arXiv subjects

Jürgen Schmidhuber

Publications and source records attributed to Jürgen Schmidhuber.

At least 37 records · Page 2Linked to original sources

arXiv2026

Planning to Explore: Curiosity-Driven Planning for LLM Test Generation

The use of LLMs for code generation has naturally extended to code testing and evaluation. As codebases grow in size and complexity, so does the need for automated test generation. Current approaches for LLM-based test generation rely on strategies that maximize immediate coverage gain, a greedy approach that plateaus on code where reaching deep branches requires setup steps that individually yield zero new coverage. Drawing on principles of Bayesian exploration, we treat the program's branch structure as an unknown environment, and an evolving coverage map as a proxy probabilistic posterior representing what the LLM has discovered so far. Our method, CovQValue, feeds the coverage map back to the LLM, generates diverse candidate plans in parallel, and selects the most informative plan by LLM-estimated Q-values, seeking actions that balance immediate branch discovery with future reachability. Our method outperforms greedy selection on TestGenEval Lite, achieving 51-77% higher branch coverage across three popular LLMs and winning on 77-84% of targets. In addition, we build a benchmark for iterative test generation, RepoExploreBench, where they achieve 40-74%. These results show the potential of curiosity-driven planning methods for LLM-based exploration, enabling more effective discovery of program behavior through sequential interaction

cs.SE↗

arXiv2026

Efficient Morphology-Control Co-Design via Stackelberg Proximal Policy Optimization

Morphology-control co-design concerns the coupled optimization of an agent's body structure and control policy. This problem exhibits a bi-level structure, where the control dynamically adapts to the morphology to maximize performance. Existing methods typically neglect the control's adaptation dynamics by adopting a single-level formulation that treats the control policy as fixed when optimizing morphology. This can lead to inefficient optimization, as morphology updates may be misaligned with control adaptation. In this paper, we revisit the co-design problem from a game-theoretic perspective, modeling the intrinsic coupling between morphology and control as a novel variant of a Stackelberg game. We propose Stackelberg Proximal Policy Optimization (Stackelberg PPO), which explicitly incorporates the control's adaptation dynamics into morphology optimization. By modeling this intrinsic coupling, our method aligns morphology updates with control adaptation, thereby stabilizing training and improving learning efficiency. Experiments across diverse co-design tasks demonstrate that Stackelberg PPO outperforms standard PPO in both stability and final performance, opening the way for dramatically more efficient robotics designs.

cs.LG↗

arXiv2026

Mixture of States: Routing Token-Level Dynamics for Multimodal Generation

We introduce MoS (Mixture of States), a novel fusion paradigm for multimodal diffusion models that merges modalities using flexible, state-based interactions. The core of MoS is a learnable, token-wise router that creates denoising timestep- and input-dependent interactions between modalities' hidden states, precisely aligning token-level features with the diffusion trajectory. This router sparsely selects the top-$k$ hidden states and is trained with an $ε$-greedy strategy, efficiently selecting contextual features with minimal learnable parameters and negligible computational overhead. We validate our design with text-to-image generation (MoS-Image) and editing (MoS-Editing), which achieve state-of-the-art results. With only 3B to 5B parameters, our models match or surpass counterparts up to $4\times$ larger. These findings establish MoS as a flexible and compute-efficient paradigm for scaling multimodal diffusion models.

cs.CV↗

arXiv2026

RACAS: Controlling Diverse Robots With a Single Agentic System

Many robotic platforms expose an API through which external software can command their actuators and read their sensors. However, transitioning from these low-level interfaces to high-level autonomous behaviour requires a complicated pipeline, whose components demand distinct areas of expertise. Existing approaches to bridging this gap either require retraining for every new embodiment or have only been validated across structurally similar platforms. We introduce RACAS (Robot-Agnostic Control via Agentic Systems), a cooperative agentic architecture in which three LLM/VLM-based modules (Monitors, a Controller, and a Memory Curator) communicate exclusively through natural language to provide closed-loop robot control. RACAS requires only a natural language description of the robot, a definition of available actions, and a task specification; no source code, model weights, or reward functions need to be modified to move between platforms. We evaluate RACAS on several tasks using a wheeled ground robot, a recently published novel multi-jointed robotic limb, and an underwater vehicle. RACAS consistently solved all assigned tasks across these radically different platforms, demonstrating the potential of agentic AI to substantially reduce the barrier to prototyping robotic solutions.

