Daily Papers

Despite remarkable progress, multimodal foundation models still exhibit surprising deficiencies in spatial intelligence. In this work, we explore scaling up multimodal foundation models to cultivate spatial intelligence within the SenseNova-SI family, built upon established multimodal foundations including visual understanding models (i.e., Qwen3-VL and InternVL3) and unified understanding and generation models (i.e., Bagel). We take a principled approach to constructing high-performing and robust spatial intelligence by systematically curating SenseNova-SI-8M: eight million diverse data samples under a rigorous taxonomy of spatial capabilities. SenseNova-SI demonstrates unprecedented performance across a broad range of spatial intelligence benchmarks: 68.7% on VSI-Bench, 43.3% on MMSI, 85.6% on MindCube, 54.6% on ViewSpatial, and 50.1% on SITE, while maintaining strong general multimodal understanding (e.g., 84.9% on MMBench-En). More importantly, we analyze the impact of data scaling, discuss early signs of emergent generalization capabilities enabled by diverse data training, analyze the risk of overfitting and language shortcuts, present a preliminary study on spatial chain-of-thought reasoning, and validate the potential downstream application. SenseNova-SI is an ongoing project, and this report will be updated continuously. All newly trained multimodal foundation models are publicly released to facilitate further research in this direction.

Foundation models in language and multimodality achieve strong generalization by aligning heterogeneous data under a unified formulation and training at scale. In this report, we investigate whether this scaling recipe can be applied to robotic manipulation to achieve genuine generalization. This is challenging because, unlike text, manipulation data is heterogeneous by nature, expensive to collect, and narrow in diversity, making alignment and scale simultaneously difficult. We present Qwen-RobotManip, a generalizable Vision-Language-Action foundation model built on Qwen-VL. Qwen-RobotManip introduces a unified alignment framework across the representation, motion, and behavioral dimensions of manipulation, making large-scale multi-source training coherent rather than conflicting. This alignment capability in turn enables Qwen-RobotManip to absorb manipulation data at a scale that prior training regimes could not sustain. A human-to-robot synthesis pipeline converts egocentric hand demonstrations into robot trajectories across 15 platforms, and a rigorous curation pipeline harmonizes heterogeneous datasets. Using only open-source datasets and human videos without proprietary data collection, Qwen-RobotManip constructs a ~38,100-hour pretraining corpus and exhibits emergent generalization capabilities, including zero-shot instruction following, robustness to perturbations, reactive error recovery, and cross-embodiment transfer. We find that standard benchmarks fail to capture pretraining quality and instead adopt OOD settings including RoboCasa365, LIBERO-Plus, EBench, RoboTwin-Clean2Rand, RoboTwin-IF, and RoboTwin-XE. Qwen-RobotManip substantially outperforms prior state-of-the-art models, including π0.5, across all OOD settings, ranks 1st in RoboChallenge with a 20% relative improvement, and is validated on real-robot platforms including AgileX ALOHA, Franka, UR, and ARX.

The 6G wireless communications aim to establish an intelligent world of ubiquitous connectivity, providing an unprecedented communication experience. Large artificial intelligence models (LAMs) are characterized by significantly larger scales (e.g., billions or trillions of parameters) compared to typical artificial intelligence (AI) models. LAMs exhibit outstanding cognitive abilities, including strong generalization capabilities for fine-tuning to downstream tasks, and emergent capabilities to handle tasks unseen during training. Therefore, LAMs efficiently provide AI services for diverse communication applications, making them crucial tools for addressing complex challenges in future wireless communication systems. This study provides a comprehensive review of the foundations, applications, and challenges of LAMs in communication. First, we introduce the current state of AI-based communication systems, emphasizing the motivation behind integrating LAMs into communications and summarizing the key contributions. We then present an overview of the essential concepts of LAMs in communication. This includes an introduction to the main architectures of LAMs, such as transformer, diffusion models, and mamba. We also explore the classification of LAMs, including large language models (LLMs), large vision models (LVMs), large multimodal models (LMMs), and world models, and examine their potential applications in communication. Additionally, we cover the training methods and evaluation techniques for LAMs in communication systems. Lastly, we introduce optimization strategies such as chain of thought (CoT), retrieval augmented generation (RAG), and agentic systems. Following this, we discuss the research advancements of LAMs across various communication scenarios. Finally, we analyze the challenges in the current research and provide insights into potential future research directions.

We survey applications of pretrained foundation models in robotics. Traditional deep learning models in robotics are trained on small datasets tailored for specific tasks, which limits their adaptability across diverse applications. In contrast, foundation models pretrained on internet-scale data appear to have superior generalization capabilities, and in some instances display an emergent ability to find zero-shot solutions to problems that are not present in the training data. Foundation models may hold the potential to enhance various components of the robot autonomy stack, from perception to decision-making and control. For example, large language models can generate code or provide common sense reasoning, while vision-language models enable open-vocabulary visual recognition. However, significant open research challenges remain, particularly around the scarcity of robot-relevant training data, safety guarantees and uncertainty quantification, and real-time execution. In this survey, we study recent papers that have used or built foundation models to solve robotics problems. We explore how foundation models contribute to improving robot capabilities in the domains of perception, decision-making, and control. We discuss the challenges hindering the adoption of foundation models in robot autonomy and provide opportunities and potential pathways for future advancements. The GitHub project corresponding to this paper (Preliminary release. We are committed to further enhancing and updating this work to ensure its quality and relevance) can be found here: https://github.com/robotics-survey/Awesome-Robotics-Foundation-Models

Large language models (LLMs) have demonstrated impressive generalization and emergent capabilities, yet their pre-training remains computationally expensive and sensitive to optimization dynamics. While Adam-based optimizers offer fast convergence by adapting learning rates coordinate-wise, recent studies reveal that their updates often suffer from poor spectral conditioning and low-rank structures, hindering efficiency. Muon addresses this issue via global spectral normalization but lacks the per-coordinate adaptivity of Adam. In this work, we propose Column-Normalized Adam (Conda), a novel optimizer that bridges the strengths of both approaches. Conda projects updates into an orthogonal subspace and applies column-wise second moment normalization based on the projected gradients, thereby achieving both improved spectral conditioning and maintaining coordinate-wise adaptivity. This design alleviates the spectral pathologies of Adam while preserving its fast convergence behavior. Extensive experiments on the LLaMA and GPT-2 series show that Conda consistently outperforms AdamW, Muon, and other baselines in pre-training. Remarkably, on the LLaMA series, Conda achieves 2-2.5 the convergence speed of AdamW, measured in both training steps and training time. Further ablations demonstrate its robustness under diverse training setups. These results collectively highlight Conda as an effective and broadly applicable optimizer for large-scale LLM training. The code is released on https://github.com/jie040109/Conda

Large language models (LLMs) have brought autonomous agents closer to artificial general intelligence (AGI) due to their promising generalization and emergent capabilities. There is, however, a lack of studies on how LLM-based agents behave, why they could potentially fail, and how to improve them, particularly in demanding real-world planning tasks. In this paper, as an effort to fill the gap, we present our study using a realistic benchmark, TravelPlanner, where an agent must meet multiple constraints to generate accurate plans. We leverage this benchmark to address four key research questions: (1) are LLM agents robust enough to lengthy and noisy contexts when it comes to reasoning and planning? (2) can few-shot prompting adversely impact the performance of LLM agents in scenarios with long context? (3) can we rely on refinement to improve plans, and (4) can fine-tuning LLMs with both positive and negative feedback lead to further improvement? Our comprehensive experiments indicate that, firstly, LLMs often fail to attend to crucial parts of a long context, despite their ability to handle extensive reference information and few-shot examples; secondly, they still struggle with analyzing the long plans and cannot provide accurate feedback for refinement; thirdly, we propose Feedback-Aware Fine-Tuning (FAFT), which leverages both positive and negative feedback, resulting in substantial gains over Supervised Fine-Tuning (SFT). Our findings offer in-depth insights to the community on various aspects related to real-world planning applications.

