Completion

Despite their substantial successes, AI agents continue to face fundamental challenges in terms of trustworthiness. Consider deep research agents, tasked with searching for information relevant to a given topic-while AI agents can perform effective information retrieval, there is little guarantee regarding the completeness of this information. Gaps in retrieved information can leave biases that mislead users even if the information they are given is correct and relevant. We introduce SeekerGym, a benchmark designed to evaluate the completeness of information retrieved by AI agents. In addition, SeekerGym also measures how well agents quantify their uncertainty in the completeness of their information; if an agent fails to retrieve all relevant information, it is useful for it to at least quantify how much might be missing. At a high level, each task in SeekerGym is a document (e.g., a Wikipedia article), and the AI agent must issue queries to retrieve passages from that document. Intuitively, the document comprehensively covers a topic, so the ability to retrieve its sections directly measures completeness of information retrieval. In addition to Wikipedia, we also consider machine learning survey papers, where the goal is to retrieve relevant sections of a survey paper. We benchmark several models and algorithms; the best approaches retrieve 42.5% of passages on Wikipedia and 29.2% on ML Surveys, leaving substantial room for improvement.

The recently established Convolution Nuclear Norm Minimization (CNNM) addresses the problem of \textit{tensor completion with arbitrary sampling} (TCAS), which involves restoring a tensor from a subset of its entries sampled in an arbitrary manner. Despite its promising performance, the optimization procedure of CNNM needs performing Singular Value Decomposition (SVD) multiple times, which is computationally expensive and hard to parallelize. To address the issue, we reformulate the optimization objective of CNNM from the perspective of convolution eigenvectors. By introducing pre-learned convolution eigenvectors which are shared among different tensors, we propose a novel method called Inductive Convolution Nuclear Norm Minimization (ICNNM), which bypasses the SVD step so as to decrease significantly the computational time. In addition, due to the extra prior knowledge encoded in the pre-learned convolution eigenvectors, ICNNM also outperforms CNNM in terms of recovery performance. Extensive experiments on video completion, prediction and frame interpolation verify the superiority of ICNNM over CNNM and several other competing methods.

We tackle the problem of sparse novel view synthesis (NVS) using video diffusion models; given $K$ ($\approx 5$) multi-view images of a scene and their camera poses, we predict the view from a target camera pose. Many prior approaches leverage generative image priors encoded via diffusion models. However, models trained on single images lack multi-view knowledge. We instead argue that video models already contain implicit multi-view knowledge and so should be easier to adapt for NVS. Our key insight is to formulate sparse NVS as a low frame-rate video completion task. However, one challenge is that sparse NVS is defined over an unordered set of inputs, often too sparse to admit a meaningful order, so the models should be $\textit{invariant}$ to permutations of that input set. To this end, we present FrameCrafter, which adapts video models (naturally trained with coherent frame orderings) to permutation-invariant NVS through several architectural modifications, including per-frame latent encodings and removal of temporal positional embeddings. Our results suggest that video models can be easily trained to "forget" about time with minimal supervision, producing competitive performance on sparse-view NVS benchmarks. Project page: https://frame-crafter.github.io/

While Large Language Models (LLMs) have demonstrated exceptional proficiency in code completion, they typically adhere to a Hard Completion (HC) paradigm, compelling the generation of fully concrete code even amidst insufficient context. Our analysis of 3 million real-world interactions exposes the limitations of this strategy: 61% of the generated suggestions were either edited after acceptance or rejected despite exhibiting over 80% similarity to the user's subsequent code, suggesting that models frequently make erroneous predictions at specific token positions. Motivated by this observation, we propose Adaptive Placeholder Completion (APC), a collaborative framework that extends HC by strategically outputting explicit placeholders at high-entropy positions, allowing users to fill directly via IDE navigation. Theoretically, we formulate code completion as a cost-minimization problem under uncertainty. Premised on the observation that filling placeholders incurs lower cost than correcting errors, we prove the existence of a critical entropy threshold above which APC achieves strictly lower expected cost than HC. We instantiate this framework by constructing training data from filtered real-world edit logs and design a cost-based reward function for reinforcement learning. Extensive evaluations across 1.5B--14B parameter models demonstrate that APC reduces expected editing costs from 19% to 50% while preserving standard HC performance. Our work provides both a theoretical foundation and a practical training framework for uncertainty-aware code completion, demonstrating that adaptive abstention can be learned end-to-end without sacrificing conventional completion quality.