cs.RO↗

arXiv2026

Mindstorms in Natural Language-Based Societies of Mind

Both Minsky's "society of mind" and Schmidhuber's "learning to think" inspire diverse societies of large multimodal neural networks (NNs) that solve problems by interviewing each other in a "mindstorm." Recent implementations of NN-based societies of minds consist of large language models (LLMs) and other NN-based experts communicating through a natural language interface. In doing so, they overcome the limitations of single LLMs, improving multimodal zero-shot reasoning. In these natural language-based societies of mind (NLSOMs), new agents -- all communicating through the same universal symbolic language -- are easily added in a modular fashion. To demonstrate the power of NLSOMs, we assemble and experiment with several of them (having up to 129 members), leveraging mindstorms in them to solve some practical AI tasks: visual question answering, image captioning, text-to-image synthesis, 3D generation, egocentric retrieval, embodied AI, and general language-based task solving. We view this as a starting point towards much larger NLSOMs with billions of agents-some of which may be humans. And with this emergence of great societies of heterogeneous minds, many new research questions have suddenly become paramount to the future of artificial intelligence. What should be the social structure of an NLSOM? What would be the (dis)advantages of having a monarchical rather than a democratic structure? How can principles of NN economies be used to maximize the total reward of a reinforcement learning NLSOM? In this work, we identify, discuss, and try to answer some of these questions.

cs.AI↗

arXiv2025

Multiple Token Divergence: Measuring and Steering In-Context Computation Density

Measuring the in-context computational effort of language models is a key challenge, as metrics like next-token loss fail to capture reasoning complexity. Prior methods based on latent state compressibility can be invasive and unstable. We propose Multiple Token Divergence (MTD), a simple measure of computational effort defined as the KL divergence between a model's full output distribution and that of a shallow, auxiliary prediction head. MTD can be computed directly from pre-trained models with multiple prediction heads, requiring no additional training. Building on this, we introduce Divergence Steering, a novel decoding method to control the computational character of generated text. We empirically show that MTD is more effective than prior methods at distinguishing complex tasks from simple ones. On mathematical reasoning benchmarks, MTD correlates positively with problem difficulty. Lower MTD is associated with more accurate reasoning. MTD provides a practical, lightweight tool for analyzing and steering the computational dynamics of language models.

cs.LG↗

arXiv2025

TUNA: Taming Unified Visual Representations for Native Unified Multimodal Models

Unified multimodal models (UMMs) aim to jointly perform multimodal understanding and generation within a single framework. We present TUNA, a native UMM that builds a unified continuous visual representation by cascading a VAE encoder with a representation encoder. This unified representation space allows end-to-end processing of images and videos for both understanding and generation tasks. Compared to prior UMMs with decoupled representations, TUNA's unified visual space avoids representation format mismatches introduced by separate encoders, outperforming decoupled alternatives in both understanding and generation. Moreover, we observe that stronger pretrained representation encoders consistently yield better performance across all multimodal tasks, highlighting the importance of the representation encoder. Finally, in this unified setting, jointly training on both understanding and generation data allows the two tasks to benefit from each other rather than interfere. Our extensive experiments on multimodal understanding and generation benchmarks show that TUNA achieves state-of-the-art results in image and video understanding, image and video generation, and image editing, demonstrating the effectiveness and scalability of its unified representation design.

cs.CV↗

arXiv2025

On the Convergence and Stability of Upside-Down Reinforcement Learning, Goal-Conditioned Supervised Learning, and Online Decision Transformers

