Optimistic Rates for Multiclass PAC Learning

Worst-case multiclass bounds do not become smaller when the best classifier is already nearly correct: what is missing is an optimistic rate, a guarantee whose fluctuation scales with the oracle risk itself. For a class of Natarajan dimension $d_N$ and Daniely-Shalev-Shwartz dimension $d_{DS}$, the optimal excess risk is known at the two endpoints ($d_{DS}/n$ realizable, $\sqrt{d_N/n}+d_{DS}/n$ agnostic [HMZ24, CEH+26, Pab26]) and open in between. We close the gap: at every fixed oracle risk $L^\star$, the optimal excess risk is $\widetildeΘ(\sqrt{L^\star d_N/n}+d_{DS}/n)$, uniformly in the alphabet size, attained by a learner that knows neither $L^\star$ nor the confidence level. The upper bound composes the cover-menu-compression architecture of [CEH+26], at the realizable rate of [Pab26], with a new comparator-facing relative compression theorem: a size-$k$ compression rule that empirically dominates a comparator $h$ has population risk at most $L(h)+O(\sqrt{L(h)Γ}+Γ)$ with $Γ=(k\log n+\log(1/δ))/n$, without stability; this transfers the comparison principle of the sharp binary theory [MQZ26] while discarding its Boolean-cube geometry, which does not lift to multiclass labels. The lower bound forces both terms using one class and one distribution at every fixed $L^\star$, by a pair-Assouad scheme calibrated to $L^\star$ and a fiber argument on the pseudo-cubes underlying the Natarajan-versus-DS separation of [BCD+22]. Both theorems extend to list learning: against the best $r$-tuple of hypotheses, the same architecture and the same two engines yield an optimistic rate and a lower bound of the same shape, forcing the fluctuation term that [Pab26] expected to be necessary against list comparators, and removing the factor $r$ from the known realizable list lower bound.

IRIS: Visual-Semantic Binding for Forgery-Resistant Watermarking of Diffusion Images

Most in-generation diffusion watermarks embed patterns independent of the image that carries them, and attackers transplant the marks onto images the generator did not produce, resulting in forgery. Binding the mark to visual semantics prevents such transplantation, yet existing bindings anchor to a proxy image rather than the image they mark. Realizing visual-semantic binding inside generation faces two challenges. The mark derives from the image itself yet enters the sampling trajectory before that image exists, and may itself shift the semantics it binds. The binding also meets opposite sensitivity demands, breaking under semantic change while holding through common processing. We present IRIS, a training-free watermarking scheme that embeds an Intrinsic Ring Identifier from Semantics. IRIS reads a content code from the non-watermarked generated image, derives a one-time ring from the code and a secret key, returns to the final low-noise steps of the same trajectory and blends the ring in, after the semantics it binds are settled. To meet the opposite sensitivity demands, the code is read through a canonicalization shared between embedding and detection, holding through common distortions and mild regeneration while flipping under semantic change. Detection recomputes the ring from the query image and the key alone, and the mark therefore fails on a foreign or spliced image, with acceptance tracking semantic displacement. On three prompt datasets IRIS detects reliably and stays close to its same-seed non-watermarked counterpart, a fidelity prior in-generation marks do not reach. While forgeries transfer fixed-pattern marks and regeneration strips post-hoc marks, IRIS alone among the compared marks withstands both.

Smartwatch Photoplethysmography-Derived Heart Age via ECG-Guided Cross-Modal Pretraining as a Digital Biomarker of Vascular Aging

Digital biomarkers of cardiovascular aging, often termed heart or vascular age, have been widely studied, but most rely on resting electrocardiography (ECG), imaging, or specialized vascular assessments. Evidence linking wearable photoplethysmography (PPG) to arterial stiffness and hypertension remains limited. We developed an ECG-guided cross-modal framework that uses synchronized smartwatch ECG to enhance PPG representation learning during pretraining while requiring only PPG at inference. The study included three OPPO cohorts across China, comprising 581,804 participants and 7,452,131 recordings. The Vascular Health Study cohort supported ECG-PPG self-supervised pretraining, fine-tuning, and internal validation, while two external cohorts assessed associations with pulse wave velocity (PWV) and prevalent hypertension. Combining subject-aware learning with ECG-PPG contrastive alignment, the PPG-only model achieved subject-level mean absolute errors of 5.895 years (Pearson r=0.819) in the PWV cohort and 4.344 years (r=0.800) in the home blood pressure monitoring cohort. Aggregating repeated recordings further improved short-term stability. After adjustment for chronological age, heart age gap was associated with PWV (partial r=0.2627, P<0.001); each 1-year increase corresponded to 0.062 m/s higher PWV, and accelerated versus decelerated heart aging was associated with 0.91 m/s higher adjusted PWV. Each 1-SD increase in adjusted heart age gap was associated with greater odds of prevalent hypertension (OR 1.72, 95% CI 1.49-1.99), while the highest versus lowest quartile had an OR of 4.25. These findings support smartwatch PPG-derived heart age gap as a scalable digital biomarker of arterial stiffness and prevalent hypertension.

