生成模型理论与方法

We develop a geometric framework for learning deterministic and stochastic forced Hamiltonian systems with neural networks. Motivated by the Lagrange-d'Alembert principle and the theory of variational integrators, we introduce the notion of a Lagrange-d'Alembert map and establish a $C^r$ convergence theorem for first-order one-step methods. Building on these results, we propose Generalized Forced Hamiltonian Neural Networks (GFHNNs), a class of structure-preserving neural networks obtained by concatenating Lagrange-d'Alembert-Euler maps, and prove a universal approximation theorem for this architecture. We further extend the framework to parameter-dependent systems, leading to Parametric Generalized Forced Hamiltonian Neural Networks (PGFHNNs). By interpreting the multiple Stratonovich integrals appearing in the Stratonovich-Taylor expansion as parameters, the same framework can be applied to stochastic forced Hamiltonian systems whenever information about the underlying Wiener process is available. Our numerical experiments demonstrate that the proposed geometric architectures provide significantly improved long-time stability and accuracy compared to non-geometric residual neural networks, while requiring substantially less training data to achieve a comparable level of performance.

Full-cycle biventricular geometry is essential for characterizing cardiac function. However, dense and temporally consistent 3D+t biventricular meshes are not routinely available, whereas end-diastolic (ED) anatomy can often be obtained reliably. We therefore investigate full-cycle biventricular motion synthesis from a single ED mesh. This task is challenging because cardiac deformation is spatially heterogeneous and phenotype dependent, while conventional global generative models often obscure localized motion patterns. In this study, we propose a region-specific and phenotype-adaptive framework that integrates motion-informed functional parcellation with conditional latent flow. A functional partition learned from reconstructed motion organizes the ventricular surface into regions with coherent dynamics and enables topology-aware regional feature exchange. A phenotype-conditioned rectified-flow model subsequently maps the ED anatomy to full-cycle motion latents through fine-grained conditioning and prototype-routed motion adapters. An optional control branch further incorporates available motion descriptors for controllable synthesis. Experiments on ACDC, M&Ms, and M&Ms-2 demonstrate consistent improvements in geometric accuracy and functional fidelity. Under ED-only synthesis, our method achieves biventricular ASSD, HD95, and vRMSE of \(1.49\pm0.34\)~mm, \(3.77\pm1.06\)~mm, and \(3.31\pm1.03\)~mm, respectively, outperforming all competing methods. Complementary functional and robustness evaluations further demonstrate that the synthesized sequences preserve physiologically plausible ventricular dynamics and generalize across cohorts and disease phenotypes. The code will be released publicly upon acceptance of the manuscript for publication.

Compositional Zero-Shot Learning (CZSL) aims to recognize unseen attribute-object compositions by leveraging knowledge of primitive concepts learned from seen compositions. Although recent works achieve impressive performance in CZSL by leveraging large vision-language models, they primarily rely on discriminative representations that may not explicitly preserve the structured relationships between primitive concepts and their compositions. Motivated by the recent success of diffusion-based classifiers and their competitive performance relative to discriminative models, we investigate whether intermediate diffusion representations can provide complementary cues for CZSL. To this end, we propose DIFFCZSL, a diffusion-augmented framework that injects generative priors from pre-trained diffusion models into CLIP-based CZSL pipelines. We extract intermediate diffusion representations and project them into the CLIP embedding space to provide auxiliary supervision on both image and text modalities. Through contrastive alignment between CLIP embeddings and diffusion features during training, our method encourages the embedding geometry toward richer composition-aware semantics, while introducing no additional cost at inference time. Extensive experiments on three public CZSL benchmarks demonstrate consistent improvements over strong CLIP-based baselines under both closed-world and open-world settings. Our results highlight the complementary strengths of generative diffusion representations and discriminative vision-language models for compositional generalization.

