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We establish several improvements to the main results of [PR19] and [CP21], refining the seminal self-improving method for generalized Poincaré inequalities from [FPW98, MP98]. These results, together with various related applications, stem from a general self-improving property for functions satisfying the local inequality $$\frac{1}{|Q|}\int_Q |f(x)-f_Q|\,dx \le a(Q)$$ for all cubes $Q\subset\mathbb{R}^n$. The functional $a$ is assumed to obey a specific discrete geometric summability condition. By restricting our focus to axis-parallel cubes in $\mathbb{R}^n$, this geometric setting allows us to obtain sharper estimates than those available in more general metric measure spaces.
Reasoning has emerged as a key capability of large language models. In linguistic tasks, this capability can be enhanced by self-improving techniques that refine reasoning paths for subsequent finetuning. However, extending these language-based self-improving approaches to vision language models (VLMs) presents a unique challenge:~visual hallucinations in reasoning paths cannot be effectively verified or rectified. Our solution starts with a key observation about visual contrast: when presented with a contrastive VQA pair, i.e., two visually similar images with synonymous questions, VLMs identify relevant visual cues more precisely. Motivated by this observation, we propose Visual Contrastive Self-Taught Reasoner (VC-STaR), a novel self-improving framework that leverages visual contrast to mitigate hallucinations in model-generated rationales. We collect a diverse suite of VQA datasets, curate contrastive pairs according to multi-modal similarity, and generate rationales using VC-STaR. Consequently, we obtain a new visual reasoning dataset, VisCoR-55K, which is then used to boost the reasoning capability of various VLMs through supervised finetuning. Extensive experiments show that
Recent advances in Multimodal Large Language Models (MLLMs) have enabled unified multimodal understanding and generation. However, they still struggle with fine-grained text-image alignment, often failing to faithfully depict objects with correct attributes such as color, shape, and spatial relations. To mitigate this issue, previous studies have explored preference optimization methods such as DPO and GRPO, but these approaches incur substantial computational cost, both in constructing preference data and in performing optimization. This has motivated self-improving preference optimization approaches, in which the MLLM autonomously generates its own training data, self-estimates preference feedback, and self-optimizes using the resulting self-constructed preference pairs. However, existing self-improving methods still overlook fine-grained, object-level semantics, allowing object hallucination to persist. To tackle this problem, we propose Object-centric Self-improving Preference Optimization (OSPO), a self-improving framework designed to enhance object-level text-image alignment. OSPO explicitly constructs object-centric preference data without relying on any external data and ex
Large-scale multi-view reconstruction models have made remarkable progress, but most existing approaches still rely on fully supervised training with ground-truth 3D/4D annotations. Such annotations are expensive and particularly scarce for dynamic scenes, limiting scalability. We propose SelfEvo, a self-improving framework that continually improves pretrained multi-view reconstruction models using unlabeled videos. SelfEvo introduces a self-distillation scheme using spatiotemporal context asymmetry, enabling self-improvement for learning-based 4D perception without external annotations. We systematically study design choices that make self-improvement effective, including loss signals, forms of asymmetry, and other training strategies. Across eight benchmarks spanning diverse datasets and domains, SelfEvo consistently improves pretrained baselines and generalizes across base models (e.g. VGGT and $π^3$), with significant gains on dynamic scenes. Overall, SelfEvo achieves up to 36.5% relative improvement in video depth estimation and 20.1% in camera estimation, without using any labeled data. Project Page: https://self-evo.github.io/.
