arXiv subjects

Jonas Hübotter

Publications and source records attributed to Jonas Hübotter.

At least 19 recordsLinked to original sources

arXiv2026

On Repulsive and Attractive Teachers: Separating Correctness from Behavior in Self-Distillation

On-policy self-distillation provides dense, token-level supervision by conditioning a model on privileged information and distilling the resulting teacher distribution back into the model. However, privileged information can change not only what the teacher knows, but also how it behaves, entangling correctness-relevant learning signals with unintended behavioral shifts. We study this effect in reasoning tasks by contrasting attractive self-distillation, which moves the model toward a privileged teacher, with repulsive self-distillation, which moves it away from a privileged teacher. We find that both objectives can induce strong and opposing behavioral shifts: attraction suppresses exploratory reasoning and promotes shorter, more confident responses, whereas repulsion increases response length, can trigger unintended switches into a model's latent thinking mode, and ultimately becomes unstable. Motivated by these observations, we study contrastive self-distillation, which combines attraction toward a correct-solution-conditioned teacher with repulsion from an incorrect-solution-conditioned teacher. In contrast to prior work that combines such distillation signals with a GRPO objective, we isolate the self-distillation objective and study its behavior on its own. We find that the shared behavioral shifts of the two teachers largely cancel, leaving a token-level signal that more directly reflects correctness. Across non-thinking, instruct-only, and already-thinking models, this contrastive objective improves reasoning performance while maintaining stable response lengths.

cs.LG↗

arXiv2026

Self-Distillation Enables Continual Learning

Continual learning, enabling models to acquire new skills and knowledge without degrading existing capabilities, remains a fundamental challenge for foundation models. While on-policy reinforcement learning can reduce forgetting, it requires explicit reward functions that are often unavailable. Learning from expert demonstrations, the primary alternative, is dominated by supervised fine-tuning (SFT), which is inherently off-policy. We introduce Self-Distillation Fine-Tuning (SDFT), a simple method that enables on-policy learning directly from demonstrations. SDFT leverages in-context learning by using a demonstration-conditioned model as its own teacher, generating on-policy training signals that preserve prior capabilities while acquiring new skills. Across skill learning and knowledge acquisition tasks, SDFT consistently outperforms SFT, achieving higher new-task accuracy while substantially reducing catastrophic forgetting. In sequential learning experiments, SDFT enables a single model to accumulate multiple skills over time without performance regression, establishing on-policy distillation as a practical path to continual learning from demonstrations.

cs.LG↗

arXiv2026

Test-time Offline Reinforcement Learning on Goal-related Experience

Foundation models compress a large amount of information in a single, large neural network, which can then be queried for individual tasks. There are strong parallels between this widespread framework and offline goal-conditioned reinforcement learning algorithms: a universal value function is trained on a large number of goals, and the policy is evaluated on a single goal in each test episode. Extensive research in foundation models has shown that performance can be substantially improved through test-time training, specializing the model to the current goal. We find similarly that test-time offline reinforcement learning on experience related to the test goal can lead to substantially better policies at modest compute costs. We propose a novel self-supervised data selection criterion, which selects transitions from an offline dataset according to their relevance to the current state and quality with respect to the evaluation goal. We demonstrate across a wide range of high-dimensional loco-navigation and manipulation tasks that fine-tuning a policy on the selected data for a few gradient steps leads to significant performance gains over standard offline pre-training. Our goal-conditioned test-time training (GC-TTT) algorithm applies this routine in a receding-horizon fashion during evaluation, adapting the policy to the current trajectory as it is being rolled out. Finally, we study compute allocation at inference, demonstrating that, at comparable costs, GC-TTT induces performance gains that are not achievable by scaling model size.

cs.LG↗

arXiv2026

Majority Voting for Code Generation

We investigate Functional Majority Voting (FMV), a method based on functional consensus for code generation with Large Language Models, which identifies a representative solution from multiple generations using their runtime execution signatures on test inputs. We find that FMV is an effective test-time inference strategy, substantially boosting performance on LiveCodeBench without a large compute overhead. Furthermore, we extend the utility of functional consensus and apply it as an aggregation strategy for label-free Test-Time Reinforcement Learning. We demonstrate that this increases pass@1 on holdout tasks, but find no evidence of self-improvement beyond the base model's performance ceiling.

