infinite stream of diverse RDBs from scratch. Pre-training on over 2 million synthetic single-table and relational tasks, RDB-PFN learns to adapt to any new database instantly via genuine in-context learning. Experiments show that RDB-PFN achieves strong few-shot performance on 19 real-world relational prediction tasks, outperforming state-of-the-art tabular foundation models evaluated on the same DFS-linearized inputs, while using a lightweight architecture and fast inference. The code is available at https://github.com/MuLabPKU/RDBPFN.

The learnware paradigm aims to establish a market of learnwares, each of which is a well-trained model combined with a specification that describes its functionality without leaking data privacy. The market enables users to efficiently reuse relevant models based on specifications on their own tasks instead of training models from scratch. Recent works have attempted to generate specifications using Reduced Kernel Mean Embedding (RKME), which maps input distributions into Reproducing Kernel Hilbert Space (RKHS) while ignoring the output space, causing models trained on similar input spaces to yield similar specifications, even when their functionalities differ. Many labeled-RKME improvements attempt to address this by indirectly modeling the input-output conditional distributions, but they remain limited to classification tasks and lack clear theoretical explanations. In this work, we propose Reduced Neural Conditional Mean Embedding (RNCME), a novel specification generation method that directly models input-output conditional distributions via Conditional Mean Embedding (CME). Our RNCME method has a clear theoretical understanding based on CME and is applicable to both regression and classification tasks. Empirical experiments demonstrate the effectiveness and efficiency of our RNCME method.

Differential privacy (DP) imposes fundamental trade-offs between privacy and statistical fidelity in synthetic data generation. While access to public data has been shown to improve these trade-offs empirically, existing approaches use public data only indirectly, through pre-processing (e.g., using pre-trained generative models) or post-processing steps (e.g., matching target statistics estimated from public datasets), while relying on domain-agnostic DP mechanisms. In this work, we lay the theoretical framework to study the principled incorporation of public data into DP mechanisms themselves. We consider normalized histograms as distribution estimators and characterize the asymptotically optimal domain-aware privacy mechanism within a specific class of DP mechanisms. We introduce PubMix, a public-data-aware DP mechanism that can be used in histogram-based data synthesis pipelines. Our experiments demonstrate that PubMix significantly improves synthetic data generation quality compared to domain-agnostic privacy mechanisms.

This paper investigates the problem of generating synthetic tabular data with differential privacy (DP) guarantees, enabling data sharing in sensitive domains. Despite extensive study, state-of-the-art methods often focus on minimizing low-order marginal query errors and overlook the challenges posed by high-order correlations. To address this gap, we extend the Private Evolution (PE) framework, originally developed for DP-compliant image and text synthesis, to tabular data. We introduce Tab-PE -- an algorithm for synthetic tabular data generation under DP constraints. Tab-PE iteratively improves a candidate dataset via an evolutionary process that leverages tabular-specialized operators to produce variations, privately scores them, and selects the highest-quality samples to retain and propagate. In contrast to the original PE, which relies on large foundation models, Tab-PE employs heuristic operators with significantly lower computational costs, making PE more practical and scalable for tabular data. Through extensive experiments on real-world and simulation datasets, we demonstrate that Tab-PE substantially outperforms prior baselines on datasets exhibiting high-order correlations. Compared to the best baseline -- AIM, Tab-PE improves classification accuracy by up to 10\% while running 28$\times$ faster.

Tabular synthesis is critical for privacy-preserving sharing and augmentation, yet diffusion models rely on implicit mechanisms to capture inter-column relationships. We introduce Geometry-Aware Tabular Diffusion (GATD), which augments tabular diffusion denoisers with pairwise angles and lengths computed from column value differences and used as inputs and auxiliary targets. Our MLP instantiation achieves state-of-the-art benchmark performance while using $3.5\times$ fewer parameters on average (up to $25\times$ for classification tasks): on ten datasets, it wins 8/10 Shape, 7/10 Trend, and 9/10 downstream utility (F1/RMSE), reducing Shape and Trend error by 27\% and 20\%. Default loss weights transfer to GNN and Transformer denoisers, improving Shape on 27/30 and Trend on 25/30 architecture-dataset cells. A matched ablation shows supervision (not extra inputs or capacity) drives the gain. This shows explicit relational supervision is a portable inductive bias for tabular diffusion.

Data is the lifeblood of AI, yet much of the most valuable data remains locked in silos due to privacy and regulations. As a result, AI remains heavily underutilized in many of the most important domains, including healthcare, education, and finance. Synthetic data generation (SDG), i.e. the generation of artificial datawith a synthesizer trained on real data, offers an appealing solution to make data available while mitigating p rivacy concerns, however existing SDG-as-a-service workflow require data holders to trust providers with access to private data. We propose FHAIM, the first fully homomorphic encryption (FHE) framework for training a marginal-based synthetic data generator on encrypted tabular data. FHAIM adapts the widely used AIM algorithm to the FHE setting using novel FHE protocols, ensuring that the private data remains encrypted throughout and is released only with differential privacy guarantees. Our empirical analysis show that FHAIM preserves the performance of AIM while maintaining feasible runtimes.