Affordance grounding focuses on predicting the specific regions of objects that are associated with the actions to be performed by robots. It plays a vital role in the fields of human-robot interaction, human-object interaction, embodied manipulation, and embodied perception. Existing models often neglect the affordance shared among different objects because they lack the Chain-of-Thought(CoT) reasoning abilities, limiting their out-of-domain (OOD) generalization and explicit reasoning capabilities. To address these challenges, we propose Affordance-R1, the first unified affordance grounding framework that integrates cognitive CoT guided Group Relative Policy Optimization (GRPO) within a reinforcement learning paradigm. Specifically, we designed a sophisticated affordance function, which contains format, perception, and cognition rewards to effectively guide optimization directions. Furthermore, we constructed a high-quality affordance-centric reasoning dataset, ReasonAff, to support training. Trained exclusively via reinforcement learning with GRPO and without explicit reasoning data, Affordance-R1 achieves robust zero-shot generalization and exhibits emergent test-time reasoning capabilities. Comprehensive experiments demonstrate that our model outperforms well-established methods and exhibits open-world generalization. To the best of our knowledge, Affordance-R1 is the first to integrate GRPO-based RL with reasoning into affordance reasoning. The code of our method and our dataset is released on https://github.com/hq-King/Affordance-R1.

We present a new robotic foundation model, called π_{0.7}, that can enable strong out-of-the-box performance in a wide range of scenarios. π_{0.7} can follow diverse language instructions in unseen environments, including multi-stage tasks with various kitchen appliances, provide zero-shot cross-embodiment generalization, for example enabling a robot to fold laundry without seeing the task before, and perform challenging tasks such as operating an espresso machine out of the box at a level of performance that matches much more specialized RL-finetuned models. The main idea behind π_{0.7} is to use diverse context conditioning during training. This conditioning information, contained in the prompt, makes it possible to steer the model precisely to perform many tasks with different strategies. It is conditioned not just on a language command that describes what it should do, but on additional multimodal information that also describes the manner or strategy in which it should do it, including metadata about task performance and subgoal images. This enables π_{0.7} to use very diverse data, including demonstrations, potentially suboptimal (autonomous) data including failures, and data from non-robot sources. Our experiments evaluate π_{0.7} across numerous tasks with multiple robot platforms, on tasks that require speed and dexterity, language following, and compositional task generalization.

Prior work has shown that fine-tuning large language models on malicious or incorrect outputs in narrow domains can induce broad misalignment and harmful behavior, a phenomenon known as emergent misalignment. However, efficient methods for reversing such misalignment remain limited. In this work, we make two contributions. First, we identify sycophancy fine-tuning, i.e., training models to passively agree with users' incorrect opinions, as a previously underexplored driver of emergent misalignment, and show that it induces broad and severe misaligned behavior. Second, we propose Alignment Gating, an efficient method for reversing emergent misalignment that inserts learnable and controllable gates into the model during fine-tuning. Through fine-tuning, these gates learn to identify the internal representations responsible for unsafe responses. Thus, amplifying or suppressing these representations then exacerbates or mitigates EM, respectively. We further find that alignment gating module exhibits strong generalization: gating weights obtained from narrow-domain fine-tuning substantially suppress broad-domain misaligned behavior while preserving the model's general capabilities.

The pursuit of data efficiency, where quality outweighs quantity, has emerged as a cornerstone in robotic manipulation, especially given the high costs associated with real-world data collection. We propose that maximizing the informational density of individual demonstrations can dramatically reduce reliance on large-scale datasets while improving task performance. To this end, we introduce Adversarial Data Collection, a Human-in-the-Loop (HiL) framework that redefines robotic data acquisition through real-time, bidirectional human-environment interactions. Unlike conventional pipelines that passively record static demonstrations, ADC adopts a collaborative perturbation paradigm: during a single episode, an adversarial operator dynamically alters object states, environmental conditions, and linguistic commands, while the tele-operator adaptively adjusts actions to overcome these evolving challenges. This process compresses diverse failure-recovery behaviors, compositional task variations, and environmental perturbations into minimal demonstrations. Our experiments demonstrate that ADC-trained models achieve superior compositional generalization to unseen task instructions, enhanced robustness to perceptual perturbations, and emergent error recovery capabilities. Strikingly, models trained with merely 20% of the demonstration volume collected through ADC significantly outperform traditional approaches using full datasets. These advances bridge the gap between data-centric learning paradigms and practical robotic deployment, demonstrating that strategic data acquisition, not merely post-hoc processing, is critical for scalable, real-world robot learning. Additionally, we are curating a large-scale ADC-Robotics dataset comprising real-world manipulation tasks with adversarial perturbations. This benchmark will be open-sourced to facilitate advancements in robotic imitation learning.

Vision-Language-Action (VLA) models have shown strong potential for general-purpose robotic manipulation, but their reliance on expert demonstrations limits their ability to learn from failures and perform self-corrections. Reinforcement learning (RL) addresses these through self-improving interactions with the physical environment, but suffers from high sample complexity on real robots. We introduce World-Model-based Policy Optimization (WMPO), a principled framework for on-policy VLA RL without interacting with the real environment. In contrast to widely used latent world models, WMPO focuses on pixel-based predictions that align the "imagined" trajectories with the VLA features pretrained with web-scale images. Crucially, WMPO enables the policy to perform on-policy GRPO that provides stronger performance than the often-used off-policy methods. Extensive experiments in both simulation and real-robot settings demonstrate that WMPO (i) substantially improves sample efficiency, (ii) achieves stronger overall performance, (iii) exhibits emergent behaviors such as self-correction, and (iv) demonstrates robust generalization and lifelong learning capabilities.

Traditional methods for reasoning segmentation rely on supervised fine-tuning with categorical labels and simple descriptions, limiting its out-of-domain generalization and lacking explicit reasoning processes. To address these limitations, we propose Seg-Zero, a novel framework that demonstrates remarkable generalizability and derives explicit chain-of-thought reasoning through cognitive reinforcement. Seg-Zero introduces a decoupled architecture consisting of a reasoning model and a segmentation model. The reasoning model interprets user intentions, generates explicit reasoning chains, and produces positional prompts, which are subsequently used by the segmentation model to generate precious pixel-level masks. We design a sophisticated reward mechanism that integrates both format and accuracy rewards to effectively guide optimization directions. Trained exclusively via reinforcement learning with GRPO and without explicit reasoning data, Seg-Zero achieves robust zero-shot generalization and exhibits emergent test-time reasoning capabilities. Experiments show that Seg-Zero-7B achieves a zero-shot performance of 57.5 on the ReasonSeg benchmark, surpassing the prior LISA-7B by 18\%. This significant improvement highlights Seg-Zero's ability to generalize across domains while presenting an explicit reasoning process. Code is available at https://github.com/dvlab-research/Seg-Zero.