This article provides a rigorous analysis of convergence and stability of Episodic Upside-Down Reinforcement Learning, Goal-Conditioned Supervised Learning and Online Decision Transformers. These algorithms performed competitively across various benchmarks, from games to robotic tasks, but their theoretical understanding is limited to specific environmental conditions. This work initiates a theoretical foundation for algorithms that build on the broad paradigm of approaching reinforcement learning through supervised learning or sequence modeling. At the core of this investigation lies the analysis of conditions on the underlying environment, under which the algorithms can identify optimal solutions. We also assess whether emerging solutions remain stable in situations where the environment is subject to tiny levels of noise. Specifically, we study the continuity and asymptotic convergence of command-conditioned policies, values and the goal-reaching objective depending on the transition kernel of the underlying Markov Decision Process. We demonstrate that near-optimal behavior is achieved if the transition kernel is located in a sufficiently small neighborhood of a deterministic kernel. The mentioned quantities are continuous (with respect to a specific topology) at deterministic kernels, both asymptotically and after a finite number of learning cycles. The developed methods allow us to present the first explicit estimates on the convergence and stability of policies and values in terms of the underlying transition kernels. On the theoretical side we introduce a number of new concepts to reinforcement learning, like working in segment spaces, studying continuity in quotient topologies and the application of the fixed-point theory of dynamical systems. The theoretical study is accompanied by a detailed investigation of example environments and numerical experiments.

stat.ML↗

arXiv2025

Huxley-Gödel Machine: Human-Level Coding Agent Development by an Approximation of the Optimal Self-Improving Machine

Recent studies operationalize self-improvement through coding agents that edit their own codebases. They grow a tree of self-modifications through expansion strategies that favor higher software engineering benchmark performance, assuming that this implies more promising subsequent self-modifications. However, we identify a mismatch between the agent's self-improvement potential (metaproductivity) and its coding benchmark performance, namely the Metaproductivity-Performance Mismatch. Inspired by Huxley's concept of clade, we propose a metric ($\mathrm{CMP}$) that aggregates the benchmark performances of the descendants of an agent as an indicator of its potential for self-improvement. We show that, in our self-improving coding agent development setting, access to the true $\mathrm{CMP}$ is sufficient to simulate how the Gödel Machine would behave under certain assumptions. We introduce the Huxley-Gödel Machine (HGM), which, by estimating $\mathrm{CMP}$ and using it as guidance, searches the tree of self-modifications. On SWE-bench Verified and Polyglot, HGM outperforms prior self-improving coding agent development methods while using fewer allocated CPU hours. Last but not least, HGM demonstrates strong transfer to other coding datasets and large language models. The agent optimized by HGM on SWE-bench Verified with GPT-5-mini and evaluated on SWE-bench Lite with GPT-5 achieves human-level performance, matching the best officially checked results of human-engineered coding agents. Our code is publicly available at https://github.com/metauto-ai/HGM.

cs.AI↗

arXiv2025

Curious Causality-Seeking Agents Learn Meta Causal World

When building a world model, a common assumption is that the environment has a single, unchanging underlying causal rule, like applying Newton's laws to every situation. In reality, what appears as a drifting causal mechanism is often the manifestation of a fixed underlying mechanism seen through a narrow observational window. This brings about a problem that, when building a world model, even subtle shifts in policy or environment states can alter the very observed causal mechanisms. In this work, we introduce the \textbf{Meta-Causal Graph} as world models, a minimal unified representation that efficiently encodes the transformation rules governing how causal structures shift across different latent world states. A single Meta-Causal Graph is composed of multiple causal subgraphs, each triggered by meta state, which is in the latent state space. Building on this representation, we introduce a \textbf{Causality-Seeking Agent} whose objectives are to (1) identify the meta states that trigger each subgraph, (2) discover the corresponding causal relationships by agent curiosity-driven intervention policy, and (3) iteratively refine the Meta-Causal Graph through ongoing curiosity-driven exploration and agent experiences. Experiments on both synthetic tasks and a challenging robot arm manipulation task demonstrate that our method robustly captures shifts in causal dynamics and generalizes effectively to previously unseen contexts.

cs.LG↗

arXiv2025

PhysGym: Benchmarking LLMs in Interactive Physics Discovery with Controlled Priors

