The rapid advancement of diffusion models has enabled high-fidelity and semantically rich text-to-image generation; however, ensuring fairness and safety remains an open challenge. Existing methods typically improve fairness and safety at the expense of semantic fidelity and image quality. In this work, we propose RespoDiff, a novel framework for responsible text-to-image generation that incorporates a dual-module transformation on the intermediate bottleneck representations of diffusion models. Our approach introduces two distinct learnable modules: one focused on capturing and enforcing responsible concepts, such as fairness and safety, and the other dedicated to maintaining semantic alignment with neutral prompts. To facilitate the dual learning process, we introduce a novel score-matching objective that enables effective coordination between the modules. Our method outperforms state-of-the-art methods in responsible generation by ensuring semantic alignment while optimizing both objectives without compromising image fidelity. Our approach improves responsible and semantically coherent generation by ~20% across diverse, unseen prompts.

We propose a method for non-parametric conditional distribution estimation based on partitioning covariate-sorted observations into contiguous bins and using the within-bin empirical CDF as the predictive distribution. Bin boundaries are chosen to minimise the total leave-one-out Continuous Ranked Probability Score (LOO-CRPS), which admits a closed-form cost function with $O(n^2 \log n)$ precomputation and $O(n^2)$ storage; the globally optimal $K$-partition is recovered by a dynamic programme in $O(n^2 K)$ time. Minimisation of within-sample LOO-CRPS turns out to be inappropriate for selecting $K$ as it results in in-sample optimism. We instead select $K$ by $K$-fold cross-validation of test CRPS, which yields a U-shaped criterion with a well-defined minimum. Having selected $K^*$ and fitted the full-data partition, we form two complementary predictive objects: the Venn prediction band and a conformal prediction set based on CRPS as the nonconformity score, which carries a finite-sample marginal coverage guarantee at any prescribed level $\varepsilon$. The conformal prediction is transductive and data-efficient, as all observations are used for both partitioning and p-value calculation, with no need to reserve a hold-out set. On real benchmarks against split-conformal competitors (Gaussian split conformal, CQR, CQR-QRF, and conformalized isotonic distributional regression), the method produces substantially narrower prediction intervals while maintaining near-nominal coverage.

Infact, the SDPmaybeinexacteven fork =3 (see Section 8). Suppose program to(2) (3) (4) (5) nonemptyfeasibleset.

It is an open question whether the search and decision versions of promise CSPs are equivalent. Most known algorithms for PCSPs solve only their \emph{decision} variant, and it is unknown whether they can be adapted to solve \emph{search} as well. The main approaches, called BLP, AIP and BLP+AIP, handle a PCSP by finding a solution to a relaxation of some integer program. We prove that rounding those solutions to a proper search certificate can be as hard as any problem in the class TFNP. In other words, these algorithms are ineffective for search. Building on the algebraic approach to PCSPs, we find sufficient conditions that imply ineffectiveness for search. Our tools are tailored to algorithms that are characterized by minions in a suitable way, and can also be used to prove undecidability results for meta-problems. This way, we show that the families of templates solvable via BLP, AIP, and BLP+AIP are undecidable. Using the same techniques we also analyze several algebraic conditions that are known to guarantee the tractability of finite-template CSPs. We prove that several meta-problems related to cyclic polymorphims and WNUs are undecidable for PCSPs. In particular, there is no algorithm deciding whether a finite PCSP template (1) admits cyclic a polymorphism, (2) admits a WNU.

Generative models of 3D cardiovascular anatomy can synthesize informative structures for clinical research and medical device evaluation, but face a trade-off between geometric controllability and realism. We propose CardioComposer: a programmable, inference-time framework for generating multi-class anatomical label maps based on interpretable ellipsoidal primitives. These primitives represent geometric attributes such as the size, shape, and position of discrete substructures. We specifically develop differentiable measurement functions based on voxel-wise geometric moments, enabling loss-based gradient guidance during diffusion model sampling. We demonstrate that these losses can constrain individual geometric attributes in a disentangled manner and provide compositional control over multiple substructures. Finally, we show that our method is compatible with a wide array of anatomical systems containing non-convex substructures, spanning cardiac, vascular, and skeletal organs.

Estimating properties of discrete distributions is a fundamental problem in statistical learning.

Online decision systems routinely operate under delayed feedback and order-sensitive (noncommutative) dynamics: actions affect which observations arrive, and in what sequence. Taking a Bregman divergence $D_Φ$ as the loss benchmark, we prove that the excess benchmark loss admits a structured lower bound $L \ge L_{\mathrm{ideal}} + g_1(λ) + g_2(\varepsilon_\star) + g_{12}(λ,\varepsilon_\star) - D_{\mathrm{ncx}}$, where $g_1$ and $g_2$ are calibrated penalties for latency and order-sensitivity, $g_{12}$ captures their geometric interaction, and $D_{\mathrm{ncx}}\ge 0$ is a nonconvexity/approximation penalty that vanishes under convex Legendre assumptions. We extend this inequality to prox-regular and weakly convex settings, obtaining robust guarantees beyond the convex case. We also give an operational recipe for estimating and monitoring the four terms via simple $2\times 2$ randomized experiments and streaming diagnostics (effective sample size, clipping rate, interaction heatmaps). The framework packages heterogeneous latency, noncommutativity, and implementation-gap effects into a single interpretable lower-bound statement that can be stress-tested and tuned in real-world systems.