NeurIPS 2026 Papers

We introduce FakeParts, a new class of AI forgery videos characterised by subtle, localised manipulations to specific spatial regions or temporal segments of otherwise authentic videos. Unlike fully synthetic content, these partial manipulations blend seamlessly with real elements, making them particularly deceptive and difficult to detect. To address this critical gap, we present FakePartsBench, the first large-scale benchmark designed to capture the full spectrum of partial forgeries and to evaluate modern detection methods. Our dataset comprises over 81K videos, including 44K FakeParts with pixel- and frame-level manipulation annotations, ranging from altered facial expressions to object substitutions and background modification. Our user studies demonstrate that FakeParts reduces human detection accuracy by up to 26\% compared to full-video forgery contents, with similar performance degradation observed in over fifteen state-of-the-art detection models. This work identifies an urgent vulnerability in current detectors and provides the necessary resources to develop methods robust to partial manipulations.

Chains of thought (CoTs) have become central in interpreting and auditing behaviors of large language models. Yet growing evidence suggests that these traces often fail to faithfully represent the computations behind a model's predictions. Several faithfulness metrics have been proposed, but whether they indeed measure faithfulness remains unknown. Answering this requires ground-truth labels, which are hard to obtain since internal computations are not directly observable. Consequently, most works proposing metrics report only absolute scores or comparisons to prior metrics, and the few existing benchmarks rely on proxies like plausibility or importance, properties orthogonal to faithfulness that can mislead about whether a CoT can be trusted. We address this challenge by constructing tasks whose outputs reveal which intermediate computations must have produced them, and developing an automated labeling pipeline that yields ground-truth faithfulness labels at both the step and CoT level. Building on this methodology, we present **BonaFide**, a benchmark of 3,066 labeled CoTs across 13 tasks and 10 models, and use it to conduct the first systematic evaluation of prominent faithfulness metrics. Our experiments show that most metrics perform near chance, exhibit strong prediction biases and degrade on longer CoTs. The best metric reaches only 0.71 AUROC at the CoT level while another reaches 0.59 at the step level, with neither transferring across settings, while entailing prohibitively high computational cost. Our results expose fundamental gaps in current faithfulness evaluation and call for the development of more reliable and efficient metrics.

Identity-preserving text-to-video generation (IPT2V) empowers users to produce diverse and imaginative videos with consistent human facial identity. Despite recent progress, existing methods often suffer from significant identity distortion under large facial pose variations or facial occlusions. In this paper, we propose FaithfulFaces, a pose-faithful facial identity preservation learning framework to improve IPT2V in complex dynamic scenes. The key of FaithfulFaces is a pose-shared identity aligner that refines and aligns facial poses across distinct views via a pose-shared dictionary and a pose variation–identity invariance constraint. By mapping single-view inputs into a global facial pose representation with explicit Euler angle embeddings, FaithfulFaces provides a pose-faithful facial prior that guides generative foundations toward robust identity-preserving generation. In particular, we develop a specialized pipeline to curate a high-quality video dataset featuring substantial facial pose diversity. Extensive experiments demonstrate that FaithfulFaces achieves state-of-the-art performance, maintaining superior identity consistency and structural clarity even as pose changes and occlusions occur. The code and dataset pipeline will be released.

Continuous-time models are a natural choice for irregular and asynchronous data. A central design choice is how to embed discrete observations into continuous time. Interpolation- and imputation-based embeddings reconstruct a continuous observation path, making the model sensitive to the choice of reconstruction. We show that this reconstruction step is unnecessary. On compact sets, universality for continuous functionals of paths transfers to universality for continuous functionals of discrete observation streams under any continuous and injective embedding. Guided by this result, and building on the rectilinear control path for Neural Controlled Differential Equations (NCDEs), we introduce a continuous and injective embedding for Log-NCDEs, a universal class of continuous-time models. This embedding records observations as increments and composes them over arbitrary query intervals to form log-signatures, giving interval-level summaries of a faithful embedding of the observed data. This avoids interpolation of observed variables, supports online computation, and allows prediction on output grids independent of the input sampling times. Experiments on synthetic controlled dynamics and real-world time-series datasets show that the representation is accurate, efficient, and robust to irregular, asynchronous, and sparse observations.