Modern language model-based AI systems are remarkably powerful, yet their capabilities remain fundamentally capped by their human creators in three key ways. First, although a model's weights can be updated via fine-tuning, acquiring new knowledge from small, specialized corpora after pretraining remains highly data-inefficient. Second, the training of these systems relies heavily on finite, human-generated data from across history. Third, the pipelines used to train AI models are confined by the algorithms that human researchers can discover and explore. This thesis takes a small step toward overcoming these inherent limitations, presenting three chapters aimed at breaking these dependencies to create continually self-improving AI. First, to overcome this data-efficiency barrier in knowledge acquisition, we propose a synthetic data approach that diversifies and amplifies small corpora into rich knowledge representations, enabling a model to effectively update its parameters from limited source material. Second, to reduce reliance on human data, we show that given a fixed amount of such data, the model can self-generate synthetic data to bootstrap its fundamental pretraining capabi
Text-to-image diffusion models have revolutionized generative AI, enabling high-quality and photorealistic image synthesis. However, their practical deployment remains hindered by several limitations: sensitivity to prompt phrasing, ambiguity in semantic interpretation (e.g., ``mouse" as animal vs. a computer peripheral), artifacts such as distorted anatomy, and the need for carefully engineered input prompts. Existing methods often require additional training and offer limited controllability, restricting their adaptability in real-world applications. We introduce Self-Improving Diffusion Agent (SIDiffAgent), a training-free agentic framework that leverages the Qwen family of models (Qwen-VL, Qwen-Image, Qwen-Edit, Qwen-Embedding) to address these challenges. SIDiffAgent autonomously manages prompt engineering, detects and corrects poor generations, and performs fine-grained artifact removal, yielding more reliable and consistent outputs. It further incorporates iterative self-improvement by storing a memory of previous experiences in a database. This database of past experiences is then used to inject prompt-based guidance at each stage of the agentic pipeline. \modelour achieved
Model steering represents a powerful technique that dynamically aligns large language models (LLMs) with human preferences during inference. However, conventional model-steering methods rely heavily on externally annotated data, not only limiting their adaptability to varying contexts but also tethering their effectiveness to annotation quality. In this paper, we present SIMS, the first self-improving model-steering framework that operates without relying on external supervision. At its core, SIMS autonomously generates and refines contrastive samples through iterative self-improvement cycles, enabling adaptive, context-specific steering. Additionally, SIMS employs novel strategies, including prompt ranking and contrast sampling, to further enhance steering efficacy. Extensive evaluation across diverse LLMs and benchmarks demonstrates that SIMS substantially outperforms existing methods in steering effectiveness and adaptability, highlighting self-improving model steering as a promising direction for future research on inference-time LLM alignment.
Today's AI systems have human-designed, fixed architectures and cannot autonomously and continuously improve themselves. The advance of AI could itself be automated. If done safely, that would accelerate AI development and allow us to reap its benefits much sooner. Meta-learning can automate the discovery of novel algorithms, but is limited by first-order improvements and the human design of a suitable search space. The Gödel machine proposed a theoretical alternative: a self-improving AI that repeatedly modifies itself in a provably beneficial manner. Unfortunately, proving that most changes are net beneficial is impossible in practice. We introduce the Darwin Gödel Machine (DGM), a self-improving system that iteratively modifies its own code (thereby also improving its ability to modify its own codebase) and empirically validates each change using coding benchmarks. Inspired by Darwinian evolution and open-endedness research, the DGM maintains an archive of generated coding agents. It grows the archive by sampling an agent from it and using a foundation model to create a new, interesting, version of the sampled agent. This open-ended exploration forms a growing tree of diverse, h
Self-improving agents aim to continuously acquire new capabilities with minimal supervision. However, current approaches face two key limitations: their self-improvement processes are often rigid, fail to generalize across tasks domains, and struggle to scale with increasing agent capabilities. We argue that effective self-improvement requires intrinsic metacognitive learning, defined as an agent's intrinsic ability to actively evaluate, reflect on, and adapt its own learning processes. Drawing inspiration from human metacognition, we introduce a formal framework comprising three components: metacognitive knowledge (self-assessment of capabilities, tasks, and learning strategies), metacognitive planning (deciding what and how to learn), and metacognitive evaluation (reflecting on learning experiences to improve future learning). Analyzing existing self-improving agents, we find they rely predominantly on extrinsic metacognitive mechanisms, which are fixed, human-designed loops that limit scalability and adaptability. Examining each component, we contend that many ingredients for intrinsic metacognition are already present. Finally, we explore how to optimally distribute metacogniti
Recent advances in large language model (LLM) reasoning through reinforcement learning rely on annotated datasets for verifiable rewards, which may limit models' ability to surpass human-level performance. While self-play offers a promising alternative, prior methods yield only marginal or even negative gains on post-trained models because they generate problems that cluster around familiar concepts rather than discovering novel ones. We introduce Open-Ended Self-Improving Reasoner (OpenSIR), a self-play framework in which a single LLM alternates teacher and student roles to generate and solve novel problems without external verifiers or annotated data. Starting from a single seed problem, OpenSIR sustains open-ended exploration through diversity rewards that push the model toward unfamiliar concepts and difficulty calibration that keeps problems learnable. Across seven math benchmarks, OpenSIR consistently improves all models, averaging +3.6 points on instruction models and +3.1 on reasoning models, while recent self-play baselines yield marginal or even negative gains; starting from a single trivial seed, it also surpasses GRPO baselines trained on over 7K annotated examples. Des
The tool-using capability of large language models (LLMs) enables them to access up-to-date external information and handle complex tasks. Current approaches to enhancing this capability primarily rely on distilling advanced models by data synthesis. However, this method incurs significant costs associated with advanced model usage and often results in data compatibility issues, led by the high discrepancy in the knowledge scope between the advanced model and the target model. To address these challenges, we propose ToolACE-DEV, a self-improving framework for tool learning. First, we decompose the tool-learning objective into sub-tasks that enhance basic tool-making and tool-using abilities. Then, we introduce a self-evolving paradigm that allows lightweight models to self-improve, reducing reliance on advanced LLMs. Extensive experiments validate the effectiveness of our approach across models of varying scales and architectures.