ClawTrack: Towards Trace-Level Evaluation and Improvement of Real-World Autonomous Agents

As LLM-based agents are deployed in complex, multi-step workflows, a critical evaluation gap has emerged: most existing benchmarks judge only final outcomes, unable to distinguish reliable reasoning from lucky success or attribute failures to specific process deficiencies, hindering attribution in long-horizon tasks. In this work, we present ClawTrack, a dual-assessment benchmark that simultaneously measures what an agent achieves (Task Score) and how it achieves it (Process Score). ClawTrack comprises 320 tasks across 8 domains with 25+ deterministic mock services. A Process Grader scores each reasoning turn along four dimensions (goal alignment, efficiency, information utilization, and result verification), anchored by 12,541 task-specific rubric items. Evaluating 21 models over 16,000+ trials, we find that: (1) process scores effectively attribute success and failure to specific reasoning dimensions, filtering lucky passes invisible to outcome-only evaluation; (2) the four dimensions are complementary, with result verification as the systematic bottleneck; (3) the framework is robust to evaluator choice across different judge LLMs; and (4) process-based trajectory filtering yields consistent post-training improvements across model scales.

Contrastive Reinforced Policy Optimization via Privileged Self-Distillation

Recent advances in post-training Large Language Models (LLMs) increasingly rely on Reinforcement Learning with Verifiable Rewards (RLVR) or On-Policy Self-Distillation (OPSD). While OPSD provides dense, logit-level supervision, it inherently suffers from exposure bias due to the privileged information of the self-teacher. In multi-turn agentic settings, this leads to reasoning route convergence and the loss of clear optimization directions. To tackle these challenges, we introduce Contrastive Reinforced Policy Optimization (CRPO), which reformulates agentic OPSD from a contrastive learning perspective. By leveraging predictive entropy to distinguish between positive positions (reflective exploration) and negative positions (exposure bias), CRPO conducts group-wise contrast to preserve reliable, fine-grained optimization signals. Extensive evaluations across 13 challenging reasoning and deep-search benchmarks demonstrate that CRPO consistently outperforms existing reinforcement learning and self-distillation baselines, significantly enhancing training stability and generalization in long-horizon interactions.

Watermark Forensics for Generative Models: An Information-Theoretic Perspective

A watermark in a generative model's output is usually asked only whether a text is machine-made. The same mark can do more: attribute it to the user who produced it, extract a hidden payload, or localize the part that survives editing. These form a forensic ladder, and we ask what each rung costs in the sample length $n$. One object organizes the answers. Let $S$ be the secret the mark carries (a user's identity or payload), and let the information profile $ν(t)=I(S;X_t\mid X_{<t})$ record how much the $t$-th token reveals about $S$ given the earlier ones. Its total mass pays for attribution and extraction; how that mass is spread pays for localization; and detection alone is paid for not by information but by presence, the distance from the marked to the unmarked distribution. The literature's two quality models, a mark subtle on every token and one that stamps a few tokens loudly, are two incomparable ways of capping this profile. Our main theorem settles the ladder's entropy column. For statistically distortion-free schemes, attributing a text to one of $N$ users costs $Θ(\log N/h)$ tokens over every stationary-ergodic source of entropy rate $h$, sharp to a $(1+o(1))$ factor: to our knowledge the first tight entropy-rate law for multi-user attribution (via exact alignment). The natural collision-counting analysis overcharges without bound; only a decoder thresholding each candidate by its own realized surprisal attains the rate while almost never implicating an innocent user. A matching converse makes the law two-sided, and extraction of an $\ell$-bit payload costs $Θ(\ell/h)$. Two gaps are real, not modeling artifacts: a $Θ(\log N)$-token window in which a text is provably machine-made yet unattributable, and a footprint-resolution uncertainty principle. Experiments on GPT-2, Pythia-410M, and Qwen2.5 recover the predicted constants.

TRACE: A Two-Channel Robust Attribution Watermark via Complementary Embeddings for LLM-Agent Trajectories

LLM agents reach users through resellers, who may rebrand a developer's agent or substitute a cheaper model. When provenance is disputed, attribution rests on the trajectory log (the record of tool calls, observations, and executed actions, not the model's reasoning), which the reseller stores and processes to meter usage. A watermark must therefore survive an adversary with full read/write access to the very evidence it is detected from; existing agent watermarks do not, as their attribution is read straight off that log. We present TRACE, to our knowledge the first agent watermark that is distortion-free in its action choices, self-synchronizing under deletion, and unconditionally invariant under rewriting. Deletion desynchronizes a position-derived key and rewriting alters content, so a deletion-robust key must come from content and a rewrite-robust key from position, and no single key serves both. A trajectory, however, has room for two watermarks. TRACE superposes a selection channel that sets which action is chosen, keyed on local content with a distortion-free sampler, so the agent's distribution is provably unchanged and detection resynchronizes after deletions, and a tally channel that sets how many records each decision group holds, keyed on the log's skeleton alone, which no rewriting can touch. We prove this behavioral watermark's signal is bought with decision entropy, each decision paying at least half its entropy and deterministic decisions nothing, and that erasing both channels forces the reseller to corrupt the trajectories it resells. On ToolBench and ALFWorld, TRACE matches the unwatermarked agent's success rate while its selection channel reaches detection scores near z = 100 on long-horizon trajectories, stays detectable under 70% step deletion, and keeps a tally channel exactly unchanged under LLM rewriting of any strength.