Existing optimal transport (OT) models primarily seek an OT map or plan between distributions by minimizing a prescribed transport cost or distortion. However, minimizing transport cost or distortion alone may fail to identify a geometrically meaningful transformation between the two distributions. To address this limitation, this paper proposes a novel coupled OT framework that leverages a small number of annotated landmarks to guide the recovery of an underlying deformation governing the distribution transformation. The coupled OT framework integrates the optimization of the transport plan and the deformation field into a unified model, where the landmark-guided deformation field and the cost-driven transport plan are coupled through a mutual-consistency constraint. As a result, the deformation is jointly determined by the annotated landmarks and cost-driven distribution matching. The proposed framework provides a principled connection between landmark-based registration and transport-based distribution matching, enabling the recovery of transport maps from sparse geometric supervision. We establish the well-definedness of the proposed model in a general variational setting and develop a finite-element-based numerical algorithm for computation whose convergence properties are systematically analyzed. The practical effectiveness of the proposed approach is verified in shape matching.

Egocentric video offers scalable manipulation data for embodied AI, yet recovering metric 3D hand trajectories remains challenging due to severe object occlusion and frequent out-of-sight gaps. Existing single-frame and windowed temporal regressors fail when hand shortly leaves the frame, while recent video diffusion models (VDMs) rely on heavy, stochastic multi-step sampling as pixel-space renderers. We instead repurpose VDM into a deterministic geometry encoder. A single forward pass over the clean latent exposes scene content beyond current observations, including occluded and out-of-sight hands. We introduce DreamHand, an offline clip-level framework that extracts features via a Deterministic Clean-Latent Encoder and decodes them with a Bidirectional Spatiotemporal Decoder. DreamHand recovers continuous bimanual trajectories with metric placement and no external detector, while a Ray-Based Camera Solver supports a second configuration that needs no test-time camera intrinsics. Across five egocentric benchmarks, DreamHand sets a new state of the art, cutting MPJPE-p by 30% on occlusion-heavy ARCTIC and 40% on HOT3D. These gains reach 46%-61% once out-of-sight hands are included in the evaluation, offering a scalable path from everyday human video to robot manipulation data.

Generative models have shown strong potential for positron emission tomography (PET) image reconstruction. Although diffusion model-based reconstruction methods have demonstrated promising performance, they often require many reverse sampling steps with data-consistency updates incorporated into the sampling process. Flow matching offers an attractive alternative because it can directly estimate clean images from intermediate states, allowing data-consistency refinement to be separated from flow propagation. In this work, we proposed flow matching-based PET image reconstruction methods. We first established PET-FlowDPS by incorporating Poisson likelihood guidance with an expectation-maximization (EM)-based preconditioner into the FlowDPS framework. We then proposed a model-based PET reconstruction method that used a pretrained flow matching model as a prior, in which the flow-based prior, PET data refinement, and stochastic propagation were interpreted within an approximate Bayesian framework. Experimental results using [$^{\text{18}}\text{F}$]FDG brain PET datasets showed that the proposed method achieved better bias-variance trade-offs across different dose levels compared with other reference methods. These results demonstrated the potential of flow matching as a generative prior for quantitative PET image reconstruction.

We study the stability of minimal representations of controlled stochastic processes (in particular, transducers) under perturbations. This question is motivated by recent experiments finding predictive-state structure in the latent representations of neural networks. We consider standard, linear and predictive transducers. We introduce notions of approximate homomorphism capturing local structural similarity between them, together with metrics comparing their induced dynamics (which we refer to as interfaces), and prove properties such as composability of the approximate homomorphisms. For standard transducers, we show that there exist simple interfaces for which there is no approximate homomorphism between the different implementations of the dynamics. In contrast, for every finite-rank interface $\mathcal I$, we prove that all minimal linear transducers implementing interfaces sufficiently close to $\mathcal I$ have an approximate homomorphism to the minimal implementation of $\mathcal I$, with error linear in the perturbation size. We prove an analogous stability result for predictive transducers under a residual metric using some mild hypothesis regarding the indistinguishability of the belief states. These results identify conditions under which canonical transducer representations are robust to perturbations, while showing that such convergence fails without additional structural restrictions. Under the assumption that these type of abstractions are embedded into the hidden layers of modern AI models, this gives some theoretical support to the hypothesis that their latent representations exhibit structural convergence.

