The Bayes-Nash equilibria of an auction are the solutions of a variational inequality, and for standard auctions its operator fails every monotonicity notion, so the theory of monotone operators is unavailable to learning in auctions. We show what replaces monotonicity for the first-price auction: a certificate that is strong but local. For uniform values the single-population operator has an exact closed form and an exact Minty identity at the equilibrium; for two bidders its Gateaux derivative there is $L^2$-coercive with best constant exactly one in every piecewise-linear bid space with $m$ pieces, while the Minty inequality holds only on a ball whose radius decays like $m^{-5/2}$. The decay is exact: $m^{5/2}$ times the radius converges to $1/(8 \cdot 3^{1/4})$, and the worst perturbations converge to an alternating geometric profile with ratio $-(2-\sqrt{3})$. Refinement shrinks the ball, not the constant; independent learners see the same constant. For a general prior and bidder count there are two certificates, at the true equilibrium and at the equilibrium of the finite-dimensional bid space a learning algorithm runs in. The first is an explicit weight $w_F$, positive for every log-concave prior, equal to the second exactly for the value distributions $F(v)=v^a$. Otherwise the learners' certificate differs by knot masses, because the discretized equilibrium's slopes oscillate with a law proved for two and three bidders, and for four under a computer-verified bottom layer. The limit of the learners' certificate is proved in closed form, a function of the prior alone, and characterizes positivity: positive uniformly in $m$ in the limit exactly when that minimum is positive, with a known rate; for one prior at every $m$ by interval arithmetic. For more bidders the limit is conjectured. The exact identities and leading-order inequalities are machine-checked in Lean.
A key milestone toward Recursive Self-Improvement (RSI) is replacing hand-crafted optimizers with meta-learned update rules (such as Disco103 and OPEN) that discover how agents learn. Yet when a self-discovered RL model trains with adapting teammates, does co-evolution sustain capability gains or trap agents in brittle conventions? Across 1,800+ runs in continuous collective robotics (VMAS) and discrete coordination (Overcooked), we establish five laws of multi-agent adaptation. First, four-cell counterfactual partner swaps expose an evaluation illusion: apparent team progress often masks focal regression (+1.066 team gain concealing -0.119 focal loss) and inflates transfer by +0.649 to +1.210. Second, a 288-run physical-coupling sweep ($α\in [0, 1.5]$) reveals a linear scaling law ($β= +0.255$, $p = 0.000488$, Spearman $ρ= 1.0$): live reciprocal feedback keeps Disco103 invariant (AUC 0.297--0.322), whereas severing feedback triggers a monotonic collapse (-0.172 to -0.490), with OPEN establishing a sensitivity spectrum (Disco103 > OPEN > MAPPO). Third, extending navigation training eightfold (1.05M steps) enables Disco103 to overtake MAPPO (+0.087 team return, +0.133 bank gain), while decoupled training boosts cross-partner completion by +10.16% (56.25% vs. 46.09%). Fourth, in Overcooked, MAPPO's self-play conventions induce a 28.13% cross-partner collision rate, whereas Disco103 cuts collisions to 12.77% and achieves 3.33x higher bank return (9.96 vs. 2.99; net gain +6.43), further improved by decoupled meta-adaptation (+1.39 with scripted partners). Finally, perturbation pulses ($p=0.00098$), auxiliary entropy diagnostics (8.485 nats), and 48 multi-lifetime meta-evolved rules ($L_2 \in [2.11, 4.91]$) trace these dynamics to partner-gradient blindness and auxiliary drift, informing multi-agent self-discoverd algorithms.
Underwater image enhancement aims to correct color and recover detail degraded by wavelength-dependent attenuation, scattering, and noise. Paired-reference supervision constrains output similarity, but does not by itself specify the color mapping, the strength of local detail corrections, or consistency with the degraded observation. We propose MCL-UIE, a paired-supervised framework that addresses these requirements by constraining restoration operations and the training objective. Monotonic Chromatic Transform (MCT) restricts global color mapping in log-LMS space through positive diagonal entries and bounded cross-channel coefficients. Uncertainty-Gated Wavelet Reconstruction (UGWR) modulates high-frequency residuals with a learned confidence gate calibrated against normalized wavelet reconstruction errors. During training, Reference-Anchored Degradation Replay (RADR) renders the enhanced image and its paired reference using shared latent degradation proxies, encouraging both to reproduce the input. The three components share a restoration network that combines structured color correction, locally controlled detail recovery, and reference-anchored replay. MCL-UIE ranks first in thirteen of sixteen full-reference dataset-metric comparisons and produces competitive visual results on no-reference benchmarks. Objective ablations indicate that confidence calibration is most effective when combined with replay supervision. RADR is used only during training and adds no inference-time computation. Our code is available at https://github.com/Wangtao-Bao/MCL-UIE.
Min Lu, Yuanfeng He, Anthony Chen, Jianhuang He, Pu Wang, Daniel Cohen-Or, Hui Huang
Artistic styles often embed abstraction beyond surface appearance, involving deliberate reinterpretation of structure rather than mere changes in texture or color. Conventional style transfer methods typically preserve the input geometry and therefore struggle to capture this deeper abstraction behavior, especially for illustrative and nonphotorealistic styles. In this work, we introduce Abstraction in Style (AiS), a generative framework that separates structural abstraction from visual stylization. Given a target image and a small set of style exemplars, AiS first derives an intermediate abstraction proxy that reinterprets the target's structure in accordance with the abstraction logic exhibited by the style. The proxy captures semantic structure while relaxing geometric fidelity, enabling subsequent stylization to operate on an abstracted representation rather than the original image. In a second stage, the abstraction proxy is rendered to produce the final stylized output, preserving visual coherence with the reference style. Both stages are implemented using a shared image space analogy, enabling transformations to be learned from visual exemplars without explicit geometric supervision. By decoupling abstraction from appearance and treating abstraction as an explicit, transferable process, AiS supports a wider range of stylistic transformations, improves controllability, and enables more expressive stylization.