Large language models can now generate complex, multi-step mathematical proofs, but reliably determining their correctness and localizing early logical errors remains a critical challenge. Existing evaluation approaches largely depend on model-based natural-language judgments, which often overlook local reasoning gaps. While formal theorem provers like Lean offer a path to rigorous verification, using them to evaluate informal text requires solving locality and semantic mismatches: a prover might bypass a local flaw by proving an overly broad target, or validate an auto-formalized statement that drifts from the original mathematical intent. To address this, we introduce FaithSieve, a Lean-assisted framework for fine-grained evaluation of natural-language mathematical proofs. FaithSieve decomposes coarse proof steps into local reasoning units, extracts typed proof obligations, and verifies them through a formal evaluation agent. Formal validation is gated by semantic alignment scoring, so Lean evidence is incorporated only when the formal statement faithfully preserves the context, objects, and logical form of the original claim. We construct two expert-verified datasets, ProofLoc-Olympiad and ProofLoc-University, to benchmark first-error localization. On the 350-problem Olympiad dataset, FaithSieve using a GPT-5.4 backbone achieves 81.43\% exact first-error accuracy, outperforming the direct-judging baseline of 72.29\%. Furthermore, on the 200-problem ProofLoc-University benchmark spanning six advanced domains, FaithSieve reaches 84.5\% exact accuracy, compared to 75.0\% for the direct judge. Our work demonstrates that decomposing proofs into fine-grained units and grounding them with faithful formal evidence significantly improves reliable evaluation of natural-language reasoning.

Personalized fine-tuning of Large Language Models (LLMs) enhances user experience but incurs substantial computational costs. Recent studies demonstrate that initializing training from style-similar fine-tuned models significantly reduces adaptation overhead, turning these models into reusable, tradable assets. However, emerging model marketplaces suffer from inherent information asymmetry: providers may misrepresent model capabilities, while model buyers cannot verify utility prior to purchase, leading to adverse selection and potential market collapse. We introduce FairTune Market to mitigate these risks. Our framework combines a posted-price mechanism with a truncated proper scoring rule, conditioning payments on performance under text-generation verification. This design incentivizes truthful reporting as an equilibrium strategy while bounding downside risk from stochastic evaluation. Compared with strong market baselines, FairTune helps buyers find better-matched starting checkpoints, reducing total downstream fine-tuning cost by 72.4\% while recovering 96.3\% of the welfare of an Oracle market with perfect style information. It also improves market health: provider misreporting drops by 96.5\% (from 0.424 to 0.015), and all providers remain profitable and willing to participate in the default setting. These gains are robust across market scales, evaluation noise levels, and niche-provider scenarios. A semi-real reuse experiment on sentence-transformer embeddings from 10 text domains further shows that FairTune achieves near-Oracle matching in a realistic style-embedding space.

Fairness has emerged as a central consideration in machine learning, motivating the study of fair range $k$-supplier clustering as a fundamental problem that focuses fairness on the selected centers. Given a set of suppliers and clients, where each supplier may belong to one or more demographic or functional groups, the objective is to select $k$ suppliers that minimize the maximum client-to-center distance while ensuring that the number of selected suppliers from each group satisfies prescribed lower and upper bounds. For disjoint supplier groups, we develop a polynomial-time $3$-approximation algorithm in the offline setting and a $(3+\epsilon)$-approximation algorithm in the streaming setting. We further consider overlapping supplier groups and show that this generalization admits a parameterized $3$-approximation algorithm whose runtime is exponential in the number of clusters. Finally, experiments on both synthetic and real-world datasets demonstrate that our algorithms achieve significantly better clustering quality and runtime efficiency in comparison with state-of-the-art methods.

Data collection is a critical component of modern machine learning pipelines. In many settings, multiple agents, such as hospitals or research labs, can collaborate to share the burden of data collection rather than each bearing it alone. But how should the work be divided among these agents fairly? Studying this question is complicated by heterogeneity in agents' data collection costs and data quality, and by the fact that fairness itself is subjective and use-case-dependent. We study these challenges in the context of PAC mean estimation, where agents wish to estimate an unknown scalar $\mu$ to within accuracy $\epsilon$ with probability at least $1-\delta$, via samples from distributions with common mean $\mu\,$. Agents may incur different costs to collect their samples, and their distributions may have different variances (data qualities). Our first contribution is a framework that casts collaborative data collection as a bargaining problem, where agents specify a notion of utility (e.g., negative cost incurred, or cost savings relative to working alone) and a welfare function over agent utilities. By maximizing the welfare over the feasible set of data collection amounts (i.e. there is enough data to satisfy $(\epsilon,\delta)$-PAC mean estimation), we obtain a fair division of work. Drawing on classical fairness axioms from the microeconomics literature, the family of admissible welfare functions takes a specific one-parameter form that includes utilitarian, egalitarian, and Nash bargaining as special cases. When agents' noise variances (data qualities) are known, this yields a clean characterization of the fair division. Our second contribution addresses the more challenging setting where variances are unknown. As the feasible set of data collection amounts itself depends on the variances, it is impossible to specify a fair division of work upfront. We propose an online algorithm that combines plug-in variance estimates with carefully calibrated forced sampling, and show that it is asymptotically optimal: the ratio of the achieved welfare to the welfare of the true fair division converges to 1 almost surely as either $\epsilon$ or $\delta$ goes to 0. We further show that our estimator asymptotically exactly meets the specified error tolerance and failure probability.