Bayesian inference via Markov Chain Monte Carlo (MCMC) provides effective parameter estimation, but its real-time application in complex physical systems is hindered by heavy computational bottlenecks and extreme sensitivity to statistical noise. We address this by proposing a neural-network-based probabilistic surrogate framework for rapid and robust MCMC inference. Using fusion plasma Thomson scattering diagnostics as a challenging, noise-dominated testbed, our approach employs a dual-head architecture to simultaneously estimate the expected physical emission spectrum and the channel-wise intrinsic measurement noise variance. By optimizing a Gaussian Negative Log-Likelihood (GNLL) objective, the learned aleatoric uncertainty dynamically buffers the sampler against pathological shot noise. Evaluations demonstrate that this surrogate framework achieves > 1500x acceleration over exact physical forward models, while simultaneously reducing inference error (RMSE) by >20% compared to standard homoscedastic neural baselines, offering a highly promising paradigm for real-time physical analysis.

We propose a conditioning mechanism for diffusion models based on multi-speed joint diffusion of the target and the condition. The mechanism learns an unconditional joint score network and enforces conditioning at inference via a plug-in correction term. The plug-in term separates the conditioning contribution from the learned unconditional dynamics, offering a transparent view of how the condition steers generation of the target distribution. Building on this, we derive explicit conditional reverse-time SDEs and approximate probability-flow ODEs, enabling principled and directly comparable conditional samplers. To reduce the induced ODE--SDE discrepancy, we introduce a log-Fokker--Planck residual regularization that improves ODE sampling quality. Experiments on conditional image generation tasks demonstrate competitive performance and support the effectiveness of the plug-in conditioning view. Additional ODE--SDE comparison experiments show that the log-Fokker--Planck residual regularization improves deterministic ODE sampling.

We introduce a failure-aware adversarial retrieval-augmented framework for improving robustness in natural language understanding. Rather than selecting synthetic examples with a fixed reward threshold, our method formulates adversarial data curation as a failure-mode contextual bandit problem. Candidate examples are generated with retrieval-augmented prompting, filtered by the current target model, automatically validated by an LLM judge ensemble, and clustered into recurring failure modes. A stochastic policy then selects which failure modes to sample for retraining, and is updated using validation-based reward that balances robustness gains, forgetting, and data cost. This makes the data curator itself the learning agent, enabling adaptive selection of the most useful model failures across training rounds. On standard benchmarks, our approach improves RoBERTa-base accuracy from 88.48% to 92.60% on SNLI, from 75.04% to 80.95% on ANLI, and from 54.67% to 71.99% on MultiNLI, while consistently outperforming prior adversarial augmentation methods. We further demonstrate transfer to FEVER fact verification, achieving up to 79.86% FEVER score and 82.45% accuracy with RoBERTa-large. Finally, we provide a theoretical interpretation showing that, under stated assumptions, failure-mode sampling can reduce shortcut-aligned gradient contributions while inducing bounded distributional drift. By combining retrieval, automated validation, contextual-bandit failure selection, and controlled adversarial retraining, our framework enables scalable robustness improvement without additional human annotation.

Hard combinatorial optimization problems, many of which are NP-hard, present fundamental algorithmic challenges. Average-case analysis on random instances has emerged as a powerful framework for understanding typical algorithmic performance beyond worst-case guarantees. A substantial body of work has established negative results: for sufficiently hard instances (often controlled by the underlying graph connectivity/constraints density), no known polynomial-time algorithm can significantly outperform naive heuristics in the double asymptotic limit where both problem size and constraints density tend to infinity. We revisit this picture by studying the finite-size behavior of some optimization algorithms across easy, intermediate, and hard regimes. Through rigorous analysis of large-graph asymptotics combined with numerical experiments on canonical problems (maximum independent set and maximum $K$-SAT), we demonstrate that while algorithms do eventually converge to theoretically predicted bounds, this convergence can be remarkably slow. In the intermediate regime where instances are already highly constrained, local algorithms achieve solutions substantially better than their predicted performance in the high-constraint-density limit. This gap between finite-regime and asymptotic behavior has important practical implications: sophisticated algorithmic design remains crucial even when asymptotic theory predicts inevitable failure.