cs.LG↗

arXiv2026

Tool-R0: Self-Evolving LLM Agents for Tool-Learning from Zero Data

Large language models (LLMs) are becoming the foundation for autonomous agents that can use tools to solve complex tasks. Reinforcement learning (RL) has emerged as a common approach for injecting such agentic capabilities, but typically under tightly controlled training setups. It often depends on carefully constructed task-solution pairs and substantial human supervision, which creates a fundamental obstacle to open-ended self-evolution toward superintelligent systems. In this paper, we propose Tool-R0 framework for training general purpose tool-calling agents from scratch with self-play RL, under a zero-data assumption. Initialized from the same base LLM, Tool-R0 co-evolves a Generator and a Solver with complementary rewards: one proposes targeted challenging tasks at the other's competence frontier and the other learns to solve them with real-world tool calls. This creates a self-evolving cycle that requires no pre-existing tasks or datasets. Evaluation on different tool-use benchmarks show that Tool-R0 yields 92.5 relative improvement over the base model and surpasses fully supervised tool-calling baselines under the same setting. Our work further provides empirical insights into self-play LLM agents by analyzing co-evolution, curriculum dynamics, and scaling behavior.

cs.LG↗

arXiv2026

Aligning Language Models from User Interactions

Multi-turn user interactions are among the most abundant data produced by language models, yet we lack effective methods to learn from them. While typically discarded, these interactions often contain useful information: follow-up user messages may indicate that a response was incorrect, failed to follow an instruction, or did not align with the user's preferences. Importantly, language models are already able to make use of this information in context. After observing a user's follow-up, the same model is often able to revise its behavior. We leverage this ability to propose a principled and scalable method for learning directly from user interactions through self-distillation. By conditioning the model on the user's follow-up message and comparing the resulting token distribution with the original policy, we obtain a target for updating the policy that captures how the model's behavior changes in hindsight. We then distill this hindsight distribution back into the current policy. Remarkably, we show that training on real-world user conversations from WildChat improves language models across standard alignment and instruction-following benchmarks, without regressing other capabilities. The same mechanism enables personalization, allowing models to continually adapt to individual users through interaction without explicit feedback. Our results demonstrate that raw user interactions that arise naturally during deployment enable alignment, personalization, and continual adaptation.

cs.CL↗

arXiv2026

Reinforcement Learning via Self-Distillation

Large language models are increasingly post-trained with reinforcement learning in verifiable domains such as code and math. Yet, current methods for reinforcement learning with verifiable rewards (RLVR) learn only from a scalar outcome reward per attempt, creating a severe credit-assignment bottleneck. Many verifiable environments actually provide rich textual feedback, such as runtime errors or judge evaluations, that explain why an attempt failed. We formalize this setting as reinforcement learning with rich feedback and introduce Self-Distillation Policy Optimization (SDPO), which converts tokenized feedback into a dense learning signal without any external teacher or explicit reward model. SDPO treats the current model conditioned on feedback as a self-teacher and distills its feedback-informed next-token predictions back into the policy. In this way, SDPO leverages the model's ability to retrospectively identify its own mistakes in-context. Across scientific reasoning, tool use, and competitive programming on LiveCodeBench v6, SDPO improves sample efficiency and final accuracy over strong RLVR baselines. Notably, SDPO also outperforms baselines in standard RLVR environments that only return scalar feedback by using successful rollouts as implicit feedback for failed attempts. Finally, applying SDPO to individual questions at test time accelerates discovery on difficult binary-reward tasks, achieving the same discovery probability as best-of-k sampling or multi-turn conversations with 3x fewer attempts.

cs.LG↗

arXiv2026

Specialization after Generalization: Towards Understanding Test-Time Training in Foundation Models

Recent empirical studies have explored the idea of continuing to train a model at test-time for a given task, known as test-time training (TTT), and have found it to yield significant performance improvements. However, there is limited understanding of why and when TTT is effective. Earlier explanations mostly focused on the observation that TTT may help when applied to out-of-distribution adaptation or used with privileged data. However, the growing scale of foundation models with most test data being in-distribution questions these explanations. We instead posit that foundation models remain globally underparameterized, with TTT providing a mechanism for specialization after generalization, focusing capacity on concepts relevant to the test task. Specifically, under the linear representation hypothesis, we propose a model in which TTT achieves a substantially smaller in-distribution test error than global training. We empirically validate our model's key assumptions by training a sparse autoencoder on ImageNet, showing that semantically related data points are explained by only a few shared concepts. Finally, we perform scaling studies across image and language tasks that confirm the practical implications of our model, identifying the regimes where specialization is most effective.