Algorithmic ranking systems increasingly dictate high-stakes outcomes, yet most fairness interventions implicitly assume that protected attributes are categorical. When sensitive attributes are inherently continuous (e.g., age, income, or health scores), standard practices rely on arbitrary discretization, which discards crucial fine-grained information and destroys the natural ordinality of the data. In this paper, we study the problem of fair ranking with continuous protected attributes without relying on thresholding. We formalize fairness via the Kendall correlation between the ranking and the continuous attribute, and measure utility loss via the Kemeny distance from an initial score-based ranking. To solve this, we propose Fair Bubble Sort (FBS), a highly efficient adjacent-swap algorithm that minimizes utility loss subject to a strict continuous fairness constraint. We provide strong theoretical guarantees, proving that FBS is exactly optimal for the unweighted Kemeny distance. Extensive experiments on synthetic and real-world datasets show that FBS is scalable and consistently outperforms discretization-based baselines, achieving a superior fairness-accuracy Pareto front.

Training smaller language models on reasoning solutions generated by a larger teacher model is the prevailing approach for transferring mathematical reasoning capabilities. However, the student tends to overfit the output distribution of the teacher and generalizes poorly when its own behavior at inference time deviates from the training data. Recent methods attempt to bridge this gap by incorporating error data, yet the corrective trajectories still reflect the reasoning patterns of the teacher, which the student cannot reliably reproduce, leaving the distribution mismatch largely unresolved. We propose a method built on the insight that effective training data should be jointly determined by what the student fails on and what it can realistically learn. Our method first profiles the failure behavior of the student on each problem through repeated sampling, characterizing it in terms of error rate and error consistency to reveal qualitatively distinct failure modes. Each mode demands a fundamentally different training signal. The diagnosed mode then guides candidate generation from the teacher via distinct prompting strategies tailored to each failure type. Among the correct candidates, our method selects the one whose initial reasoning steps after the point of divergence are most reproducible by the student. These first corrective steps constitute the primary bottleneck, while the remaining steps follow an already corrected context and can therefore be continued more readily. This contrasts with standard reranking approaches, which score the trajectory as a whole and thereby dilute the signal at the critical reasoning transition. Experiments on GSM8K, MATH, and three out-of-distribution benchmarks for Llama-3.1-8B and DeepSeek-Math-7B demonstrate that our method achieves superior performance compared with other strong methods. The code and trained weights will be publicly available.

Confirmation bias, the tendency to seek evidence that supports rather than challenges one's belief, hinders one's reasoning ability. We examine whether large language models (LLMs) exhibit confirmation bias by adapting the rule-discovery study from human psychology: given a sequence of three numbers (a "triple"), an agent engages in an interactive feedback loop where it (1) proposes a new triple, (2) receives feedback on whether it satisfies the hidden rule, and (3) guesses the rule. Across eleven LLMs of multiple families and scales, we find that LLMs exhibit confirmation bias, often proposing triples to confirm their hypothesis rather than trying to falsify it. This leads to slower and less frequent discovery of the hidden rule. We further explore intervention strategies (e.g., encouraging the agent to consider counter examples) developed for humans. We find prompting LLMs with such instruction consistently decreases confirmation bias in LLMs, improving rule discovery rates from 42\% to 56\% on average. Lastly, we mitigate confirmation bias by distilling intervention-induced behavior into LLMs, showing promising generalization to a new task, the Blicket test. Our work shows that confirmation bias is a limitation of LLMs in hypothesis exploration, and that it can be mitigated via injecting interventions designed for humans.