Graph generation models have advanced significantly with deep learning, yet they remain limited in scalability, flexibility, and ability to model underlying structures. We present GraphK, a novel encoder-sampler-decoder framework for graph generation that overcomes these challenges through structural flexibility and computational efficiency. Unlike autoregressive approaches constrained by vocabulary size (i.e. number of nodes in graph generation), GraphK allows for both upscaling (generating graphs with more nodes than the input) and downscaling, providing a flexible control over output graph size. By learning permutation-invariant latent representations and sampling new node embeddings via maximum likelihood estimation, GraphK generalizes across graph sizes and structures. For edge generation, we employ edge prediction with a KDTree-based top-k neighbor search in the latent space, reducing computational cost. Based on the manifold smoothness assumption, our method effectively captures graph properties. Experiments on synthetic and real-world datasets show that GraphK outperforms existing methods, accurately learns graph structures, and generates synthetic graphs without explicit definitions.

We address two open questions in streaming PCA via Oja's algorithm: sharp operator-norm convergence for general rank under sub-Gaussian data, and distributional inference for the resulting subspace estimator. Existing convergence analyses, even in the rank-one case, either assume bounded data or leave non-vanishing remainder terms that prevent adaptation to a polynomially vanishing tail spectrum, while existing distributional results are confined to the rank-one case. Our convergence theory removes these remainder terms and yields a sharp rate. In the dense-tail spiked covariance regime, this rate matches the minimax rate up to logarithmic factors. More generally, we prove a matching lower bound, up to logarithmic factors, across both dense-tail and sparse-tail regimes under a mild nondegeneracy condition. The analysis yields a linearization of Oja's iterates, which in turn enables a high-dimensional Gaussian approximation for the general-rank subspace estimation error with an explicit limiting covariance. We also establish a row-wise Gaussian approximation over convex sets for the aligned difference, recovering prior rank-one results as special cases. For practical inference, we develop an online multiplier bootstrap algorithm and prove its consistency. Beyond streaming PCA, our techniques contribute to Gaussian approximation and bootstrap inference for nonconvex stochastic approximation.

We present Depth Anything V4 (DAV4), a framework for dynamic 4D scene reconstruction from monocular video. Our key contribution is the application of Riemannian Flow Matching (RFM) to 4D Gaussian Splatting parameters, defining probability paths directly on non-Euclidean manifolds (scale, rotation, opacity), ensuring all intermediate states are valid. Through controlled experiments, we isolate RFM's contribution from test-time optimization (TTO) and pre-training. A deterministic MLP baseline with the same data, architecture, and TTO achieves F-score 0.762; RFM achieves 0.806 - the +0.044 gain is RFM's isolated contribution. We provide corrected computational cost analysis: pre-training is 360 GPU-hours, amortizing for large-scale deployment (over 10,000 scenes). Uncertainty is quantified via Negative Gaussian Log-Likelihood and Expected Calibration Error. DAV4 outperforms prior Depth Anything models and per-scene 4D-GS on dynamic reconstruction and novel-view synthesis, while using no human-annotated depth labels as training losses.

Inverse learning within a statistical framework has a wide range of applications. It has garnered significant attention in machine learning, artificial intelligence, and related fields, where the goal is to infer unknown parameters from indirect and noisy observations. This work investigates the stable approximation of $u^{\dagger}$ which solves the equation $Au=g$, with $A$ being a linear operator between appropriate vector spaces. We will consider the domain to be a non-reflexive Banach Space and the co-domain to be a space of real-valued functions on a metric space $X$. The function $g$ is characterized by a finite number of independently and identically distributed data points, which are assumed to follow some unknown probability measure $ρ$. We employ Tikhonov regularization with an arbitrary convex functional to obtain the regularized solution corresponding to the given data point. The convergence analysis is carried out with respect to the Bregman distance, and an upper bound for the error is derived in probability terms. The theoretical findings are then supported by numerical experiments.