We present a smoothly broken power law functional form (that we refer to as a Broken Neural Scaling Law (BNSL)) that accurately models & extrapolates the scaling behaviors of deep neural networks (i.e. how the evaluation metric of interest varies as amount of compute used for training (or inference), number of model parameters, training dataset size, model input size, number of training steps, or upstream performance varies) for various architectures & for each of various tasks within a large & diverse set of upstream & downstream tasks, in zero-shot, prompted, & finetuned settings. This set includes large-scale vision, language, audio, video, diffusion, generative modeling, multimodal learning, contrastive learning, AI alignment, AI capabilities, robotics, out-of-distribution (OOD) generalization, continual learning, transfer learning, uncertainty estimation / calibration, OOD detection, adversarial robustness, distillation, sparsity, retrieval, quantization, pruning, fairness, molecules, computer programming/coding, math word problems, "emergent phase transitions", arithmetic, supervised learning, unsupervised/self-supervised learning, & reinforcement learning (single agent & multi-agent). When compared to other functional forms for neural scaling, this functional form yields extrapolations of scaling behavior that are considerably more accurate on this set. Moreover, this functional form accurately models & extrapolates scaling behavior that other functional forms are incapable of expressing such as the nonmonotonic transitions present in the scaling behavior of phenomena such as double descent & the delayed, sharp inflection points present in the scaling behavior of tasks such as arithmetic. Lastly, we use this functional form to glean insights about the limit of the predictability of scaling behavior. Code is available at https://github.com/ethancaballero/broken_neural_scaling_laws

Modern generative models demonstrate impressive capabilities, likely stemming from an ability to identify and manipulate abstract concepts underlying their training data. However, fundamental questions remain: what determines the concepts a model learns, the order in which it learns them, and its ability to manipulate those concepts? To address these questions, we propose analyzing a model's learning dynamics via a framework we call the concept space, where each axis represents an independent concept underlying the data generating process. By characterizing learning dynamics in this space, we identify how the speed at which a concept is learned, and hence the order of concept learning, is controlled by properties of the data we term concept signal. Further, we observe moments of sudden turns in the direction of a model's learning dynamics in concept space. Surprisingly, these points precisely correspond to the emergence of hidden capabilities, i.e., where latent interventions show the model possesses the capability to manipulate a concept, but these capabilities cannot yet be elicited via naive input prompting. While our results focus on synthetically defined toy datasets, we hypothesize a general claim on emergence of hidden capabilities may hold: generative models possess latent capabilities that emerge suddenly and consistently during training, though a model might not exhibit these capabilities under naive input prompting.

Grokking, i.e., test performance keeps improving long after training loss converged, has been recently witnessed in neural network training, making the mechanism of generalization and other emerging capabilities such as reasoning mysterious. While prior studies usually train small models on a few toy or highly-specific tasks for thousands of epochs, we conduct the first study of grokking on checkpoints during one-pass pretraining of a 7B large language model (LLM), i.e., OLMoE. We compute the training loss and evaluate generalization on diverse benchmark tasks, including math reasoning, code generation, and commonsense/domain-specific knowledge retrieval tasks. Our study, for the first time, verifies that grokking still happens in the pretraining of large-scale foundation models, though different data may enter grokking stages asynchronously. We further demystify grokking's "emergence of generalization" by investigating LLM internal dynamics. Specifically, we find that training samples' pathways (i.e., expert choices across layers) evolve from random, instance-specific to more structured and shareable between samples during grokking. Also, the complexity of a sample's pathway reduces despite the converged loss. These indicate a memorization-to-generalization conversion, providing a mechanistic explanation of delayed generalization. In the study, we develop two novel metrics to quantify pathway distance and the complexity of a single pathway. We show their ability to predict the generalization improvement on diverse downstream tasks. They are efficient, simple to compute and solely dependent on training data. Hence, they have practical value for pretraining, enabling us to monitor the generalization performance without finetuning and test. Theoretically, we show that more structured pathways reduce model complexity and improve the generalization bound.

Can machines truly think, reason and act in domains like humans? This enduring question continues to shape the pursuit of Artificial General Intelligence (AGI). Despite the growing capabilities of models such as GPT-4.5, DeepSeek, Claude 3.5 Sonnet, Phi-4, and Grok 3, which exhibit multimodal fluency and partial reasoning, these systems remain fundamentally limited by their reliance on token-level prediction and lack of grounded agency. This paper offers a cross-disciplinary synthesis of AGI development, spanning artificial intelligence, cognitive neuroscience, psychology, generative models, and agent-based systems. We analyze the architectural and cognitive foundations of general intelligence, highlighting the role of modular reasoning, persistent memory, and multi-agent coordination. In particular, we emphasize the rise of Agentic RAG frameworks that combine retrieval, planning, and dynamic tool use to enable more adaptive behavior. We discuss generalization strategies, including information compression, test-time adaptation, and training-free methods, as critical pathways toward flexible, domain-agnostic intelligence. Vision-Language Models (VLMs) are reexamined not just as perception modules but as evolving interfaces for embodied understanding and collaborative task completion. We also argue that true intelligence arises not from scale alone but from the integration of memory and reasoning: an orchestration of modular, interactive, and self-improving components where compression enables adaptive behavior. Drawing on advances in neurosymbolic systems, reinforcement learning, and cognitive scaffolding, we explore how recent architectures begin to bridge the gap between statistical learning and goal-directed cognition. Finally, we identify key scientific, technical, and ethical challenges on the path to AGI.

The rapid advancement of artificial intelligence, particularly with the development of Large Language Models (LLMs) built on the transformer architecture, has redefined the capabilities of natural language processing. These models now exhibit remarkable performance across various language-related tasks, such as text generation, question answering, translation, and summarization, often rivaling human-like comprehension. More intriguingly, LLMs have demonstrated emergent abilities extending beyond their core functions, showing proficiency in tasks like commonsense reasoning, code generation, and arithmetic. This survey paper explores the foundational components, scaling mechanisms, and architectural strategies that drive these capabilities. Emphasizing models like GPT and LLaMA, we analyze the impact of exponential data and computational growth on LLM performance, while also addressing the trade-offs associated with scaling. We also examine LLM applications across sectors, such as healthcare, finance, education, and law, highlighting their adaptability and potential to solve domain-specific challenges. Central to this work are the questions of how LLMs generalize across diverse tasks, exhibit planning, and reasoning abilities, and whether these emergent abilities can be systematically elicited or enhanced. In particular, we provide some insights into the CoT (Chain of Thought) and PoT (Plan of Thought) abilities within LLMs, focusing on how pre-training data influences their emergence. Additionally, we investigate LLM-modulo frameworks that integrate external systems, allowing LLMs to handle complex, dynamic tasks. By analyzing these factors, this paper aims to foster the ongoing discussion on the capabilities and limits of LLMs, promoting their responsible development and application in novel and increasingly complex environments.

Scaling up language models has been shown to predictably improve performance and sample efficiency on a wide range of downstream tasks. This paper instead discusses an unpredictable phenomenon that we refer to as emergent abilities of large language models. We consider an ability to be emergent if it is not present in smaller models but is present in larger models. Thus, emergent abilities cannot be predicted simply by extrapolating the performance of smaller models. The existence of such emergence implies that additional scaling could further expand the range of capabilities of language models.

Weird generalization is a phenomenon in which models fine-tuned on data from a narrow domain (e.g. insecure code) develop surprising traits that manifest even outside that domain (e.g. broad misalignment)-a phenomenon that prior work has highlighted as a critical safety concern. Here, we present an extended replication study of key weird generalization results across an expanded suite of models and datasets. We confirm that surprising (and dangerous) traits can emerge under certain circumstances, but we find that weird generalization is exceptionally brittle: it emerges only for specific models on specific datasets, and it vanishes under simple training-time, prompt-based interventions. We find that the most effective interventions provide prompt context that makes the generalized behavior the expected behavior. However, we show that even very generic interventions that do not anticipate specific generalized traits can still be effective in mitigating weird generalization's effects. Our findings thus help clarify the nature of the safety threat that weird generalization poses and point toward an easily implemented set of solutions.