We identify a structural weakness in current large language model (LLM) alignment: refusal mechanisms in these models are *fail-open*. While existing approaches tend to encode refusal behaviors across multiple latent features, suppressing a single feature (via prompt-based jailbreaks) is sufficient to collapse alignment, leading to unsafe generation. Motivated by this, we propose *fail-closed alignment* as a design principle for robust LLM safety: refusal mechanisms should remain effective even under partial failures via redundant, independent causal pathways. We present a concrete instantiation of this principle: a progressive alignment framework that iteratively identifies and ablates previously learned refusal directions, forcing the model to reconstruct safety along new, independent subspaces. Across six jailbreak attacks, we achieve the strongest overall robustness (1.7% average attack success rate) while largely preserving generation quality and preventing excessive over-refusals, with negligible computational overhead. Additional analyses confirm that models trained with our method encode multiple, causally independent refusal directions that prompt-based jailbreaks cannot fully suppress, providing empirical support for fail-closed alignment as a principled foundation for robust LLM safety.

While long chain-of-thought (CoT) distillation significantly improves the reasoning abilities of language models, its underlying mechanism remains poorly understood. Current pipelines generally rely on rejection sampling to gather reasoning traces across diverse prompts, assuming that factual correctness and broad problem coverage are indispensable. Surprisingly, we find that training exclusively on flawed reasoning trajectories or a restricted prompt set yields nearly comparable performance. Driven by this counterintuitive finding, we propose the Behavioral Hypothesis: **the essence of Long-CoT distillation is behavioral alignment with structured reasoning patterns, rather than factual knowledge memorization.** We then validate this by demonstrating substantial reasoning gains even when models are fine-tuned exclusively on previously mastered problems—effectively isolating behavioral alignment from novel knowledge injection. Having established that reasoning patterns are the true bottleneck, we investigate how to learn them across varying levels of complexity optimally. We reveal a critical interplay: while the recent probability-based loss excels at learning simple patterns, the standard cross-entropy loss is essential for scaling to complex CoTs. We believe these insights demystify CoT distillation and provide a principled foundation for the future development of reasoning models.

A generative model is factored when each latent dimension independently controls one factor of variation: changing a single latent predictably changes one semantic attribute while leaving the rest unchanged, enabling controllable generation, compositional generalization, and reproducible representations. Existing approaches either constrain the latent distribution, e.g., requiring it to shift with an auxiliary variable, or regularize the model, e.g., sparsity, quantization, or Hessian penalties, neither of which matches how modern conditional generative models actually work: a conditioning signal u reshapes the generator g(·, u) while the latent prior stays fixed. We prove an identifiability theorem showing that generating mechanism diversity, the natural variation that arises when u sufficiently reshapes g, is sufficient for the model to be provably factored, with no parametric assumption on the latent distribution. To actively enforce this condition, we propose Mechanistic Contrastive Learning (MCL), a model-agnostic contrastive objective over generator Jacobians. Empirically, MCL achieves state-of-the-art latent concept disentanglement on three benchmarks equipped with a latent diffusion model, and improves prediction quality and zero-shot cross-task transfer in latent action world models with a 1.4B video generative model as the backbone.

Recovering $360^\circ$ HDR environment maps from unconstrained portraits is a fundamental yet ill-posed challenge in inverse rendering. Existing approaches typically suffer from a critical trade-off: traditional facial reflection-based methods yield low-fidelity, blurry results that lack practical utility, while recent generative models often resort to unconstrained panoramic hallucination (i.e., synthesizing environments with no physical grounding), which leads to severe overfitting and inaccurate lighting. In this paper, we present FaceProbe, an inpainting-driven framework that treats the human face as a reliable, physically-grounded light probe. Instead of synthesizing the environment from scratch, we reformulate the task as a masked completion and outpainting problem. By preserving the peripheral context of the input image and utilizing the portrait as a structural condition, our architecture leverages the generative priors of Diffusion Transformers (DiT) to extend sparse observations into high-fidelity, sharp $360^\circ$ HDR panoramas. To further eliminate color shifts and highlight inaccuracies, we introduce OLAT-GRPO, a post-training alignment mechanism based on Group Relative Policy Optimization. By subjecting the generated maps to image-based relighting on One-Light-At-a-Time (OLAT) datasets, we evaluate their physical validity through relighting consistency. This allows us to explicitly prune inconsistent denoising paths and align the model with multi-objective rewards, ensuring energy conservation and spectral accuracy. Extensive evaluations demonstrate that FaceProbe achieves a paradigm-shifting improvement. Most notably, in the critical portrait relighting task, our method reduces estimation errors by 54.4\% in Angular Error and 48.5\% in si-RMSE over state-of-the-art methods, delivering a robust and highly usable solution for photorealistic rendering and world model applications.