In the Code World Model paradigm an LLM synthesizes an executable world model that a classical planner searches, and the model is accepted when it reproduces sampled transitions. We ask what that acceptance certifies in continuous control. We define the pipeline's danger as an expected risk and isolate its exact factor: the probability that N i.i.d. gate rollouts all miss a critical event of probability r is exactly (1-r)^N; an independent acceptance sample adds its budget to the exponent. On three hybrid instruments the accepted mode-blind model is exploited: the planner is pinned at the mode boundary at a regret of nearly the whole attainable return. We prove a localization budget, valid at boundary points: models with Lipschitz constant at most L differing by eta at a point disagree above tolerance eps on a region of volume at least kappa((eta-eps)/L)^(d+m); the discontinuous reset modes studied pay no such budget. With real LLM synthesis, GPT-5.x repairs an omitted 1D clamp in 105 of 111 mode-containing draws — every attempt exact on 50 of 56 instrument-stream blocks (95% CI [0.781, 0.960]). On 2D regions no artifact recovers the rule (0/156); eight targeted interventions leave the failure in place, and positive controls locate it: a located rule is not induced, while given form and location the constants follow exactly. A version-space certificate proves identification is class-relative: at the widest dose the declared fit succeeds in 20/20 blocks and every sample-consistent circle is within tolerance in 18/20. We prove a class of entry rules exactly consistent with every sample yet harmless at play, so identifiability is a measurable property of the instrument. Re-scoring all 1034 artifacts on independent samples confirms acceptance certifies sample consistency and no more: where the gate is provably informative it covers about two percent of the exploited planner's queries.

Flow matching models for video generation achieve impressive performance but suffer from high computational overhead due to iterative denoising. In fact, the original model is not necessary for all denoising steps, allowing some steps to use lightweight alternatives for faster sampling. However, directly using caching or lightweight models can deviate from the original denoising trajectory, resulting in suboptimal performance. Through empirical analysis, we find that lightweight models can robustly capture the magnitude components of the original model's output, while caching provides reliable directional guidance. Building on this insight, we propose the Magnitude-Direction Decoupling (MDD) method, which adaptively employs a direction-calibrated lightweight model as a substitute for the original model to accelerate inference and effectively correct deviations in the denoising trajectory. Moreover, MDD further reduces inference costs by reusing magnitude information under classifier-free guidance (CFG). As a result, MDD offers a more reliable and lightweight solution to accelerate sampling. Experiments show that MDD outperforms existing acceleration methods, delivering promising speedups (e.g., up to 2.95x on Wan2.1) while preserving high visual fidelity and content richness.

Although text-to-image diffusion models exhibit remarkable generative power, concept erasure techniques are essential for preventing harmful content. Existing adversarial probes evaluate these methods by testing whether erased concepts can still be recovered. However, existing erasure and probe methods remain largely text-centric, focusing on whether the text-to-image mapping is severed while overlooking whether the corresponding visual knowledge remains. To investigate this question from a visual perspective, we leverage diffusion inversion to probe whether a generative trajectory can reconstruct visual instances of an erased concept. Under a null-text condition, standard inversion avoids the textual pathway but amplifies approximation errors, hindering faithful trajectory recovery. To address this challenge, we introduce TINA+, a diffusion-consistent Text-free INversion Attack equipped with optimization-based inversion. We also find that unconstrained diffusion inversion may discover spurious trajectories, even allowing a randomly initialized diffusion model to reconstruct the target concept. Such trajectories may falsely indicate residual visual knowledge. TINA+ therefore introduces Diffusion-Consistent Trajectory Regularization to suppress this failure mode. By penalizing trajectories that fall far below the expected marginal energy evolution of diffusion, TINA+ suppresses spurious inversion paths while preserving its ability to recover erased concepts. Experiments across twelve erasure methods, four concept-erasure tasks, and different model architectures demonstrate that TINA+ reliably probes residual visual knowledge through diffusion-consistent visual trajectories. These results provide stronger evidence that current methods often obscure concepts by severing text-image links rather than eliminating the underlying visual knowledge.

Diffusion models have achieved remarkable success in image and video generation, yet the high computational cost of iterative sampling remains a critical bottleneck for practical deployment. Feature caching has emerged as a promising acceleration paradigm by reusing or predicting intermediate features across timesteps. However, existing training-free methods apply uniform prediction strategies that cannot adapt to the heterogeneous feature dynamics, causing significant quality degradation under high acceleration ratios. We propose LinCa, a feature caching framework based on learnable invertible networks. LinCa decomposes cached features into sub-components with distinct continuity properties via a lightweight invertible network and applies differentiated prediction orders matched to each component. The strict invertibility guarantees lossless reconstruction back to the original feature space, forming a unified Decompose-Predict-Reconstruct pipeline. By training separate predictors for different models and timestep segments, LinCa adapts to heterogeneous feature dynamics. Experiments on FLUX, Qwen-Image, and HunyuanVideo demonstrate that LinCa, with less than 0.2% additional parameters, significantly outperforms existing methods and maintains near-lossless quality at 5-7x speedup. Code: https://github.com/QHR69/LinCa