cs.LG↗

arXiv2025

DISCOVER: Automated Curricula for Sparse-Reward Reinforcement Learning

Sparse-reward reinforcement learning (RL) can model a wide range of highly complex tasks. Solving sparse-reward tasks is RL's core premise, requiring efficient exploration coupled with long-horizon credit assignment, and overcoming these challenges is key for building self-improving agents with superhuman ability. Prior work commonly explores with the objective of solving many sparse-reward tasks, making exploration of individual high-dimensional, long-horizon tasks intractable. We argue that solving such challenging tasks requires solving simpler tasks that are relevant to the target task, i.e., whose achieval will teach the agent skills required for solving the target task. We demonstrate that this sense of direction, necessary for effective exploration, can be extracted from existing RL algorithms, without leveraging any prior information. To this end, we propose a method for directed sparse-reward goal-conditioned very long-horizon RL (DISCOVER), which selects exploratory goals in the direction of the target task. We connect DISCOVER to principled exploration in bandits, formally bounding the time until the target task becomes achievable in terms of the agent's initial distance to the target, but independent of the volume of the space of all tasks. We then perform a thorough evaluation in high-dimensional environments. We find that the directed goal selection of DISCOVER solves exploration problems that are beyond the reach of prior state-of-the-art exploration methods in RL.

cs.LG↗

arXiv2025

Learning on the Job: Test-Time Curricula for Targeted Reinforcement Learning

Humans are good at learning on the job: We learn how to solve the tasks we face as we go along. Can a model do the same? We propose an agent that assembles a task-specific curriculum, called test-time curriculum (TTC-RL), and applies reinforcement learning to continue training the model for its target task. The test-time curriculum avoids time-consuming human curation of datasets by automatically selecting the most task-relevant data from a large pool of available training data. Our experiments demonstrate that reinforcement learning on a test-time curriculum consistently improves the model on its target tasks, across a variety of evaluations and models. Notably, on challenging math and coding benchmarks, TTC-RL improves the pass@1 of Qwen3-8B by approximately 1.8x on AIME25 and 2.1x on CodeElo. Moreover, we find that TTC-RL significantly raises the performance ceiling compared to the initial model, increasing pass@8 on AIME25 from 40% to 62% and on CodeElo from 28% to 43%. Our findings show the potential of test-time curricula in extending the test-time scaling paradigm to continual training on thousands of task-relevant experiences during test-time.

cs.LG↗

arXiv2025

Local Mixtures of Experts: Essentially Free Test-Time Training via Model Merging

Mixture of expert (MoE) models are a promising approach to increasing model capacity without increasing inference cost, and are core components of many state-of-the-art language models. However, current MoE models typically use only few experts due to prohibitive training and inference cost. We propose Test-Time Model Merging (TTMM) which scales the MoE paradigm to an order of magnitude more experts and uses model merging to avoid almost any test-time overhead. We show that TTMM is an approximation of test-time training (TTT), which fine-tunes an expert model for each prediction task, i.e., prompt. TTT has recently been shown to significantly improve language models, but is computationally expensive. We find that performance of TTMM improves with more experts and approaches the performance of TTT. Moreover, we find that with a 1B parameter base model, TTMM is more than 100x faster than TTT at test-time by amortizing the cost of TTT at train-time. Thus, TTMM offers a promising cost-effective approach to scale test-time training.

cs.LG↗

arXiv2025

Maximizing Prefix-Confidence at Test-Time Efficiently Improves Mathematical Reasoning

Recent work has shown that language models can self-improve by maximizing their own confidence in their predictions, without relying on external verifiers or reward signals. In this work, we study the test-time scaling of language models for mathematical reasoning tasks, where the model's own confidence is used to select the most promising attempts. Surprisingly, we find that we can achieve significant performance gains by continuing only the most promising attempt, selected by the model's prefix-confidence. We systematically evaluate prefix-confidence scaling on five mathematical reasoning datasets: the school-level GSM8K and MATH500, and the competition-level AMC23, AIME24, and AIME25. We find that prefix-confidence scaling with prefixes of only 32 tokens achieves a better accuracy-compute trade-off than majority voting. Moreover, prefix-confidence scaling appears less susceptible than BoN to length biases. Finally, we also evaluate test-time training with prefix-confidence and find that, while outperforming the base model, it does not improve over prefix-confidence scaling.

cs.LG↗

arXiv2025

LITE: Efficiently Estimating Gaussian Probability of Maximality

We consider the problem of computing the probability of maximality (PoM) of a Gaussian random vector, i.e., the probability for each dimension to be maximal. This is a key challenge in applications ranging from Bayesian optimization to reinforcement learning, where the PoM not only helps with finding an optimal action, but yields a fine-grained analysis of the action domain, crucial in tasks such as drug discovery. Existing techniques are costly, scaling polynomially in computation and memory with the vector size. We introduce LITE, the first approach for estimating Gaussian PoM with almost-linear time and memory complexity. LITE achieves SOTA accuracy on a number of tasks, while being in practice several orders of magnitude faster than the baselines. This also translates to a better performance on downstream tasks such as entropy estimation and optimal control of bandits. Theoretically, we cast LITE as entropy-regularized UCB and connect it to prior PoM estimators.

