🤖 AI Daily Digest

We present Edit3r, a feed-forward framework that reconstructs and edits 3D scenes in a single pass from unposed, view-inconsistent, instruction-edited images. Unlike prior methods requiring per-scene optimization, Edit3r directly predicts instruction-aligned 3D edits, enabling fast and photorealistic rendering without optimization or pose estimation. A key challenge in training such a model lies in the absence of multi-view consistent edited images for supervision. We address this with (i) a SAM2-based recoloring strategy that generates reliable, cross-view-consistent supervision, and (ii) an asymmetric input strategy that pairs a recolored reference view with raw auxiliary views, encouraging the network to fuse and align disparate observations. At inference, our model effectively handles images edited by 2D methods such as InstructPix2Pix, despite not being exposed to such edits during training. For large-scale quantitative evaluation, we introduce DL3DV-Edit-Bench, a benchmark built on the DL3DV test split, featuring 20 diverse scenes, 4 edit types and 100 edits in total. Comprehensive quantitative and qualitative results show that Edit3r achieves superior semantic alignment and enhanced 3D consistency compared to recent baselines, while operating at significantly higher inference speed, making it promising for real-time 3D editing applications.

Online joint estimation of unknown parameters and states in a dynamical system with uncertainty quantification is crucial in many applications. For example, digital twins dynamically update their knowledge of model parameters and states to support prediction and decision-making. Reliability and computational speed are vital for DTs. Online parameter-state estimation ensures computational efficiency, while uncertainty quantification is essential for making reliable predictions and decisions. In parameter-state estimation, the joint distribution of the state and model parameters conditioned on the data, termed the joint posterior, provides accurate uncertainty quantification. Because the joint posterior is generally intractable to compute, this paper presents an online variational inference framework to compute its approximation at each time step. The approximation is factorized into a marginal distribution over the model parameters and a state distribution conditioned on the parameters. This factorization enables recursive updates through a two-stage procedure: first, the parameter posterior is approximated via variational inference; second, the state distribution conditioned on the parameters is computed using Gaussian filtering based on the estimated parameter posterior. The algorithmic design is supported by a theorem establishing upper bounds on the joint posterior approximation error. Numerical experiments demonstrate that the proposed method (i) matches the performance of the joint particle filter in low-dimensional problems, accurately inferring both unobserved states and unknown parameters of dynamical and observation models; (ii) remains robust under noisy, partial observations and model discrepancies in a chaotic Lorenz 96 system; and (iii) scales effectively to a high-dimensional convection-diffusion system, where it outperforms the joint ensemble Kalman filter.

We construct and validate a set of multi-purpose mock galaxy catalogs designed to capture, to different degrees of accuracy, the main characteristics of the Nancy Grace Roman Space Telescope survey. These catalogs provide a foundation for void statistics and various CMB cross-correlation analyses. Our approach differs from traditional halo occupation or abundance matching methods by directly translating a reference mock catalog -- containing basic properties of the host halos -- into a new simulation (in our case Agora). This technique, which we call analog matching, assigns a halo counterpart in the new simulation to each reference galaxy through a nearest-neighbor search in a multi-dimensional parameter space. This space can include halo mass, environmental measures and other galaxy-specific attributes. By varying the composition of this parameter vector, we can generate catalogs of differing complexity and conduct systematic tests to examine the influence of modelling choices on LSS statistics. We find that analog matching based on halo mass alone, or halo mass and galaxy-type indicators, successfully reproduces the expected Roman emission-line galaxy statistics. We also show that reproducing two-dimensional galaxy clustering does not guarantee consistent void properties. Our results highlight the importance of matching void statistics for improved mock accuracy, and demonstrate that measuring voids provides independent and sensitive constraints on galaxy-halo connections beyond the matter power spectrum. An important by-product of our setup is that it is fully general and can be applied to any combination of simulation and reference catalog, provided that the desired parameter space for both is specified. The resulting Roman-Agora mock catalogs offer a versatile resource for LSS x CMB studies and a benchmark for assessing the impact of mock accuracy on cosmological observables.

We consider a recently introduced fair repetitive scheduling problem involving a set of clients, each asking for their associated job to be daily scheduled on a single machine across a finite planning horizon. The goal is to determine a job processing permutation for each day, aiming to minimize the maximum total completion time experienced by any client. This problem is known to be NP-hard for quite restrictive settings, with previous work offering exact solution methods for highly-structured special cases. In this paper, we focus on the design of approximation algorithms with provable performance guarantees. Our main contributions can be briefly summarized as follows: (i) When job processing times are day-dependent, we devise a polynomial-time LP-based $2$-approximation, as well as a polynomial-time approximation scheme for a constant number of days. (ii) With day-invariant processing times, we obtain a surprisingly simple $(\frac{1+\sqrt{2}}{2}+ε)$-approximation in polynomial time. This setting is also shown to admit a quasi-polynomial-time approximation scheme for an arbitrary number of days. The key technical component driving our approximation schemes is a novel batching technique, where jobs are conceptually grouped into batches, subsequently leading either to a low-dimensional dynamic program or to a compact configuration LP. Concurrently, while developing our constant-factor approximations, we propose a host of lower-bounding mechanisms that may be of broader interest.

We consider classification problems for manifolds and discrete subgroups of Lie groups from a descriptive set-theoretic point of view. This work is largely foundational in conception and character, recording both a framework for general study and Borel complexity computations for some of the most fundamental classes of manifolds. We show, for example, that for all $n\geq 0$, the homeomorphism problem for compact topological $n$-manifolds is Borel equivalent to the relation $=_{\mathbb{N}}$ of equality on the natural numbers, while the homeomorphism problem for noncompact topological $2$-manifolds is of maximal complexity among equivalence relations classifiable by countable structures. A nontrivial step in the latter consists of proving Borel measurable formulations of the Jordan--Schoenflies and surface triangulation theorems. Turning our attention to groups and geometric structures, we show, strengthening results of Stuck--Zimmer and Andretta--Camerlo--Hjorth, that the conjugacy relation on discrete subgroups of any noncompact semisimple Lie group is essentially countable universal. So too, as a corollary, is the isometry relation for complete hyperbolic $n$-manifolds for any $n\geq 2$, generalizing a result of Hjorth--Kechris. We then show that the isometry relation for complete hyperbolic $n$-manifolds with finitely generated fundamental group is, in contrast, Borel equivalent to the equality relation $=_{\mathbb{R}}$ on the real numbers when $n=2$, but that it is not concretely classifiable when $n=3$; thus there exists no Borel assignment of numerical complete invariants to finitely generated Kleinian groups up to conjugacy. We close with a survey of the most immediate open questions.

This paper develops a discrete theory of real Riemann surfaces based on quadrilateral cellular decompositions (quad-graphs) and a linear discretization of the Cauchy-Riemann equations. We construct a discrete analogue of an antiholomorphic involution and classify the topological types of discrete real Riemann surfaces, recovering the classical results on the number of real ovals and the separation of the surface. Central to our approach is the construction of a symplectic homology basis adapted to the discrete involution. Using this basis, we prove that the discrete period matrix admits the same canonical decomposition $Π= \frac{1}{2} H + i T$ as in the smooth setting, where $H$ encodes the topological type and $T$ is purely imaginary. This structural result bridges the gap between combinatorial models and the classical theory of real algebraic curves.