The scientific scale-up of large language models (LLMs) necessitates a comprehensive understanding of their scaling properties. However, the existing literature on the scaling properties only yields an incomplete answer: optimization loss decreases predictably as the model size increases, in line with established scaling law; yet no scaling law for task has been established and the task performances are far from predictable during scaling. Task performances typically show minor gains on small models until they improve dramatically once models exceed a size threshold, exemplifying the ``emergent abilities''. In this study, we discover that small models, although they exhibit minor performance, demonstrate critical and consistent task performance improvements that are not captured by conventional evaluation strategies due to insufficient measurement resolution. To measure such improvements, we introduce PassUntil, an evaluation strategy through massive sampling in the decoding phase. We conduct quantitative investigations into the scaling law of task performance. Firstly, a strict task scaling law is identified, enhancing the predictability of task performances. Remarkably, we are able to predict the performance of the 2.4B model on code generation with merely 0.05\% deviation before training starts. Secondly, underpinned by PassUntil, we observe concrete evidence of emergent abilities and ascertain that they are not in conflict with the continuity of performance improvement. Their semblance to break-through is that their scaling curve cannot be fitted by standard scaling law function. We then introduce a mathematical definition for the emergent abilities. Through the definition, we refute a prevalent ``multi-step reasoning hypothesis'' regarding the genesis of emergent abilities and propose a new hypothesis with a satisfying fit to the observed scaling curve.

Recent studies have put into question the belief that emergent abilities in language models are exclusive to large models. This skepticism arises from two observations: 1) smaller models can also exhibit high performance on emergent abilities and 2) there is doubt on the discontinuous metrics used to measure these abilities. In this paper, we propose to study emergent abilities in the lens of pre-training loss, instead of model size or training compute. We demonstrate that the models with the same pre-training loss, but different model and data sizes, generate the same performance on various downstream tasks. We also discover that a model exhibits emergent abilities on certain tasks -- regardless of the continuity of metrics -- when its pre-training loss falls below a specific threshold. Before reaching this threshold, its performance remains at the level of random guessing. This inspires us to redefine emergent abilities as those that manifest in models with lower pre-training losses, highlighting that these abilities cannot be predicted by merely extrapolating the performance trends of models with higher pre-training losses.

Recent work claims that large language models display emergent abilities, abilities not present in smaller-scale models that are present in larger-scale models. What makes emergent abilities intriguing is two-fold: their sharpness, transitioning seemingly instantaneously from not present to present, and their unpredictability, appearing at seemingly unforeseeable model scales. Here, we present an alternative explanation for emergent abilities: that for a particular task and model family, when analyzing fixed model outputs, emergent abilities appear due to the researcher's choice of metric rather than due to fundamental changes in model behavior with scale. Specifically, nonlinear or discontinuous metrics produce apparent emergent abilities, whereas linear or continuous metrics produce smooth, continuous predictable changes in model performance. We present our alternative explanation in a simple mathematical model, then test it in three complementary ways: we (1) make, test and confirm three predictions on the effect of metric choice using the InstructGPT/GPT-3 family on tasks with claimed emergent abilities; (2) make, test and confirm two predictions about metric choices in a meta-analysis of emergent abilities on BIG-Bench; and (3) show to choose metrics to produce never-before-seen seemingly emergent abilities in multiple vision tasks across diverse deep networks. Via all three analyses, we provide evidence that alleged emergent abilities evaporate with different metrics or with better statistics, and may not be a fundamental property of scaling AI models.

Large language models have exhibited emergent abilities, demonstrating exceptional performance across diverse tasks for which they were not explicitly trained, including those that require complex reasoning abilities. The emergence of such abilities carries profound implications for the future direction of research in NLP, especially as the deployment of such models becomes more prevalent. However, one key challenge is that the evaluation of these abilities is often confounded by competencies that arise in models through alternative prompting techniques, such as in-context learning and instruction following, which also emerge as the models are scaled up. In this study, we provide the first comprehensive examination of these emergent abilities while accounting for various potentially biasing factors that can influence the evaluation of models. We conduct rigorous tests on a set of 18 models, encompassing a parameter range from 60 million to 175 billion parameters, across a comprehensive set of 22 tasks. Through an extensive series of over 1,000 experiments, we provide compelling evidence that emergent abilities can primarily be ascribed to in-context learning. We find no evidence for the emergence of reasoning abilities, thus providing valuable insights into the underlying mechanisms driving the observed abilities and thus alleviating safety concerns regarding their use.

When do machine learning systems fail to generalize, and what mechanisms could improve their generalization? Here, we draw inspiration from cognitive science to argue that one weakness of machine learning systems is their failure to exhibit latent learning -- learning information that is not relevant to the task at hand, but that might be useful in a future task. We show how this perspective links failures ranging from the reversal curse in language modeling to new findings on agent-based navigation. We then highlight how cognitive science points to episodic memory as a potential part of the solution to these issues. Correspondingly, we show that a system with an oracle retrieval mechanism can use learning experiences more flexibly to generalize better across many of these challenges. We also identify some of the essential components for effectively using retrieval, including the importance of within-example in-context learning for acquiring the ability to use information across retrieved examples. In summary, our results illustrate one possible contributor to the relative data inefficiency of current machine learning systems compared to natural intelligence, and help to understand how retrieval methods can complement parametric learning to improve generalization.

A fundamental open challenge in modern LLM scaling is the lack of understanding around emergent capabilities. In particular, language model pretraining loss is known to be highly predictable as a function of compute. However, downstream capabilities are far less predictable -- sometimes even exhibiting emergent jumps -- which makes it challenging to anticipate the capabilities of future models. In this work, we first pose the task of emergence prediction: given access to current LLMs that have random few-shot accuracy on a task, can we predict whether future models (GPT-N+1) will have non-trivial accuracy on that task? We then discover a simple insight for this problem: finetuning LLMs on a given task can shift the point in scaling at which emergence occurs towards less capable models. To operationalize this insight, we can finetune LLMs with varying amounts of data and fit a parametric function that predicts when emergence will occur (i.e., "emergence laws"). We validate this approach using four standard NLP benchmarks where large-scale open-source LLMs already demonstrate emergence (MMLU, GSM8K, CommonsenseQA, and CoLA). Using only small-scale LLMs, we find that, in some cases, we can accurately predict whether models trained with up to 4x more compute have emerged. Finally, we present a case study of two realistic uses for emergence prediction.

Grokking is the intriguing phenomenon where a model learns to generalize long after it has fit the training data. We show both analytically and numerically that grokking can surprisingly occur in linear networks performing linear tasks in a simple teacher-student setup with Gaussian inputs. In this setting, the full training dynamics is derived in terms of the training and generalization data covariance matrix. We present exact predictions on how the grokking time depends on input and output dimensionality, train sample size, regularization, and network initialization. We demonstrate that the sharp increase in generalization accuracy may not imply a transition from "memorization" to "understanding", but can simply be an artifact of the accuracy measure. We provide empirical verification for our calculations, along with preliminary results indicating that some predictions also hold for deeper networks, with non-linear activations.

The ability of language models to learn a task from a few examples in context has generated substantial interest. Here, we provide a perspective that situates this type of supervised few-shot learning within a much broader spectrum of meta-learned in-context learning. Indeed, we suggest that any distribution of sequences in which context non-trivially decreases loss on subsequent predictions can be interpreted as eliciting a kind of in-context learning. We suggest that this perspective helps to unify the broad set of in-context abilities that language models exhibit x2014 such as adapting to tasks from instructions or role play, or extrapolating time series. This perspective also sheds light on potential roots of in-context learning in lower-level processing of linguistic dependencies (e.g. coreference or parallel structures). Finally, taking this perspective highlights the importance of generalization, which we suggest can be studied along several dimensions: not only the ability to learn something novel, but also flexibility in learning from different presentations, and in applying what is learned. We discuss broader connections to past literature in meta-learning and goal-conditioned agents, and other perspectives on learning and adaptation. We close by suggesting that research on in-context learning should consider this broader spectrum of in-context capabilities and types of generalization.