The learnware paradigm enables model reuse by pairing each submitted model with a specification, a public artifact used to identify helpful models without raw-data exchange. This design creates a privacy surface: a useful specification must reveal capability-relevant information, but such information should not expose sensitive properties of training data or user tasks. Is it achievable in practice? To answer this question, this paper establishes the first framework for analyzing the incremental risk introduced by specifications in learnware, and provides theoretical guarantees for the widely used reduced kernel mean embedding (RKME) specification. Specifically, we formulate learnware-inversion as a family of statistical decision games and define the risk of specification as the incremental Bayes value from observing the model alone to observing the complete learnware. For the RKME specification, we derive risk bounds through an RKHS-smoothed total-variation bridge and the stability analysis of its reduced-set generator. We further instantiate the framework for common attacks and show that a properly sized RKME specification introduces negligible additional privacy risk while retaining sufficient information for learnware identification.

Synthetic data becomes crucial for large language model training, but its effectiveness is highly inconsistent. We provide an information-theoretic account of this inconsistency: synthetic data improves a model only when the generation-training loop is information-open, i.e., shaped by external signals (verifiers, environments, or rubrics) that inject task-relevant information beyond the model's current distribution. When the loop is information-closed (relying on the model's own outputs without such signals), the data processing inequality ensures that task-relevant information can only decrease, making collapse a predicted outcome. Among information-open pipelines, both efficiency and generalization hinge on the meta-level of supervision: a coarser signal such as binary correctness treats all acceptable outputs as equivalent, so the behavior it teaches is not tied to any particular domain or surface form and generalizes naturally across tasks and domains. These observations lead to a guiding thesis: learning preferentially converges to the most information-efficient signal component available, which accelerates learning when that component is the intended one, but causes reward hacking when a spurious pattern happens to be simpler.

Aggregation-Free Federated Learning enables joint training by sharing synthetic data, aiming to eliminate data heterogeneity across clients. However, existing methods fail to explicitly separate the principal and residual components of dataset, leading to biased synthetic data. In this paper, we propose a novel Unbiased Synthetic Data optimization method FedUSD for Aggregation-Free Federated Learning, which is achieved by exploring the High-energy Orthogonal Base (HOB) and variance of dataset in feature space. Our FedUSD is inspired by the discovery that principal component concentrates in HOB while residual component independently reflects in variance, regardless of networks. Based on the observation, we develop a method that mathematically optimizes synthetic data by matching both HOB and variance with those of real data. Besides, we experimentally show the superior effectiveness of leveraging HOB and variance to separately extract the principal and residual components over existing methods. We also theoretically prove that FedUSD achieves unbiased synthetic data and thus convergence. Without introducing any constraints, FedUSD thereby yields significant improvements over the state-of-the-arts in terms of global model performance, under equivalent communicational costs. For example, on the SVHN dataset, FedUSD improves 6.74\% to 30.82\% which is higher than others with Dirichlet coefficient $\alpha=0.01$.

Noise-based certified machine unlearning currently faces a hard ceiling: the noise magnitude required to certify unlearning typically destroys model utility, particularly for large-scale deletion requests. While leveraging public data is a standard technique in differential privacy to relax this tension, its role in unlearning remains unexplored. We address this gap by introducing **Asymmetric Langevin Unlearning (ALU)**, a framework that uses public data to mitigate privacy costs. We prove that public data injection suppresses the unlearning cost by a factor of $O(1/n_{\mathrm{pub}}^2)$, guaranteeing a strict computational advantage over retraining. This establishes a new control mechanism: practitioners can mitigate the need for high noise—and the associated utility loss—by increasing the volume of public data. Crucially, we analyze the realistic setting of **distribution mismatch**, explicitly characterizing how shifts between public and private sources impact utility. We show that ALU enables "mass unlearning'' of constant dataset fractions -- a regime where standard symmetric methods become impractical -- while maintaining high utility. Empirical evaluations using variational Rényi divergence and membership inference attacks confirm that ALU effectively thwarts privacy attacks while preserving utility under reasonable distribution shifts.

Relational Foundation Models (RFMs) facilitate data-driven decision-making by learning from complex multi-table databases. However, the diverse relational databases needed to train such models are rarely public due to privacy constraints. While there are methods to generate synthetic tabular data of arbitrary size, incorporating schema structure and primary--foreign key connectivity for multi-table generation remains challenging. Here we introduce PluRel, a framework to synthesize multi-tabular relational databases from scratch. In a step-by-step fashion, PluRel models (1) schemas with directed graphs, (2) inter-table primary-foreign key connectivity with bipartite graphs, and, (3) feature distributions in tables via conditional causal mechanisms. The design space across these stages supports the synthesis of a wide range of diverse databases, while being computationally lightweight. Using PluRel, we observe for the first time that (1) RFM pretraining loss exhibits power-law scaling with the number of synthetic databases and total pretraining tokens, (2) scaling the number of synthetic databases improves generalization to real databases, and (3) synthetic pretraining yields strong base models for continued pretraining on real databases. Overall, our framework and results position synthetic data scaling as a promising paradigm for RFMs. Webpage: https://snap-stanford.github.io/plurel