Sampling from a diffusion model typically requires many forward passes through a large neural network, making generation computationally expensive. While much work has focused on efficient solvers and samplers, comparatively little attention has been paid to selecting the sampling timesteps themselves. A recent line of work optimizes theoretically derived surrogates for sample quality rather than the quality metric itself. We propose Optimizing Your Sampling (OYS), which instead treats timestep selection as a black-box optimization problem, optimizing the target metric directly with Bayesian optimization. OYS outperforms both the default schedules and those of Align Your Steps on text-to-image generation, and improves over the default schedules on inpainting and other image tasks, in both quantitative and human evaluations. OYS requires no additional training, is applicable even to distilled models, and improves both simple and sophisticated samplers such as Euler and DPM-Solver++. A 5-step OYS schedule retains 89%-94% of the quality of a 50-step schedule while reducing inference cost by 10x.

Bayesian imaging inverse problems often require sampling from high-dimensional posterior distributions. While recent score-based and diffusion models provide expressive Bayesian priors, their sampling procedures remain inherently sequential and computationally expensive for large-scale imaging applications. We propose PiX-MC, a time-parallel posterior sampling framework based on proximal Langevin dynamics and Picard iteration. The proximal-likelihood formulation exploits the fact that many imaging likelihoods admit efficient, problem-specific proximal operators, while Picard refinement exposes parallelism across discretization nodes and naturally supports multi-GPU implementation. To further improve practical scalability and sampling performance, we develop multi-block and annealed variants of the proposed framework. We establish convergence guarantees under transparent assumptions, accommodating non-log-concave posteriors, imperfect learned score models, multi-block implementations, and annealing schedules. Experiments on a diverse collection of imaging inverse problems demonstrate that PiX-MC substantially reduces wall-clock time while preserving reconstruction quality. On a $512\times512\times80$ sparse-view computed tomography (CT) problem, annealed multi-block PiX-MC achieves up to a $50\times$ runtime speedup over the standard Langevin sampler using eight GPUs.

Compute-optimal scaling laws guide the training of frontier language models yet remain largely unexplored for visual generation. We present a systematic scaling law study for text-to-image diffusion models using Abra, a controlled family of flow-matching transformers trained across three orders of magnitude worth of compute ($10^{19}$ to $10^{22}$ FLOPs), reaching significantly larger compute budgets than previous works. We demonstrate that diffusion models scale just as predictably as language models but require far more data to train optimally: compute optimality occurs at approximately $200$ image tokens per parameter, ten times the Chinchilla compute-optimal prescription for LLMs. We show that unlike language models, diffusion models are robust to overtraining and that practitioners should err on the side of more data rather than a larger model. Finally, we show that this predictability extends beyond training loss to generative quality metrics, optimal CFG settings, representation quality, and even the shape of the training curves, which collapse onto a universal form.

RISC-V standardizes two processor-trace formats, N-Trace and E-Trace, that share a hart-to-encoder instruction trace interface but differ in compression, messages, and framing. To the best of our knowledge, as of August 2026, no publicly available synthesizable N-Trace encoder and no published hardware encoder with both back ends behind a common front end have been reported. We present CTTE (CEDARtools.TraceEncoder), an open SystemVerilog encoder with a protocol-agnostic front end and selectable N-Trace/Nexus or E-Trace back ends. CTTE implements the N-Trace 1.0 program-trace message set in both instruction-trace modes, supports parameterized N-Trace address width, follows the RISC-V Trace Control Interface, and announces output-bandwidth loss before state re-convergence on the evaluated N-Trace path. CTTE has been integrated with six RISC-V cores from five suppliers. We evaluate 64-bit RISC-V systems booting Linux, including a two-hart SMP system, and demonstrate source-side process-context filtering that doubles observation depth for a target process in a fixed buffer. Verification combines instruction-exact round trips, RTL invariants, formal model checking, and machine-judged hardware campaigns with negative controls. With hardware and configuration held constant, workload choice changes trace cost from 0.21 to 4.90 bits per retired instruction. A common front end also enables controlled back-end comparisons while exposing synchronization and transport effects that must be separated from wire-format effects. RTL, register sources, tests, formal properties, decoder extensions, and build scripts are released under CERN-OHL-S-2.0; proprietary integration is available under an Accemic commercial license.