Accurate 3D reconstruction of vertebral anatomy from ultrasound is important for guiding minimally invasive spine interventions, but it remains challenging due to acoustic shadowing and view-dependent signal variations. We propose an occupancy-based shape completion method that reconstructs complete 3D anatomical geometry from partial ultrasound observations. Crucially for intra-operative applications, our approach extracts the anatomical surface directly from the image, avoiding the need for anatomical labels during inference. This label-free completion relies on a coupled latent space representing both the image appearance and the underlying anatomical shape. By leveraging a Neural Implicit Representation (NIR) that jointly models both spatial occupancy and acoustic interactions, the method uses acoustic parameters to become implicitly aware of the unseen regions without explicit shadowing labels through tracking acoustic signal transmission. We show that this method outperforms state-of-the-art shape completion for B-mode ultrasound by 80% in HD95 score. We validate our approach both in-silico and on phantom US images with registered mesh models from CT labels, demonstrating accurate reconstruction of occluded anatomy and robust generalization across diverse imaging conditions. Code and data will be released on publication.

Evaluating the real-world capabilities of AI systems requires grounding benchmark performance in human-interpretable measures of task difficulty. Existing approaches that rely on direct human task completion time annotations are costly, noisy, and difficult to scale across benchmarks. In this work, we propose BRIDGE, a unified psychometric framework that learns a latent difficulty scale from model responses and anchors it to human task completion time. Using a two-parameter logistic Item Response Theory model, we jointly estimate latent task difficulty and model capability from model performance data across multiple benchmarks. We demonstrate that latent task difficulty varies linearly with the logarithm of human completion time, allowing human task completion time to be inferred for new benchmarks from model performance alone. Leveraging this alignment, we forecast frontier model capabilities in terms of human task length and independently reproduce METR's exponential scaling results, with the 50% solvable task horizon doubling approximately every 6 months.

Two deep ReLU networks can have entirely different architectures and parameters, yet realize the same function. We provide a complete characterization of this nonuniqueness. This is effected by building a symbolic calculus for deep ReLU networks, equivalence and simplification of networks becoming derivation of formulae, in close parallel to Shannon's analysis of switching circuits through Boolean logic. Inspired by Shannon, who turned circuit synthesis into the manipulation of Boolean formulae by the axioms of Boolean algebra, we turn ReLU network identification into the derivation of Łukasiewicz formulae by the axioms of many-valued (MV) logic. Two non-degenerate ReLU networks realize the same function on the unit cube if and only if one is obtained from the other by finitely many applications of the MV axioms for integer weights and biases, the divisible MV axioms for rational ones, and the Riesz MV axioms for real ones. The MV logic axioms characterize all symmetries of ReLU networks, the single-layer ones, which for tanh networks are the only kind, and the deep ones, spanning three or more layers. Our framework consists of three steps, an extraction algorithm turning a network into a substitution graph, whose represented formula has the network's input-output map as its truth function, a completeness theorem, by which functionally equivalent formulae are interderivable, and a construction algorithm returning from graphs to networks. The substitution graph is layered, carrying at each node a formula in the variables of the layer feeding it, encodes the network uniquely, and induces a new normal form for MV logic, compositional rather than flat as in the literature, hence retaining the algebraic structure of the network, with three local operations--node rewrite, layer collapse, layer expansion--realizing every derivation.

Modern AI agents increasingly rely on search infrastructure to execute complex, neuro-symbolic reasoning workflows. These workflows often compile into deeply nested, non-monotonic Boolean queries over text fields. However, standard query evaluation strategies over inverted indices face severe theoretical limits when handling these structures. Stateful iterator models (Document-at-a-Time) are structurally bounded by $\text{NC}^1$ formula evaluation, suffering a worst-case $O(2^{|Q|})$ exponential blowup in query complexity when unrolling re-convergent logic. Conversely, recursive materialization models (Term-at-a-Time) incur an $Ω(|U|)$ space complexity penalty (the Universal Scan) when evaluating logical negation over the document universe. In this paper, we establish the theoretical boundaries of executing complex logic natively over an inverted index. We formalize a retrieval language ($\mathcal{L}_R$) based on Directed Acyclic Graphs (DAGs) and prove that its evaluation problem is strictly \textbf{$\mathbf{P}$-Complete}. To make evaluation tractable, we introduce \texttt{ComputePN}, a deterministic, sparsity-aware evaluation algorithm. By decoupling logical negation from universe-scale materialization via a novel Positive-Negative dual representation, and utilizing native DAG memoization, \texttt{ComputePN} strictly bounds evaluation time to $O(|Q| \cdot |U_{\mathit{active}}|)$. This approach successfully evaluates $\mathbf{P}$-Complete queries natively over the index, avoiding both the combinatorial tree-expansion bottleneck and the universal scan penalty, laying the formal foundation for computational retrieval.