We investigate a self-improving property of variational integrals in a weighted framework under generalized Orlicz growth conditions. Assuming that the weight belongs to an appropriate Muckenhoupt class and the growth function satisfies standard structural conditions, we prove that the gradient of any local quasiminimizer has local higher integrability. In addition, we establish the existence of minimizers for the associated functional.
Large Language Models (LLMs) have enabled self-improving AI systems that iteratively generate, evaluate, and refine their outcomes. Recent studies show that prompt-optimization-based self-improvement can outperform state-of-the-art reinforcement-learning fine-tuning of LLMs, but performance is typically measured by generation efficiency. However, in many applications, the constraint is evaluation efficiency: obtaining reliable feedback is far more costly than generating candidates. To optimize for evaluation efficiency, we extend Upper Confidence Bound-Bayesian Optimization (UCB-BO), a framework known for optimal evaluation-efficiency guarantees, to the language domain. Doing so is challenging for two reasons: (i) gradients needed for UCB-BO are ill-defined in discrete prompt space; and (ii) UCB-style exploration relies on a surrogate model and acquisition function, which only live implicitly in the LLM. We overcome these challenges by proving that combining simple textual gradients (LLM-proposed local edits) with the Best-of-N selection strategy statistically emulates ascent along the gradient of the canonical UCB acquisition function. Based on this result, we propose TextBO, a si
Large language models often struggle with length generalization and solving complex problem instances beyond their training distribution. We present a self-improvement approach where models iteratively generate and learn from their own solutions, progressively tackling harder problems while maintaining a standard transformer architecture. Across diverse tasks including arithmetic, string manipulation, and maze solving, self-improving enables models to solve problems far beyond their initial training distribution-for instance, generalizing from 10-digit to 100-digit addition without apparent saturation. We observe that in some cases filtering for correct self-generated examples leads to exponential improvements in out-of-distribution performance across training rounds. Additionally, starting from pretrained models significantly accelerates this self-improvement process for several tasks. Our results demonstrate how controlled weak-to-strong curricula can systematically teach a model logical extrapolation without any changes to the positional embeddings, or the model architecture.
Video generative models trained on expert demonstrations have been utilized as performant text-conditioned visual planners for solving robotic tasks. However, generalization to unseen tasks remains a challenge. Whereas improved generalization may be facilitated by leveraging learned prior knowledge from additional pre-collected offline data sources, such as web-scale video datasets, in the era of experience we aim to design agents that can continuously improve in an online manner from self-collected behaviors. In this work we thus propose the Self-Improving Loops for Visual Robotic Planning (SILVR), where an in-domain video model iteratively updates itself on self-produced trajectories, and steadily improves its performance for a specified task of interest. We apply SILVR to a diverse suite of MetaWorld tasks, as well as two manipulation tasks on a real robot arm, and find that performance improvements continuously emerge over multiple iterations for novel tasks unseen during initial in-domain video model training. We demonstrate that SILVR is robust in the absence of human-provided ground-truth reward functions or expert-quality demonstrations, and is preferable to alternate appro
As systems trend toward superintelligence, a natural modeling premise is that agents can self-improve along every facet of their own design. We formalize this with a five-axis decomposition and a decision layer, separating incentives from learning behavior and analyzing axes in isolation. Our central result identifies and introduces a sharp utility-learning tension, the structural conflict in self-modifying systems whereby utility-driven changes that improve immediate or expected performance can also erode the statistical preconditions for reliable learning and generalization. Our findings show that distribution-free guarantees are preserved iff the policy-reachable model family is uniformly capacity-bounded; when capacity can grow without limit, utility-rational self-changes can render learnable tasks unlearnable. Under standard assumptions common in practice, these axes reduce to the same capacity criterion, yielding a single boundary for safe self-modification.