Evaluating the scientific discovery capabilities of large language model based agents, particularly how they cope with varying environmental complexity and utilize prior knowledge, requires specialized benchmarks currently lacking in the landscape. To address this gap, we introduce \textsc{PhysGym}, a novel benchmark suite and simulation platform for rigorously assessing LLM-based scientific reasoning in interactive physics environments. \textsc{PhysGym}'s primary contribution lies in its sophisticated control over the level of prior knowledge provided to the agent. This allows researchers to dissect agent performance along axes including the complexity of the problem and the prior knowledge levels. The benchmark comprises a suite of interactive simulations, where agents must actively probe environments, gather data sequentially under constraints and formulate hypotheses about underlying physical laws. \textsc{PhysGym} provides standardized evaluation protocols and metrics for assessing hypothesis accuracy and model fidelity. We demonstrate the benchmark's utility by presenting results from baseline LLMs, showcasing its ability to differentiate capabilities based on varying priors and task complexity.

cs.LG↗

arXiv2025

Beyond Outlining: Heterogeneous Recursive Planning for Adaptive Long-form Writing with Language Models

Long-form writing agents require flexible integration and interaction across information retrieval, reasoning, and composition. Current approaches rely on predefined workflows and rigid thinking patterns to generate outlines before writing, resulting in constrained adaptability during writing. In this paper we propose WriteHERE, a general agent framework that achieves human-like adaptive writing through recursive task decomposition and dynamic integration of three fundamental task types: retrieval, reasoning, and composition. Our methodology features: 1) a planning mechanism that interleaves recursive task decomposition and execution, eliminating artificial restrictions on writing workflow; and 2) integration of task types that facilitates heterogeneous task decomposition. Evaluations on both fiction writing and technical report generation show that our method consistently outperforms state-of-the-art approaches across all automatic evaluation metrics, demonstrating the effectiveness and broad applicability of our proposed framework. We have publicly released our code and prompts to facilitate further research.

cs.AI↗

arXiv2025

Fast and scalable retrosynthetic planning with a transformer neural network and speculative beam search

AI-based computer-aided synthesis planning (CASP) systems are in demand as components of AI-driven drug discovery workflows. However, the high latency of such CASP systems limits their utility for high-throughput synthesizability screening in de novo drug design. We propose a method for accelerating multi-step synthesis planning systems that rely on SMILES-to-SMILES transformers as single-step retrosynthesis models. Our approach reduces the latency of SMILES-to-SMILES transformers powering multi-step synthesis planning in AiZynthFinder through speculative beam search combined with a scalable drafting strategy called Medusa. Replacing standard beam search with our approach allows the CASP system to solve 26\% to 86\% more molecules under the same time constraints of several seconds. Our method brings AI-based CASP systems closer to meeting the strict latency requirements of high-throughput synthesizability screening and improving general user experience.

cs.LG↗

arXiv2025

Scaling Value Iteration Networks to 5000 Layers for Extreme Long-Term Planning

The Value Iteration Network (VIN) is an end-to-end differentiable neural network architecture for planning. It exhibits strong generalization to unseen domains by incorporating a differentiable planning module that operates on a latent Markov Decision Process (MDP). However, VINs struggle to scale to long-term and large-scale planning tasks, such as navigating a 100x100 maze -- a task that typically requires thousands of planning steps to solve. We observe that this deficiency is due to two issues: the representation capacity of the latent MDP and the planning module's depth. We address these by augmenting the latent MDP with a dynamic transition kernel, dramatically improving its representational capacity, and, to mitigate the vanishing gradient problem, introduce an "adaptive highway loss" that constructs skip connections to improve gradient flow. We evaluate our method on 2D/3D maze navigation environments, continuous control, and the real-world Lunar rover navigation task. We find that our new method, named Dynamic Transition VIN (DT-VIN), scales to 5000 layers and solves challenging versions of the above tasks. Altogether, we believe that DT-VIN represents a concrete step forward in performing long-term large-scale planning in complex environments.