We aim to understand grokking, a phenomenon where models generalize long after overfitting their training set. We present both a microscopic analysis anchored by an effective theory and a macroscopic analysis of phase diagrams describing learning performance across hyperparameters. We find that generalization originates from structured representations whose training dynamics and dependence on training set size can be predicted by our effective theory in a toy setting. We observe empirically the presence of four learning phases: comprehension, grokking, memorization, and confusion. We find representation learning to occur only in a "Goldilocks zone" (including comprehension and grokking) between memorization and confusion. We find on transformers the grokking phase stays closer to the memorization phase (compared to the comprehension phase), leading to delayed generalization. The Goldilocks phase is reminiscent of "intelligence from starvation" in Darwinian evolution, where resource limitations drive discovery of more efficient solutions. This study not only provides intuitive explanations of the origin of grokking, but also highlights the usefulness of physics-inspired tools, e.g., effective theories and phase diagrams, for understanding deep learning.

Systematic generalization refers to the capacity to understand and generate novel combinations from known components. Despite recent progress by large language models (LLMs) across various domains, these models often fail to extend their knowledge to novel compositional scenarios, revealing notable limitations in systematic generalization. There has been an ongoing debate about whether neural networks possess the capacity for systematic generalization, with recent studies suggesting that meta-learning approaches designed for compositionality can significantly enhance this ability. However, these insights have largely been confined to linguistic problems, leaving their applicability to other tasks an open question. In this study, we extend meta-learning for compositionality to the domain of abstract spatial reasoning. To this end, we introduce Compositional-ARC-a dataset designed to evaluate the capacity of models to systematically generalize from known geometric transformations (e.g., translation, rotation) of abstract two-dimensional objects to novel combinations of these transformations (e.g., translation+rotation). Our results show that a small transformer-based encoder-decoder model, trained via meta-learning for compositionality, can systematically generalize to previously unseen transformation compositions. Notably, despite having only 5.7M parameters, this model significantly outperforms state-of-the-art LLMs-including o3-mini, GPT-4o, and Gemini 2.0 Flash, which fail to exhibit similar systematic behavior-and performs on par with the winning model of the ARC prize 2024, an 8B-parameter LLM trained via test-time training. Our findings highlight the effectiveness of meta-learning in promoting systematicity beyond linguistic tasks, suggesting a promising direction toward more robust and generalizable models.

The primary paradigm for multi-task training in natural language processing is to represent the input with a shared pre-trained language model, and add a small, thin network (head) per task. Given an input, a target head is the head that is selected for outputting the final prediction. In this work, we examine the behaviour of non-target heads, that is, the output of heads when given input that belongs to a different task than the one they were trained for. We find that non-target heads exhibit emergent behaviour, which may either explain the target task, or generalize beyond their original task. For example, in a numerical reasoning task, a span extraction head extracts from the input the arguments to a computation that results in a number generated by a target generative head. In addition, a summarization head that is trained with a target question answering head, outputs query-based summaries when given a question and a context from which the answer is to be extracted. This emergent behaviour suggests that multi-task training leads to non-trivial extrapolation of skills, which can be harnessed for interpretability and generalization.

Large language models exhibit surprising emergent generalization properties, yet also struggle on many simple reasoning tasks such as arithmetic and parity. This raises the question of if and when Transformer models can learn the true algorithm for solving a task. We study the scope of Transformers' abilities in the specific setting of length generalization on algorithmic tasks. Here, we propose a unifying framework to understand when and how Transformers can exhibit strong length generalization on a given task. Specifically, we leverage RASP (Weiss et al., 2021) -- a programming language designed for the computational model of a Transformer -- and introduce the RASP-Generalization Conjecture: Transformers tend to length generalize on a task if the task can be solved by a short RASP program which works for all input lengths. This simple conjecture remarkably captures most known instances of length generalization on algorithmic tasks. Moreover, we leverage our insights to drastically improve generalization performance on traditionally hard tasks (such as parity and addition). On the theoretical side, we give a simple example where the "min-degree-interpolator" model of learning from Abbe et al. (2023) does not correctly predict Transformers' out-of-distribution behavior, but our conjecture does. Overall, our work provides a novel perspective on the mechanisms of compositional generalization and the algorithmic capabilities of Transformers.

We study implicit reasoning, i.e. the ability to combine knowledge or rules within a single forward pass. While transformer-based large language models store substantial factual knowledge and rules, they often fail to compose this knowledge for implicit multi-hop reasoning, suggesting a lack of compositional generalization over their parametric knowledge. To address this limitation, we study recurrent-depth transformers, which enables iterative computation over the same transformer layers. We investigate two compositional generalization challenges under the implicit reasoning scenario: systematic generalization, i.e. combining knowledge that is never used for compositions during training, and depth extrapolation, i.e. generalizing from limited reasoning depth (e.g. training on up to 5-hop) to deeper compositions (e.g. 10-hop). Through controlled studies with models trained from scratch, we show that while vanilla transformers struggle with both generalization challenges, recurrent-depth transformers can effectively make such generalization. For systematic generalization, we find that this ability emerges through a three-stage grokking process, transitioning from memorization to in-distribution generalization and finally to systematic generalization, supported by mechanistic analysis. For depth extrapolation, we show that generalization beyond training depth can be unlocked by scaling inference-time recurrence, with more iterations enabling deeper reasoning. We further study how training strategies affect extrapolation, providing guidance on training recurrent-depth transformers, and identify a key limitation, overthinking, where excessive recurrence degrades predictions and limits generalization to very deep compositions.

While large language models (LLMs) have shown exceptional capabilities in understanding complex queries and performing sophisticated tasks, their generalization abilities are often deeply entangled with memorization, necessitating more precise evaluation. To address this challenge, we introduce Scylla, a dynamic evaluation framework that quantitatively measures the generalization abilities of LLMs. Scylla disentangles generalization from memorization via assessing model performance on both in-distribution (ID) and out-of-distribution (OOD) data through 20 tasks across 5 levels of complexity. Through extensive experiments, we uncover a non-monotonic relationship between task complexity and the performance gap between ID and OOD data, which we term the generalization valley. Specifically, this phenomenon reveals a critical threshold - referred to as critical complexity - where reliance on non-generalizable behavior peaks, indicating the upper bound of LLMs' generalization capabilities. As model size increases, the critical complexity shifts toward higher levels of task complexity, suggesting that larger models can handle more complex reasoning tasks before over-relying on memorization. Leveraging Scylla and the concept of critical complexity, we benchmark 28LLMs including both open-sourced models such as LLaMA and Qwen families, and close-sourced models like Claude and GPT, providing a more robust evaluation and establishing a clearer understanding of LLMs' generalization capabilities.

Systematic, compositional generalization beyond the training distribution remains a core challenge in machine learning -- and a critical bottleneck for the emergent reasoning abilities of modern language models. This work investigates out-of-distribution (OOD) generalization in Transformer networks using a GSM8K-style modular arithmetic on computational graphs task as a testbed. We introduce and explore a set of four architectural mechanisms aimed at enhancing OOD generalization: (i) input-adaptive recurrence; (ii) algorithmic supervision; (iii) anchored latent representations via a discrete bottleneck; and (iv) an explicit error-correction mechanism. Collectively, these mechanisms yield an architectural approach for native and scalable latent space reasoning in Transformer networks with robust algorithmic generalization capabilities. We complement these empirical results with a detailed mechanistic interpretability analysis that reveals how these mechanisms give rise to robust OOD generalization abilities.

Large language models have evolved data-efficient generalists, benefiting from the universal language interface and large-scale pre-training. However, constructing a data-efficient generalist for dense visual prediction presents a distinct challenge due to the variation in label structures across different tasks. Consequently, generalization to unseen dense prediction tasks in the low-data regime is not straightforward and has received less attention from previous vision generalists. In this study, we explore a universal model that can flexibly adapt to unseen dense label structures with a few examples, enabling it to serve as a data-efficient vision generalist in diverse real-world scenarios. To this end, we base our method on a powerful meta-learning framework and explore several axes to improve its performance and versatility for real-world problems, such as flexible adaptation mechanisms and scalability. We evaluate our model across a spectrum of unseen real-world scenarios where low-shot learning is desirable, including video, 3D, medical, biological, and user-interactive tasks. Equipped with a generic architecture and an effective adaptation mechanism, our model flexibly adapts to all of these tasks with at most 50 labeled images, showcasing a significant advancement over existing data-efficient generalist approaches. Codes are available at https://github.com/GitGyun/chameleon.