stat.ML↗

arXiv2025

Active Fine-Tuning of Multi-Task Policies

Pre-trained generalist policies are rapidly gaining relevance in robot learning due to their promise of fast adaptation to novel, in-domain tasks. This adaptation often relies on collecting new demonstrations for a specific task of interest and applying imitation learning algorithms, such as behavioral cloning. However, as soon as several tasks need to be learned, we must decide which tasks should be demonstrated and how often? We study this multi-task problem and explore an interactive framework in which the agent adaptively selects the tasks to be demonstrated. We propose AMF (Active Multi-task Fine-tuning), an algorithm to maximize multi-task policy performance under a limited demonstration budget by collecting demonstrations yielding the largest information gain on the expert policy. We derive performance guarantees for AMF under regularity assumptions and demonstrate its empirical effectiveness to efficiently fine-tune neural policies in complex and high-dimensional environments.

cs.LG↗

arXiv2025

Transductive Active Learning: Theory and Applications

We study a generalization of classical active learning to real-world settings with concrete prediction targets where sampling is restricted to an accessible region of the domain, while prediction targets may lie outside this region. We analyze a family of decision rules that sample adaptively to minimize uncertainty about prediction targets. We are the first to show, under general regularity assumptions, that such decision rules converge uniformly to the smallest possible uncertainty obtainable from the accessible data. We demonstrate their strong sample efficiency in two key applications: active fine-tuning of large neural networks and safe Bayesian optimization, where they achieve state-of-the-art performance.

cs.LG↗

arXiv2025

Efficiently Learning at Test-Time: Active Fine-Tuning of LLMs

Recent efforts in fine-tuning language models often rely on automatic data selection, commonly using Nearest Neighbors retrieval from large datasets. However, we theoretically show that this approach tends to select redundant data, limiting its effectiveness or even hurting performance. To address this, we introduce SIFT, a data selection algorithm designed to reduce uncertainty about the model's response given a prompt, which unifies ideas from retrieval and active learning. Whereas Nearest Neighbor retrieval typically fails in the presence of information duplication, SIFT accounts for information duplication and optimizes the overall information gain of the selected examples. We focus our evaluations on fine-tuning at test-time for prompt-specific language modeling on the Pile dataset, and show that SIFT consistently outperforms Nearest Neighbor retrieval, with minimal computational overhead. Moreover, we show that our uncertainty estimates can predict the performance gain of test-time fine-tuning, and use this to develop an adaptive algorithm that invests test-time compute proportional to realized performance gains. We provide the $\texttt{activeft}$ (Active Fine-Tuning) library which can be used as a drop-in replacement for Nearest Neighbor retrieval.

cs.LG↗

arXiv2025

Probabilistic Artificial Intelligence

Artificial intelligence commonly refers to the science and engineering of artificial systems that can carry out tasks generally associated with requiring aspects of human intelligence, such as playing games, translating languages, and driving cars. In recent years, there have been exciting advances in learning-based, data-driven approaches towards AI, and machine learning and deep learning have enabled computer systems to perceive the world in unprecedented ways. Reinforcement learning has enabled breakthroughs in complex games such as Go and challenging robotics tasks such as quadrupedal locomotion. A key aspect of intelligence is to not only make predictions, but reason about the uncertainty in these predictions, and to consider this uncertainty when making decisions. This is what this manuscript on "Probabilistic Artificial Intelligence" is about. The first part covers probabilistic approaches to machine learning. We discuss the differentiation between "epistemic" uncertainty due to lack of data and "aleatoric" uncertainty, which is irreducible and stems, e.g., from noisy observations and outcomes. We discuss concrete approaches towards probabilistic inference and modern approaches to efficient approximate inference. The second part of the manuscript is about taking uncertainty into account in sequential decision tasks. We consider active learning and Bayesian optimization -- approaches that collect data by proposing experiments that are informative for reducing the epistemic uncertainty. We then consider reinforcement learning and modern deep RL approaches that use neural network function approximation. We close by discussing modern approaches in model-based RL, which harness epistemic and aleatoric uncertainty to guide exploration, while also reasoning about safety.

cs.AI↗

arXiv2024

Active Few-Shot Fine-Tuning

We study the question: How can we select the right data for fine-tuning to a specific task? We call this data selection problem active fine-tuning and show that it is an instance of transductive active learning, a novel generalization of classical active learning. We propose ITL, short for information-based transductive learning, an approach which samples adaptively to maximize information gained about the specified task. We are the first to show, under general regularity assumptions, that such decision rules converge uniformly to the smallest possible uncertainty obtainable from the accessible data. We apply ITL to the few-shot fine-tuning of large neural networks and show that fine-tuning with ITL learns the task with significantly fewer examples than the state-of-the-art.

cs.LG↗