The Exact Worst-Case Tail Probability under Bounded Kurtosis

We determine exactly what a kurtosis bound buys for one-sided tail control. For the class $\mathcal{C}(κ)$ of real random variables with mean $0$, variance $1$, and fourth moment at most $κ$, the skewness left free, we compute the worst-case tail probability $V_1(t,κ)=\sup_{X\in\mathcal{C}(κ)}\mathbb{P}(X\geq t)$ for every threshold $t>0$ and every $κ\geq 1$. The answer is a four-regime map: a Cantelli tongue $b(κ)\le t\le c(κ)$ on which the two-moment bound $1/(1+t^2)$ remains tight and the kurtosis constraint is worthless; a tail regime $t\geq c(κ)$ with the closed form $V_1=(κ-1)/((t^2-1)^2+κ-1)$; a plateau regime, present only for $κ\le 3/2$, on which the worst case freezes and the value does not depend on $t$; and a central regime described exactly by an explicit algebraic system, provably admitting no closed form in nested square roots. Beyond $c(κ)$ the one-sided and two-sided worst cases coincide: Cantelli's improvement over Chebyshev is annihilated by fourth-moment information. The minimal degree of a sum-of-squares proof of the tight bound is $2$ on the closed tongue and $4$ everywhere else, an exact phase diagram of proof degree. Every closed-form regime carries an explicit dual certificate and an explicit extremal distribution, re-verified on parameter grids by an independent checker in exact arithmetic. The closed forms invert to exact worst-case quantiles, sharpen a median-of-means constant, and give the exact per-direction tail available to degree-4 reasoning under certifiable kurtosis. We found the map through an AI-guided search around the certifying pipeline, LemmaForge, which is validated on classical benchmarks, independently reproduces the symmetric-slice bound of Zelen (1954), and recovers the $2\sqrt{3}-3$ constant of He, Zhang, and Zhang (2010) at $t=0$.

OPERA: Aligning Open-Ended Reasoning via Objective Perplexity-based Reinforcement Learning

Reinforcement Learning (RL) has enabled LLMs to excel in objective reasoning tasks such as mathematics and code generation. However, applying RL to open-ended tasks, such as creative writing, remains challenging because LLM-as-a-judge reward models often exhibit stylistic biases and positional inconsistencies, leading to unstable supervision. To address this, we propose OPERA (Objective Perplexity-based Reflective Alignment), which replaces unreliable external judges with intrinsic rewards derived from perplexity dynamics. Specifically, we derive an intrinsic reward signal from perplexity dynamics, quantifying uncertainty reduction at critical reflective states. During the cold-start phase, we introduce a data synthesis method that leverages carefully designed guiding words to generate diverse reasoning traces, along with perplexity-prioritized rollouts that utilize internal log-probabilities to identify logically consistent reasoning branches. This pipeline yields a large-scale dataset comprising 20,000 high-quality reasoning trajectories. Empirical evaluations consistently demonstrate the scalability and efficacy of our approach in alignment for open-ended tasks. Implementing OPERA on Qwen3-8B establishes a new state-of-the-art among open-source models, achieving parity with or surpassing proprietary models like Gemini2.5 and MiniMax-M2.5 in some open-ended tasks. The code is available at https://github.com/pangpang-xuan/OPERA.

BoxCtrl: 3D-Aware Visual Prompting for Geometric Image Editing

As instruction-based editing models and multimodal large language models advance, diverse image editing tasks have become feasible. However, achieving precise and consistent geometric image editing, such as translating, scaling, and rotating in 3D space, remains a major challenge. In this work, we introduce BoxCtrl, a 3D-aware visual prompting framework. Unlike text-only or coarse 2D-guided approaches, our method introduces informative RGB 3D bounding boxes projected onto 2D images as visual prompts. The three orthogonal faces of each box are painted with distinct RGB colors, simultaneously encoding position, size, and orientation to provide a compact, intuitive in-context visual example. The key to BoxCtrl's success lies in these well-designed bounding boxes, which decouple geometric control from appearance control. This enables the model to learn consistent correspondences between faces of the same color in the latent space, leading to a precise understanding of geometric intentions and accurate editing results. We introduce a two-stage training paradigm: Supervised Fine-Tuning (SFT) followed by Reinforcement Learning (RL). To address paired data scarcity, we construct a large-scale synthetic dataset for SFT, equipping the model with fundamental editing capabilities. To bridge the synthetic-to-real domain gap, we incorporate an online RL stage leveraging unpaired real-world data. Guided by a reward function evaluating geometric accuracy and visual fidelity, our SFT-RL strategy significantly enhances geometric precision while maintaining photorealistic quality. Extensive experiments demonstrate that BoxCtrl achieves state-of-the-art performance across translation, rotation, scaling, and composite editing tasks.