We introduce Holographic Invariant Storage (HIS), a protocol that assembles known properties of bipolar Vector Symbolic Architectures into a design-time safety contract for LLM context-drift mitigation. The contract provides three closed-form guarantees evaluable before deployment: single-signal recovery fidelity converging to $1/\sqrt{2} \approx 0.707$ (regardless of noise depth or content), continuous-noise robustness $2Φ(1/σ) - 1$, and multi-signal capacity degradation $\approx\sqrt{1/(K+1)}$. These bounds, validated by Monte Carlo simulation ($n = 1{,}000$), enable a systems engineer to budget recovery fidelity and codebook capacity at design time -- a property no timer or embedding-distance metric provides. A pilot behavioral experiment (four LLMs, 2B--7B, 720 trials) confirms that safety re-injection improves adherence at the 2B scale; full results are in an appendix.

Recovering linear subspaces from data is a fundamental and important task in statistics and machine learning. Motivated by heterogeneity in Federated Learning settings, we study a basic formulation of this problem: the principal component analysis (PCA), with a focus on dealing with irregular noise. Our data come from $n$ users with user $i$ contributing data samples from a $d$-dimensional distribution with mean $\mu_i$. Our goal is to recover the linear subspace shared by $\mu_1,\ldots,\mu_n$ using the data points from all users, where every data point from user $i$ is formed by adding an independent mean-zero noise vector to $\mu_i$. If we only have one data point from every user, subspace recovery is information-theoretically impossible when the covariance matrices of the noise vectors can be non-spherical, necessitating additional restrictive assumptions in previous work. We avoid these assumptions by leveraging at least two data points from each user, which allows us to design an efficiently-computable estimator under non-spherical and user-dependent noise. We prove an upper bound for the estimation error of our estimator in general scenarios where the number of data points and amount of noise can vary across users, and prove an information-theoretic error lower bound that not only matches the upper bound up to a constant factor, but also holds even for spherical Gaussian noise. This implies that our estimator does not introduce additional estimation error (up to a constant factor) due to irregularity in the noise. We show additional results for a linear regression problem in a similar setup.

In this paper, we introduce a novel technique called Tree-Ring Watermarking that robustly fingerprints diffusion model outputs. Unlike existing methods that perform post-hoc modifications to images after sampling, Tree-Ring Watermarking subtly influences the entire sampling process, resulting in a model fingerprint that is invisible to humans. The watermark embeds a pattern into the initial noise vector used for sampling. These patterns are structured in Fourier space so that they are invariant to convolutions, crops, dilations, flips, and rotations. After image generation, the watermark signal is detected by inverting the diffusion process to retrieve the noise vector, which is then checked for the embedded signal. We demonstrate that this technique can be easily applied to arbitrary diffusion models, including text-conditioned Stable Diffusion, as a plug-in with negligible loss in FID. Our watermark is semantically hidden in the image space and is far more robust than watermarking alternatives that are currently deployed.

Climate change has intensified the frequency and severity of wildfires, making rapid and accurate prediction of fire spread essential for effective mitigation and response. Physics-based simulators such as FARSITE offer high-fidelity predictions but are computationally intensive, limiting their applicability in real-time decision-making, while existing deep learning models often yield overly smooth predictions that fail to capture the complex, nonlinear dynamics of wildfire propagation. This study proposes an autoregressive conditional generative adversarial network (CGAN) for probabilistic wildfire spread prediction. By formulating the prediction task as an autoregressive problem, the model learns sequential state transitions, ensuring long-term prediction stability. Experimental results demonstrate that the proposed CGAN-based model outperforms conventional deep learning models in both overall predictive accuracy and boundary delineation of fire perimeters. These results demonstrate that adversarial learning allows the model to capture the strong nonlinearity and uncertainty of wildfire spread, instead of simply fitting the pixel average. Furthermore, the autoregressive framework facilitates systematic temporal forecasting of wildfire evolution. The proposed CGAN-based autoregressive framework enhances both the accuracy and physical interpretability of wildfire spread prediction, offering a promising foundation for time-sensitive response and evacuation planning.

Diffusion models are state-of-the-art generative models, yet their samples often fail to satisfy application objectives such as safety constraints or domain-specific validity. Existing techniques for alignment require gradients, internal model access, or large computational budgets resulting in high compute demands, or lack of support for certain objectives. In response, we introduce an inference-time alignment framework based on evolutionary algorithms. We treat diffusion models as black boxes and search their latent space to maximize alignment objectives. Given equal or less running time, our method achieves 3-35% higher ImageReward scores than gradient-free and gradient-based methods. On the Open Image Preferences dataset, our method achieves competitive results across four popular alignment objectives. In terms of computational efficiency, we require 55% to 76% less GPU memory and are 72% to 80% faster than gradient-based methods.

While zero-shot diffusion-based compression methods have seen significant progress in recent years, they remain notoriously slow and computationally demanding. This paper presents an efficient zero-shot diffusion-based compression method that runs substantially faster than existing methods, while maintaining performance that is on par with the state-of-the-art techniques. Our method builds upon the recently proposed Denoising Diffusion Codebook Models (DDCMs) compression scheme. Specifically, DDCM compresses an image by sequentially choosing the diffusion noise vectors from reproducible random codebooks, guiding the denoiser's output to reconstruct the target image. We modify this framework with Turbo-DDCM, which efficiently combines a large number of noise vectors at each denoising step, thereby significantly reducing the number of required denoising operations. This modification is also coupled with an improved encoding protocol. Furthermore, we introduce two flexible variants of Turbo-DDCM, a priority-aware variant that prioritizes user-specified regions and a distortion-controlled variant that compresses an image based on a target PSNR rather than a target BPP. Comprehensive experiments position Turbo-DDCM as a compelling, practical, and flexible image compression scheme.

Pretrained diffusion models have demonstrated strong capabilities in zero-shot inverse problem solving by incorporating observation information into the generation process of the diffusion models. However, this presents an inherent dilemma: excessive integration can disrupt the generative process, while insufficient integration fails to emphasize the constraints imposed by the inverse problem. To address this, we propose \emph{Noise Combination Sampling}, a novel method that synthesizes an optimal noise vector from a noise subspace to approximate the measurement score, replacing the noise term in the standard Denoising Diffusion Probabilistic Models process. This enables conditional information to be naturally embedded into the generation process without reliance on step-wise hyperparameter tuning. Our method can be applied to a wide range of inverse problem solvers, including image compression, and, particularly when the number of generation steps $T$ is small, achieves superior performance with negligible computational overhead, significantly improving robustness and stability.