Despite groundbreaking advancements in generative models during the last decade, concerns about their lack of fairness, reinforcing societal inequalities and harming marginalized groups, remain under-addressed and difficult to act upon. This position paper argues that fairness failures in generative models, albeit driven by multiple factors, are ultimately stemming from an evaluation problem: fairness findings are rarely comparable across papers or actionable for deployment decisions. This paper diagnoses recurring empirical and conceptual failure modes in current practice and motivates a shift from ad-hoc bias checks to standardized, generative-specific evaluation. We propose Fairness Cards as a minimal reporting artifact that makes evaluation choices explicit (prompt families, counterfactual protocols, metrics, and refusal handling) enabling reproducibility, comparability, and accountability. We conclude with additional recommendations towards a paradigm shift in evaluation standards. Our project page can be found at https://mariiavladimirova.github.io/fairness-cards .

Generative image semantic communication converts an image into a text description and then performs text-to-image reconstruction at the receiver via diffusion-based generative models. This paradigm has attracted broad attention due to its extremely low bandwidth cost. However, existing methods still face two critical bottlenecks across image-to-text (I2T) semantic extraction at the transmitter and text-to-image (T2I) semantic reconstruction at the receiver: (i) semantic loss and distortion in I2T, where holistic image descriptions may omit fine-grained object attributes and spatial-position information, causing the generated text to deviate from the original image semantics; and (ii) insufficient semantic faithfulness in T2I, where even with the same semantically faithful text description, different initial noise settings may lead diffusion-based reconstruction to produce images with different levels of semantic consistency with the original image. These issues jointly limit the semantic faithfulness of image reconstruction. To address them, we propose TISC, a text-driven image semantic communication framework tailored for faithful reconstruction. TISC incorporates two key designs: (1) Tree-Structured Attribute Semantic Extraction (TSASE), which decomposes semantic extraction into global scene, background, and object-level attribute descriptions, covering spatial position, shape/pose, color, material, and other physical attributes for each detected object; and (2) an Initial Noise Optimization (INO) mechanism, which selects an initial noise seed at the transmitter according to a comprehensive similarity score that jointly considers visual and semantic consistency. Experiments on multiple datasets show that TSASE improves object-position recovery and semantic description faithfulness, while the INO parameter study supports the adopted configuration for noise selection.

In over-the-counter corporate bond markets, dealers compete for client trades by quoting bid and ask prices. Tighter quotes attract more business, but also informed customers more likely to trade ahead of adverse price moves, leaving the dealer holding the risk. As dealers increasingly use machine learning to set quotes, they retrain these models on the trades their own quotes attract, creating a feedback loop in which each model reshapes the market that generates its next training data. The question is therefore not only whether a quoting model performs well, but whether the market it creates stays stable as the model learns from it. Existing performative prediction theory gives a sharp stability condition, yet expresses it through abstract properties of the learning objective a trading desk cannot measure before deployment. We introduce REFLEX, a framework that replaces those unobservable quantities with three measurable features of dealer behavior: how strongly trading volume responds to tighter quotes, how sharply the dealer's objective bends around its optimum, and how quickly informed flow increases as spreads narrow. REFLEX combines these into a single retraining modulus, a pre-deployment stability margin estimated from a desk's own quote and execution history that predicts whether repeated retraining will converge or amplify itself. In simulation, predicted and measured stability agree within 8%, and competing dealers increase instability by 1.74x with two and 3.16x with three, as predicted. Where ordinary retraining becomes unstable at modulus 1.21, a structurally anchored correction converges as blind retraining collapses. Calibrated over 36 years of public market data, stability headroom falls roughly 4.4x for investment grade and 4.3x for high yield from calm to crisis regimes. Ultimately, REFLEX turns an abstract convergence theorem into a market-level safety margin.