Instruction tuning -- fine-tuning a large language model (LLM) on pairs of instructions and desired outcomes -- is an approach that enables pre-trained language models to perform real-world tasks and follow human instructions. Its practical success depends on the model learning a broader set of instructions than those it was trained on. Yet the factors that determine model generalization to such unseen tasks are not well understood. %To understand the driving factors of generalization, In this paper, we experiment with string rewrites, a symbolic task that serves as a building block for Turing complete Markov algorithms while allowing experimental control of "inputs" and "instructions". We investigate the trade-off between the number of instructions the model is trained on and the number of training samples provided for each instruction and observe that the diversity of the instruction set determines generalization. Generalization emerges once a diverse enough set of tasks is provided, even though very few examples are provided for each task. Instruction diversity also ensures robustness with respect to non-uniform distributions of instructions in the training set.

Whether neural networks can learn abstract reasoning or whether they merely rely on superficial statistics is a topic of recent debate. Here, we propose a dataset and challenge designed to probe abstract reasoning, inspired by a well-known human IQ test. To succeed at this challenge, models must cope with various generalisation `regimes' in which the training and test data differ in clearly-defined ways. We show that popular models such as ResNets perform poorly, even when the training and test sets differ only minimally, and we present a novel architecture, with a structure designed to encourage reasoning, that does significantly better. When we vary the way in which the test questions and training data differ, we find that our model is notably proficient at certain forms of generalisation, but notably weak at others. We further show that the model's ability to generalise improves markedly if it is trained to predict symbolic explanations for its answers. Altogether, we introduce and explore ways to both measure and induce stronger abstract reasoning in neural networks. Our freely-available dataset should motivate further progress in this direction.

The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of machine learning benchmarks has remained challenging. We propose what is to our knowledge the first model-agnostic measure of the inherent generalization difficulty of tasks. Our inductive bias complexity measure quantifies the total information required to generalize well on a task minus the information provided by the data. It does so by measuring the fractional volume occupied by hypotheses that generalize on a task given that they fit the training data. It scales exponentially with the intrinsic dimensionality of the space over which the model must generalize but only polynomially in resolution per dimension, showing that tasks which require generalizing over many dimensions are drastically more difficult than tasks involving more detail in fewer dimensions. Our measure can be applied to compute and compare supervised learning, reinforcement learning and meta-learning generalization difficulties against each other. We show that applied empirically, it formally quantifies intuitively expected trends, e.g. that in terms of required inductive bias, MNIST < CIFAR10 < Imagenet and fully observable Markov decision processes (MDPs) < partially observable MDPs. Further, we show that classification of complex images < few-shot meta-learning with simple images. Our measure provides a quantitative metric to guide the construction of more complex tasks requiring greater inductive bias, and thereby encourages the development of more sophisticated architectures and learning algorithms with more powerful generalization capabilities.

Generalist robot policies, trained on large and diverse datasets, have demonstrated the ability to generalize across a wide spectrum of behaviors, enabling a single policy to act in varied real-world environments. However, they still fall short on new tasks not covered in the training data. When finetuned on limited demonstrations of a new task, these policies often overfit to the specific demonstrations--not only losing their prior abilities to solve a wide variety of generalist tasks but also failing to generalize within the new task itself. In this work, we aim to develop a method that preserves the generalization capabilities of the generalist policy during finetuning, allowing a single policy to robustly incorporate a new skill into its repertoire. Our goal is a single policy that both learns to generalize to variations of the new task and retains the broad competencies gained from pretraining. We show that this can be achieved through a simple yet effective strategy: interpolating the weights of a finetuned model with that of the pretrained model. We show, across extensive simulated and real-world experiments, that such model merging produces a single model that inherits the generalist abilities of the base model and learns to solve the new task robustly, outperforming both the pretrained and finetuned model on out-of-distribution variations of the new task. Moreover, we show that model merging performance scales with the amount of pretraining data, and enables continual acquisition of new skills in a lifelong learning setting, without sacrificing previously learned generalist abilities.

The mechanism by which RL contributes to reasoning capabilities-whether it incentivizes the synthesis of new skills or merely amplifies existing behaviors-remains a subject of intense debate. In this work, we investigate this question through the lens of Complementary Reasoning, a complex task that requires integrating internal parametric knowledge with external contextual information. Using a controlled synthetic dataset of human biographies, we strictly decouple this ability into two atomic skills: Parametric Reasoning (relying on internal knowledge) and Contextual Reasoning (depending on external information). To rigorously assess capability boundaries, we evaluate generalization across three distinct levels of difficulty: I.I.D., Composition, and Zero-shot settings. We find that while SFT is sufficient for in-distribution performance, it struggles with O.O.D. generalization, particularly in Zero-shot settings where relational combinations are novel. Crucially, we identify the SFT Generalization Paradox: Models supervised solely on the composite task achieve near-perfect in-distribution accuracy but collapse on out-of-distribution generalization, indicating their reliance on rote memorization of path shortcuts. In contrast, we find that RL acts as a reasoning synthesizer rather than a probability amplifier. However, we uncover a strict atomic prerequisite: RL can only synthesize these complex strategies if the base model has first mastered the independent atomic skills (Parametric and Contextual) via SFT. These findings challenge the view of RL as a mere amplifier, suggesting that given sufficient atomic foundations, RL can actively synthesize complex reasoning strategies from learned primitives without explicit supervision on such complex strategies. This indicates that decoupled atomic training followed by RL offers a scalable path to generalization for complex reasoning tasks.

Vision-language-action (VLA) models can enable broad open world generalization, but require large and diverse datasets. It is appealing to consider whether some of this data can come from human videos, which cover diverse real-world situations and are easy to obtain. However, it is difficult to train VLAs with human videos alone, and establishing a mapping between humans and robots requires manual engineering and presents a major research challenge. Drawing inspiration from advances in large language models, where the ability to learn from diverse supervision emerges with scale, we ask whether a similar phenomenon holds for VLAs that incorporate human video data. We introduce a simple co-training recipe, and find that human-to-robot transfer emerges once the VLA is pre-trained on sufficient scenes, tasks, and embodiments. Our analysis suggests that this emergent capability arises because diverse pretraining produces embodiment-agnostic representations for human and robot data. We validate these findings through a series of experiments probing human to robot skill transfer and find that with sufficiently diverse robot pre-training our method can nearly double the performance on generalization settings seen only in human data.

Generalist robot policies trained on large-scale datasets such as Open X-Embodiment (OXE) demonstrate strong performance across a wide range of tasks. However, they often struggle to generalize beyond the distribution of their training data. In this paper, we investigate the underlying cause of this limited generalization capability. We identify shortcut learning -- the reliance on task-irrelevant features -- as a key impediment to generalization. Through comprehensive theoretical and empirical analysis, we uncover two primary contributors to shortcut learning: (1) limited diversity within individual sub-datasets, and (2) significant distributional disparities across sub-datasets, leading to dataset fragmentation. These issues arise from the inherent structure of large-scale datasets like OXE, which are typically composed of multiple sub-datasets collected independently across varied environments and embodiments. Our findings provide critical insights into dataset collection strategies that can reduce shortcut learning and enhance the generalization ability of generalist robot policies. Moreover, in scenarios where acquiring new large-scale data is impractical, we demonstrate that carefully selected robotic data augmentation strategies can effectively reduce shortcut learning in existing offline datasets, thereby improving generalization capabilities of generalist robot policies, e.g., pi_0, in both simulation and real-world environments. More information at https://lucky-light-sun.github.io/proj/shortcut-learning-in-grps/.