Multimodal emotion and intent recognition is essential for automated human-computer interaction, It aims to analyze users' speech, text, and visual information to predict their emotions or intent. One of the significant challenges is that missing modalities due to sensor malfunctions or incomplete data. Traditional methods that attempt to reconstruct missing information often suffer from over-coupling and imprecise generation processes, leading to suboptimal outcomes. To address these issues, we introduce an Attention-based Diffusion model for Missing Modalities feature Completion (ADMC). Our framework independently trains feature extraction networks for each modality, preserving their unique characteristics and avoiding over-coupling. The Attention-based Diffusion Network (ADN) generates missing modality features that closely align with authentic multimodal distribution, enhancing performance across all missing-modality scenarios. Moreover, ADN's cross-modal generation offers improved recognition even in full-modality contexts. Our approach achieves state-of-the-art results on the IEMOCAP and MIntRec benchmarks, demonstrating its effectiveness in both missing and complete modality scenarios.

Semantic map completion, which predicts the layout of unobserved regions from partial observations, is a critical capability for indoor robot navigation. Existing approaches either rely on high-dimensional discrete codebooks that inflate memory, or on iterative diffusion sampling that is too slow for real-time use. We present FastMap, a lightweight two-stage framework for completing top-down categorical semantic maps. First, a lookup-free BitVAE exploits the inherently binary (one-hot) structure of semantic maps to compress each map patch into compact bitwise tokens, yielding a 0.41GB model that is 3.7 times smaller than the prior masked-modeling baseline. Second, a Masked AutoEncoder (MAE)-style transformer reconstructs missing tokens in a single forward pass at 0.011s/map. To support object goal navigation, we additionally introduce an object-aware masking strategy that masks the target category during training and conditions generation on a learnable category embedding, without adding inference cost. On the Gibson benchmark, FastMap achieves 34.10% mIoU and 45.84% semantic Success Rate (sSR), more than doubling the previous best (21.88%), and reaches 83.8% Success Rate on downstream ObjectNav, the highest among the compared navigation methods.

Deep research agents are increasingly capable of web search, tool use, multimodal evidence analysis, and information synthesis. However, existing benchmarks mainly evaluate medium-horizon exploration and rarely test whether agents can sustain long, dependency-heavy research processes. We introduce Mr. LHDR (Multimodal real-world Long-Horizon Deep Research), a benchmark for evaluating real-world deep research over long, irreducible chains of interdependent evidence across eight categories. Each question is constructed from a hidden Node-Relation graph and requires an average of 12.1 necessary intermediate conclusions with a mean dependency depth of 10.4 before reaching a short, unique, and verifiable answer. Questions incorporate multimodal evidence, including images, maps, PDFs, logos, charts, tables, and video frames, with at least one non-text element that changes the reasoning state. Mr. LHDR evaluates both final answers and the correctness of intermediate conclusions under annotated dependencies. We evaluate general models, deep research systems, and agent frameworks using Overall Accuracy (OA), Strict Accuracy (SA), Checklist Score (CS), and Dependency-Aware Checklist Score (DACS). Results show that even the strongest system achieves only 43.1% OA and 34.3% SA, indicating that final-answer accuracy substantially overestimates complete research success. Removing images reduces DACS by 12.6 points, demonstrating the importance of multimodal evidence, while SA consistently declines as reasoning chains become longer. These findings reveal sustained, dependency-consistent evidence integration, rather than isolated fact retrieval, as a key bottleneck for current deep research agents.

Depth completion aims to predict a dense depth map from a color image with sparse depth measurements. Although deep learning methods have achieved state-of-the-art (SOTA), effectively handling the sparse and irregular nature of input depth data in deep networks remains a significant challenge, often limiting performance, especially under high sparsity. To overcome this limitation, we introduce the Gaussian Belief Propagation Network (GBPN), a novel hybrid framework synergistically integrating deep learning with probabilistic graphical models for end-to-end depth completion. Specifically, a scene-specific Markov Random Field (MRF) is dynamically constructed by the Graphical Model Construction Network (GMCN), and then inferred via Gaussian Belief Propagation (GBP) to yield the dense depth distribution. Crucially, the GMCN learns to construct not only the data-dependent potentials of MRF but also its structure by predicting adaptive non-local edges, enabling the capture of complex, long-range spatial dependencies. Furthermore, we enhance GBP with a serial & parallel message passing scheme, designed for effective information propagation, particularly from sparse measurements. Extensive experiments demonstrate that GBPN achieves SOTA performance on the NYUv2 and KITTI benchmarks. Evaluations across varying sparsity levels, sparsity patterns, and datasets highlight GBPN's superior performance, notable robustness, and generalizable capability.