Reliable optimization is central to neural network (NN) training, yet Adam, the default optimizer for modern LLMs, rests on a fragile foundation. This thesis develops a principled grounding for Adam and motivates new designs. First, we revisit Adam's divergence--convergence debate and show the existence of a problem-dependent phase transition: with properly chosen, batch-size-dependent hyperparameters, Adam converges, whereas under small-$β_2$ regimes it can diverge. Second, we investigate why Adam substantially outperforms SGD on Transformers through Hessian structure. We find that the Hessian evolves toward a near-block-diagonal form along training, accompanied by strong block heterogeneity. We prove that this structure makes Adam's diagonal preconditioner effective. We further show that this special Hessian structure originates from consecutive multiplications of large matrix variables, and we provide a rigorous analysis based on random matrix theory. Finally, these insights motivate Adam-mini, a new optimizer that reduces Adam's memory footprint by 50% while preserving its performance. Our results also have broader implications beyond Adam: they reveal new local structures in matrix-based nonconvex problems, and also help understand and improve recent NN optimizers, such as Muon.

Generative modeling has shown increasing promise for predicting cellular perturbation effects under chemical compound treatments. Existing approaches either model perturbation as a distribution-to-distribution mapping without explicit concentration handling, or treat concentration as a discrete class label, precluding continuous dose control. We introduce a joint flow matching approach that simultaneously models cell latents and drug concentration via a dual-timestep formulation, enabling dose-conditioned single-cell morphing through the invertibility of flow matching. The joint formulation induces a monotonic dose-response geometry in latent space and additionally supports concentration estimation from cell morphology. As proof of concept, we further demonstrate generalization to an unseen dose held out during training. Empirically, our method achieves competitive or improved per-concentration metrics on two compounds compared with representative baselines, while enabling capabilities structurally unavailable to discrete-class methods.

Recent advances in diffusion models and Transformer architectures have led to significant progress in text-to-video generation. However, these models often suffer from semantic errors such as missing objects, incorrect attributes, or mismatched actions. Although some semantic correction methods perform optimization before sampling or refinement after sampling, how to detect and correct semantic deviations during the video generation process remains underexplored. In this paper, we introduce a training-free, interpretable mid-generation correction framework that integrates multimodal large language model (MLLM) feedback directly into the diffusion sampling loop. Our framework achieves diffusion trajectory correction by injecting semantic evaluation signals during video synthesis, enabling the model to optimize the generated content through continuous self-reflection. We propose two key modules: a Semantic Assessment Supervisor that generates intermediate preview frames for semantic evaluations and deviation diagnostics, and a Semantic Modification Assistant that corrects semantic drift during inference via a controllable latent trajectory intervention. Our method improves semantic alignment, visual fidelity, and temporal consistency without modifying model parameters. We validate the effectiveness of our approach through extensive experiments across multiple benchmarks.

Model Inversion Attacks (MIAs) aim to reconstruct representative training samples of target identities from face recognition models, exposing critical security vulnerabilities. Existing methods typically rely on indirect guidance or highly stochastic guidance, making it difficult to stably optimize generation trajectories toward target facial images. In this paper, we propose Steering Flow Model Inversion (SFMI), a novel two-stage white-box model inversion method that reformulates inversion as a trajectory-steering task. Specifically, Step I, Learning a Generic Flow Matching Prior, pre-trains a generic unconditional Flow Matching model to encode the manifold of human faces as a robust prior. Step II, Attacking with Progressive Guidance Scheduler (PGS), injects time-dependent target-specific gradients during sampling. By backpropagating through the target model to obtain gradients from intermediate generated states, PGS progressively injects adaptive guidance signals into the vector field. This process effectively steers the current generative flow from random noise toward the high-density regions of the target class. Under an identity-disjoint cross-evaluation setting using the CelebA dataset, SFMI achieves an ACC of 0.9248, an FID of 22.61, and an LPIPS of 0.3874 on the ArcFace target. Extensive experiments on multiple target models demonstrate that SFMI achieves competitive state-of-the-art performance in attack success and visual fidelity under the evaluated white-box protocol.