Generalization, the ability to perform well beyond the training context, is a hallmark of biological and artificial intelligence, yet anticipating unseen failures remains a central challenge. Conventional approaches often take a ``bottom-up'' mechanistic route by reverse-engineering interpretable features or circuits to build explanatory models. While insightful, these methods often struggle to provide the high-level, predictive signals for anticipating failure in real-world deployment. Here, we propose using a ``top-down'' approach to studying generalization failures inspired by medical biomarkers: identifying system-level measurements that serve as robust indicators of a model's future performance. Rather than mapping out detailed internal mechanisms, we systematically design and test network markers to probe structure, function links, identify prognostic indicators, and validate predictions in real-world settings. In image classification, we find that task-relevant geometric properties of in-distribution (ID) object manifolds consistently forecast poor out-of-distribution (OOD) generalization. In particular, reductions in two geometric measures, effective manifold dimensionality and utility, predict weaker OOD performance across diverse architectures, optimizers, and datasets. We apply this finding to transfer learning with ImageNet-pretrained models. We consistently find that the same geometric patterns predict OOD transfer performance more reliably than ID accuracy. This work demonstrates that representational geometry can expose hidden vulnerabilities, offering more robust guidance for model selection and AI interpretability.

The recent advent of large language models has reinvigorated debate over whether human cognitive capacities might emerge in such generic models given sufficient training data. Of particular interest is the ability of these models to reason about novel problems zero-shot, without any direct training. In human cognition, this capacity is closely tied to an ability to reason by analogy. Here, we performed a direct comparison between human reasoners and a large language model (the text-davinci-003 variant of GPT-3) on a range of analogical tasks, including a non-visual matrix reasoning task based on the rule structure of Raven's Standard Progressive Matrices. We found that GPT-3 displayed a surprisingly strong capacity for abstract pattern induction, matching or even surpassing human capabilities in most settings; preliminary tests of GPT-4 indicated even better performance. Our results indicate that large language models such as GPT-3 have acquired an emergent ability to find zero-shot solutions to a broad range of analogy problems.

We investigate the generalization capabilities of small language models under two popular adaptation paradigms: few-shot prompting and supervised fine-tuning. While prompting is often favored for its parameter efficiency and flexibility, it remains unclear how robust this approach is in low-resource settings and under distributional shifts. This paper presents a comparative study of prompting and fine-tuning across task formats, prompt styles, and model scales, with a focus on their behavior in both in-distribution and out-of-distribution (OOD) settings. Beyond accuracy, we analyze the internal representations learned by each approach to assess the stability and abstraction of task-specific features. Our findings highlight critical differences in how small models internalize and generalize knowledge under different adaptation strategies. This work offers practical guidance for model selection in low-data regimes and contributes empirical insight into the ongoing debate over prompting versus fine-tuning. Code for the experiments is available at the following

Unified Multimodal Models (UMMs) have shown remarkable progress in visual generation. Yet, existing benchmarks predominantly assess Crystallized Intelligence, which relies on recalling accumulated knowledge and learned schemas. This focus overlooks Generative Fluid Intelligence (GFI): the capacity to induce patterns, reason through constraints, and adapt to novel scenarios on the fly. To rigorously assess this capability, we introduce GENIUS (GEN Fluid Intelligence EvalUation Suite). We formalize GFI as a synthesis of three primitives. These include Inducing Implicit Patterns (e.g., inferring personalized visual preferences), Executing Ad-hoc Constraints (e.g., visualizing abstract metaphors), and Adapting to Contextual Knowledge (e.g., simulating counter-intuitive physics). Collectively, these primitives challenge models to solve problems grounded entirely in the immediate context. Our systematic evaluation of 12 representative models reveals significant performance deficits in these tasks. Crucially, our diagnostic analysis disentangles these failure modes. It demonstrates that deficits stem from limited context comprehension rather than insufficient intrinsic generative capability. To bridge this gap, we propose a training-free attention intervention strategy. Ultimately, GENIUS establishes a rigorous standard for GFI, guiding the field beyond knowledge utilization toward dynamic, general-purpose reasoning. Our dataset and code will be released at: https://github.com/arctanxarc/GENIUS{https://github.com/arctanxarc/GENIUS}.

Abstraction ability is crucial in human intelligence, which can also benefit various tasks in NLP study. Existing work shows that LLMs are deficient in abstract ability, and how to improve it remains unexplored. In this work, we design the framework AbsInstruct to enhance LLMs' abstraction ability through instruction tuning. The framework builds instructions with in-depth explanations to assist LLMs in capturing the underlying rationale of abstraction. Meanwhile, we introduce a plausibility estimator to select instructions that are more consistent with the abstraction knowledge of LLMs to be aligned. Then, our framework combines abstraction instructions with general-purpose ones to build a hybrid dataset. Extensive experiments and analyses demonstrate that our framework can considerably enhance LLMs' abstraction ability with strong generalization performance while maintaining their general instruction-following abilities.

Recent large-scale language models (LLMs) with long Chain-of-Thought reasoning-such as DeepSeek-R1-have achieved impressive results on Olympiad-level mathematics benchmarks. However, they often rely on a narrow set of strategies and struggle with problems that require a novel way of thinking. To systematically investigate these limitations, we introduce OMEGA-Out-of-distribution Math Problems Evaluation with 3 Generalization Axes-a controlled yet diverse benchmark designed to evaluate three axes of out-of-distribution generalization, inspired by Boden's typology of creativity: (1) Exploratory-applying known problem solving skills to more complex instances within the same problem domain; (2) Compositional-combining distinct reasoning skills, previously learned in isolation, to solve novel problems that require integrating these skills in new and coherent ways; and (3) Transformative-adopting novel, often unconventional strategies by moving beyond familiar approaches to solve problems more effectively. OMEGA consists of programmatically generated training-test pairs derived from templated problem generators across geometry, number theory, algebra, combinatorics, logic, and puzzles, with solutions verified using symbolic, numerical, or graphical methods. We evaluate frontier (or top-tier) LLMs and observe sharp performance degradation as problem complexity increases. Moreover, we fine-tune the Qwen-series models across all generalization settings and observe notable improvements in exploratory generalization, while compositional generalization remains limited and transformative reasoning shows little to no improvement. By isolating and quantifying these fine-grained failures, OMEGA lays the groundwork for advancing LLMs toward genuine mathematical creativity beyond mechanical proficiency.

Large language models like GPT-4 exhibit emergent capabilities across general-purpose tasks, such as basic arithmetic, when trained on extensive text data, even though these tasks are not explicitly encoded by the unsupervised, next-token prediction objective. This study investigates how small transformers, trained from random initialization, can efficiently learn arithmetic operations such as addition, multiplication, and elementary functions like square root, using the next-token prediction objective. We first demonstrate that conventional training data is not the most effective for arithmetic learning, and simple formatting changes can significantly improve accuracy. This leads to sharp phase transitions as a function of training data scale, which, in some cases, can be explained through connections to low-rank matrix completion. Building on prior work, we then train on chain-of-thought style data that includes intermediate step results. Even in the complete absence of pretraining, this approach significantly and simultaneously improves accuracy, sample complexity, and convergence speed. We also study the interplay between arithmetic and text data during training and examine the effects of few-shot prompting, pretraining, and model scale. Additionally, we discuss length generalization challenges. Our work highlights the importance of high-quality, instructive data that considers the particular characteristics of the next-word prediction objective for rapidly eliciting arithmetic capabilities.