Vital sign measurement using cameras presents opportunities for comfortable, ubiquitous health monitoring. Remote photoplethysmography (rPPG), a foundational technology, enables cardiac measurement through minute changes in light reflected from the skin. However, practical deployment is limited by the computational constraints of performing analysis on front-end devices and the accuracy degradation of transmitting data through compressive channels that reduce signal quality. We propose a memory efficient rPPG algorithm - FacePhys - built on temporal-spatial state space duality, which resolves the trilemma of model scalability, cross-dataset generalization, and real-time operation. Leveraging a transferable heart state, FacePhys captures subtle periodic variations across video frames while maintaining a minimal computational overhead, enabling training on extended video sequences and supporting low-latency inference. FacePhys establishes a new state-of-the-art, with a substantial 49% reduction in error. Our solution enables real-time inference with a memory footprint of 3.6 MB and per-frame latency of 9.46 ms -- surpassing existing methods by 83% to 99%. The training code, a real-time inference demo for mobile browsers, and the demonstration video can be found in the supplementary materials.

Existing image watermarking methods typically entangle visual content with spatial structure, making them highly sensitive to geometric transformations and alignment discrepancies, especially in the presence of deepfake manipulations. In this paper, we propose a semantic-driven facial watermarking framework for robust identity recovery. The key idea is to decouple identity-related semantic information from spatial layout and encode it into a compact and spatially robust semantic representation. Specifically, we decompose a face into semantic components and aggregate deep features into component-wise latent representations, which are quantized via independent codebooks and converted into a compact bitstream for embedding. After decoding, the embedded semantic information is recovered and used to reconstruct identity-consistent facial content, even under slight geometric distortions and tampering. Experiments on CelebA-HQ and FFHQ demonstrate that our method significantly outperforms existing watermarking approaches in terms of reconstruction quality, identity preservation, and retrieval accuracy under both photometric and geometric attacks, validating the effectiveness of semantic component-wise encoding for reliable face recovery.

Editing a local segment in a talking head video without reshooting the entire scene remains challenging and underexplored. Given local edits, such as insertion, deletion, or substitution, talking head video editing must synthesize a replacement segment while leaving the rest unchanged. This requires variable-duration local rewriting while preserving identity, unedited regions, and boundary continuity, which standard speech-driven generation and lip synchronization do not directly address. Moreover, direct supervision is infeasible, as it requires paired videos of the same person and scene differing only in a local spoken segment, which does not exist in the real world. We instead formulate talking head video editing as facial motion infilling, a self-supervised pretext task that recovers masked facial motion from speech and surrounding motion context in ordinary video--speech pairs. The key insight is that local video editing can be simulated during training by masking a motion span and reconstructing it from speech and visible motion context. Based on this formulation, we introduce FacEDiT, a mask-controlled talking head model with local temporal attention bias and temporal smoothness regularization for improved lip--speech alignment and transition continuity. We also introduce FacEDiTBench, the first benchmark for talking head video editing, covering diverse edit types and lengths with dedicated evaluation metrics. Extensive experiments show that FacEDiT produces accurate, speech-aligned edits with strong identity preservation and seamless boundary transitions. Beyond editing, the same facial motion infilling model extends to portrait animation and lip synchronization by simply changing the mask pattern, establishing FacEDiT as a unified framework for talking head video editing and generation. \textit{We will release the code and data upon acceptance.

Implicit neural representations (INRs) have emerged as powerful tools for encoding signals, yet dominant MLP-based designs often suffer from slow convergence, overfitting to noise, and poor extrapolation. We introduce FUTON (Fourier Tensor Network), which models signals as generalized Fourier series whose coefficients are parameterized by a low-rank tensor decomposition. FUTON implicitly expresses signals as weighted combinations of orthonormal, separable basis functions, combining complementary inductive biases: Fourier bases capture smoothness and periodicity, while the low-rank parameterization enforces low-dimensional spectral structure. We provide theoretical guarantees through a universal approximation theorem and derive an inference algorithm with empirically linear complexity in both the spectral resolution and the input dimension. On image and volume representation, FUTON consistently outperforms state-of-the-art MLP-based INRs while training 2–5× faster.