We extend the moduli-theoretic framework of psychometric batteries to the domain of dynamical systems. While previous work established the AAI capability score as a static functional on the space of agent representations, this paper formalizes the agent as a flow $ν_r$ parameterized by computational resource $r$, governed by a recursive Generator-Verifier-Updater (GVU) operator. We prove that this operator generates a vector field on the parameter manifold $Θ$, and we identify the coefficient of self-improvement $κ$ as the Lie derivative of the capability functional along this flow. The central contribution of this work is the derivation of the Variance Inequality, a spectral condition that is sufficient (under mild regularity) for the stability of self-improvement. We show that a sufficient condition for $κ> 0$ is that, up to curvature and step-size effects, the combined noise of generation and verification must be small enough. We then apply this formalism to unify the recent literature on Language Self-Play (LSP), Self-Correction, and Synthetic Data bootstrapping. We demonstrate that architectures such as STaR, SPIN, Reflexion, GANs and AlphaZero are specific topological real
Foundation models trained on web-scale data have revolutionized robotics, but their application to low-level control remains largely limited to behavioral cloning. Drawing inspiration from the success of the reinforcement learning stage in fine-tuning large language models, we propose a two-stage post-training approach for robotics. The first stage, Supervised Fine-Tuning (SFT), fine-tunes pretrained foundation models using both: a) behavioral cloning, and b) steps-to-go prediction objectives. In the second stage, Self-Improvement, steps-to-go prediction enables the extraction of a well-shaped reward function and a robust success detector, enabling a fleet of robots to autonomously practice downstream tasks with minimal human supervision. Through extensive experiments on real-world and simulated robot embodiments, our novel post-training recipe unveils significant results on Embodied Foundation Models. First, we demonstrate that the combination of SFT and Self-Improvement is significantly more sample-efficient than scaling imitation data collection for supervised learning, and that it leads to policies with significantly higher success rates. Further ablations highlight that the co
Large Language Models (LLMs) have demonstrated remarkable self-improvement capabilities, whereby models iteratively revise their outputs through self-generated feedback. While this reflective mechanism has shown promise in enhancing task performance, recent studies suggest that it may also introduce undesirable biases-most notably, self-bias, or the tendency of LLMs to favor their own prior outputs. In this work, we extend this line of inquiry by investigating the impact on confidence estimation. We evaluate three representative self-improvement paradigms-basic prompting, Chain-of-Thought (CoT) prompting, and tuning-based methods and find that iterative self-improvement can lead to systematic overconfidence, as evidenced by a steadily increasing Expected Calibration Error (ECE) and lower accuracy with high confidence. We then further explore the integration of confidence calibration techniques with self-improvement. Specifically, we compare three strategies: (1) applying calibration after multiple rounds of self-improvement, (2) calibrating before self-improvement, and (3) applying calibration iteratively at each self-improvement step. Our results show that iterative calibration is
Training AI models is challenging, particularly when crafting behavior instructions. Traditional methods rely on machines (supervised learning) or manual pattern discovery, which results in not interpretable models or time sink. While Large Language Models (LLMs) simplify instruction writing through natural language, articulating intended model behavior still remains difficult. We introduce Visionary Tuning, a human-in-the-loop self-playing followed by automatic self-refinement to improve behavior specification. Our system helps users clarify desired behavior through self-playing and generates prompts through self-improving, Our first evaluation involves user study conducted on a system implementation of Visionary Tuning within the context of chatbot behavior. Our system self-play itself by simulating user interactions to identify patterns and create effective prompts based on the pattern. In a within-subject study (N=12), participants pinpointed more patterns through self-playing and crafted better prompts. Surprisingly, users felt more or less success level in specifying the model behavior. Follow-up crowd studies (N=60) confirmed that the chatbot adhered to instructions without