cs.LG↗

arXiv2025

Fairness Overfitting in Machine Learning: An Information-Theoretic Perspective

Despite substantial progress in promoting fairness in high-stake applications using machine learning models, existing methods often modify the training process, such as through regularizers or other interventions, but lack formal guarantees that fairness achieved during training will generalize to unseen data. Although overfitting with respect to prediction performance has been extensively studied, overfitting in terms of fairness loss has received far less attention. This paper proposes a theoretical framework for analyzing fairness generalization error through an information-theoretic lens. Our novel bounding technique is based on Efron-Stein inequality, which allows us to derive tight information-theoretic fairness generalization bounds with both Mutual Information (MI) and Conditional Mutual Information (CMI). Our empirical results validate the tightness and practical relevance of these bounds across diverse fairness-aware learning algorithms. Our framework offers valuable insights to guide the design of algorithms improving fairness generalization.

cs.LG↗

arXiv2025

Directly Forecasting Belief for Reinforcement Learning with Delays

Reinforcement learning (RL) with delays is challenging as sensory perceptions lag behind the actual events: the RL agent needs to estimate the real state of its environment based on past observations. State-of-the-art (SOTA) methods typically employ recursive, step-by-step forecasting of states. This can cause the accumulation of compounding errors. To tackle this problem, our novel belief estimation method, named Directly Forecasting Belief Transformer (DFBT), directly forecasts states from observations without incrementally estimating intermediate states step-by-step. We theoretically demonstrate that DFBT greatly reduces compounding errors of existing recursively forecasting methods, yielding stronger performance guarantees. In experiments with D4RL offline datasets, DFBT reduces compounding errors with remarkable prediction accuracy. DFBT's capability to forecast state sequences also facilitates multi-step bootstrapping, thus greatly improving learning efficiency. On the MuJoCo benchmark, our DFBT-based method substantially outperforms SOTA baselines. Code is available at https://github.com/QingyuanWuNothing/DFBT.

cs.LG↗

arXiv2025

Mixture of Sparse Attention: Content-Based Learnable Sparse Attention via Expert-Choice Routing

Recent advances in large language models highlighted the excessive quadratic cost of self-attention. Despite the significant research efforts, subquadratic attention methods still suffer from inferior performance in practice. We hypothesize that dynamic, learned content-based sparsity can lead to more efficient attention mechanisms. We present Mixture of Sparse Attention (MoSA), a novel approach inspired by Mixture of Experts (MoE) with expert choice routing. MoSA dynamically selects tokens for each attention head, allowing arbitrary sparse attention patterns. By selecting $k$ tokens from a sequence of length $T$, MoSA reduces the computational complexity of each attention head from $O(T^2)$ to $O(k^2 + T)$. This enables using more heads within the same computational budget, allowing higher specialization. We show that among the tested sparse attention variants, MoSA is the only one that can outperform the dense baseline, sometimes with up to 27% better perplexity for an identical compute budget. MoSA can also reduce the resource usage compared to dense self-attention. Despite using torch implementation without an optimized kernel, perplexity-matched MoSA models are simultaneously faster in wall-clock time, require less memory for training, and drastically reduce the size of the KV-cache compared to the dense transformer baselines.

cs.LG↗

arXiv2025

Can Video Diffusion Model Reconstruct 4D Geometry?

Reconstructing dynamic 3D scenes (i.e., 4D geometry) from monocular video is an important yet challenging problem. Conventional multiview geometry-based approaches often struggle with dynamic motion, whereas recent learning-based methods either require specialized 4D representation or sophisticated optimization. In this paper, we present Sora3R, a novel framework that taps into the rich spatiotemporal priors of large-scale video diffusion models to directly infer 4D pointmaps from casual videos. Sora3R follows a two-stage pipeline: (1) we adapt a pointmap VAE from a pretrained video VAE, ensuring compatibility between the geometry and video latent spaces; (2) we finetune a diffusion backbone in combined video and pointmap latent space to generate coherent 4D pointmaps for every frame. Sora3R operates in a fully feedforward manner, requiring no external modules (e.g., depth, optical flow, or segmentation) or iterative global alignment. Extensive experiments demonstrate that Sora3R reliably recovers both camera poses and detailed scene geometry, achieving performance on par with state-of-the-art methods for dynamic 4D reconstruction across diverse scenarios.

cs.CV↗