The proliferation of pretrained models, as a result of advancements in pretraining techniques, has led to the emergence of a vast zoo of publicly available models. Effectively utilizing these resources to obtain models with robust out-of-distribution generalization capabilities for downstream tasks has become a crucial area of research. Previous research has primarily focused on identifying the most powerful models within the model zoo, neglecting to fully leverage the diverse inductive biases contained within. This paper argues that the knowledge contained in weaker models is valuable and presents a method for leveraging the diversity within the model zoo to improve out-of-distribution generalization capabilities. Specifically, we investigate the behaviors of various pretrained models across different domains of downstream tasks by characterizing the variations in their encoded representations in terms of two dimensions: diversity shift and correlation shift. This characterization enables us to propose a new algorithm for integrating diverse pretrained models, not limited to the strongest models, in order to achieve enhanced out-of-distribution generalization performance. Our proposed method demonstrates state-of-the-art empirical results on a variety of datasets, thus validating the benefits of utilizing diverse knowledge.

Robotic manipulation policies often struggle to generalize to novel objects, limiting their real-world utility. In contrast, cognitive science suggests that children develop generalizable dexterous manipulation skills by mastering a small set of simple toys and then applying that knowledge to more complex items. Inspired by this, we study if similar generalization capabilities can also be achieved by robots. Our results indicate robots can learn generalizable grasping using randomly assembled objects that are composed from just four shape primitives: spheres, cuboids, cylinders, and rings. We show that training on these "toys" enables robust generalization to real-world objects, yielding strong zero-shot performance. Crucially, we find the key to this generalization is an object-centric visual representation induced by our proposed detection pooling mechanism. Evaluated in both simulation and on physical robots, our model achieves a 67% real-world grasping success rate on the YCB dataset, outperforming state-of-the-art approaches that rely on substantially more in-domain data. We further study how zero-shot generalization performance scales by varying the number and diversity of training toys and the demonstrations per toy. We believe this work offers a promising path to scalable and generalizable learning in robotic manipulation. Demonstration videos, code, checkpoints and our dataset are available on our project page: https://lego-grasp.github.io/ .

Many recent studies have found evidence for emergent reasoning capabilities in large language models (LLMs), but debate persists concerning the robustness of these capabilities, and the extent to which they depend on structured reasoning mechanisms. To shed light on these issues, we study the internal mechanisms that support abstract reasoning in LLMs. We identify an emergent symbolic architecture that implements abstract reasoning via a series of three computations. In early layers, symbol abstraction heads convert input tokens to abstract variables based on the relations between those tokens. In intermediate layers, symbolic induction heads perform sequence induction over these abstract variables. Finally, in later layers, retrieval heads predict the next token by retrieving the value associated with the predicted abstract variable. These results point toward a resolution of the longstanding debate between symbolic and neural network approaches, suggesting that emergent reasoning in neural networks depends on the emergence of symbolic mechanisms.

Large language models have emergent capabilities that come unexpectedly at scale, but we need a theoretical framework to explain why and how they emerge. We prove that language models are actually non-ergodic systems while providing a mathematical framework based on Stuart Kauffman's theory of the adjacent possible (TAP) to explain capability emergence. Our resource-constrained TAP equation demonstrates how architectural, training, and contextual constraints interact to shape model capabilities through phase transitions in semantic space. We prove through experiments with three different language models that capacities emerge through discrete transitions guided by constraint interactions and path-dependent exploration. This framework provides a theoretical basis for understanding emergence in language models and guides the development of architectures that can guide capability emergence.

The surprising ability of Large Language Models (LLMs) to perform well on complex reasoning with only few-shot chain-of-thought prompts is believed to emerge only in very large-scale models (100+ billion parameters). We show that such abilities can, in fact, be distilled down from GPT-3.5 (ge 175B) to T5 variants (le 11B). We propose model specialization, to specialize the model's ability towards a target task. The hypothesis is that large models (commonly viewed as larger than 100B) have strong modeling power, but are spread on a large spectrum of tasks. Small models (commonly viewed as smaller than 10B) have limited model capacity, but if we concentrate their capacity on a specific target task, the model can achieve a decent improved performance. We use multi-step math reasoning as our testbed because it is a very typical emergent ability. We show two important aspects of model abilities: (1). there exists a very complex balance/ tradeoff between language models' multi-dimensional abilities; (2). by paying the price of decreased generic ability, we can clearly lift up the scaling curve of models smaller than 10B towards a specialized multi-step math reasoning ability. We further give comprehensive discussions about important design choices for better generalization, including the tuning data format, the start model checkpoint, and a new model selection method. We hope our practice and discoveries can serve as an important attempt towards specialized smaller models in the new research paradigm set by LLMs.

Continued pretraining (CPT) is a popular approach to adapt existing large language models (LLMs) to new languages. When doing so, it is common practice to include a portion of English data in the mixture, but its role has not been carefully studied to date. In this work, we show that including English does not impact validation perplexity, yet it is critical for the emergence of downstream capabilities in the target language. We introduce a language-agnostic benchmark for in-context learning (ICL), which reveals catastrophic forgetting early on CPT when English is not included. This in turn damages the ability of the model to generalize to downstream prompts in the target language as measured by perplexity, even if it does not manifest in terms of accuracy until later in training, and can be tied to a big shift in the model parameters. Based on these insights, we introduce curriculum learning and exponential moving average (EMA) of weights as effective alternatives to mitigate the need for English. All in all, our work sheds light into the dynamics by which emergent abilities arise when doing CPT for language adaptation, and can serve as a foundation to design more effective methods in the future.

Large language models can solve new tasks without task-specific fine-tuning. This ability, also known as in-context learning (ICL), is considered an emergent ability and is primarily seen in large language models with billions of parameters. This study investigates if such emergent properties are strictly tied to model size or can be demonstrated by smaller models trained on reduced-scale data. To explore this, we simplify pre-training data and pre-train 36 causal language models with parameters varying from 1 million to 165 million parameters. We show that models trained on this simplified pre-training data demonstrate enhanced zero-shot capabilities across various tasks in simplified language, achieving performance comparable to that of pre-trained models six times larger on unrestricted language. This suggests that downscaling the language allows zero-shot learning capabilities to emerge in models with limited size. Additionally, we find that these smaller models pre-trained on simplified data demonstrate a power law relationship between the evaluation loss and the three scaling factors: compute, dataset size, and model size.

We study a fundamental problem in the evaluation of large language models that we call training on the test task. Unlike wrongful practices like training on the test data, leakage, or data contamination, training on the test task is not a malpractice. Rather, the term describes a growing set of practices that utilize knowledge about evaluation tasks at training time. We demonstrate that training on the test task confounds both relative model evaluations and claims about emergent capabilities. We argue that the seeming superiority of one model family over another may be explained by a different degree of training on the test task. To this end, we propose an effective method to adjust for the effect of training on the test task on benchmark evaluations. Put simply, to fine-tune each model under comparison on the same task-relevant data prior to evaluation. We then show that instances of emergent behavior disappear gradually as models train on the test task. Our work promotes a new perspective on the evaluation of large language models, with broad implications for benchmarking and the study of emergent capabilities.

Emergent chain-of-thought (CoT) reasoning capabilities promise to improve performance and explainability of large language models (LLMs). However, uncertainties remain about how reasoning strategies formulated for previous model generations generalize to new model generations and different datasets. In this small-scale study, we compare different reasoning strategies induced by zero-shot prompting across six recently released LLMs (davinci-002, davinci-003, GPT-3.5-turbo, GPT-4, Flan-T5-xxl and Cohere command-xlarge) on a mixture of six question-answering datasets, including datasets from scientific and medical domains. Our findings demonstrate that while some variations in effectiveness occur, gains from CoT reasoning strategies remain robust across different models and datasets. GPT-4 has the most benefit from current state-of-the-art reasoning strategies and exhibits the best performance by applying a prompt previously discovered through automated discovery.

Neural networks often exhibit emergent behavior, where qualitatively new capabilities arise from scaling up the amount of parameters, training data, or training steps. One approach to understanding emergence is to find continuous progress measures that underlie the seemingly discontinuous qualitative changes. We argue that progress measures can be found via mechanistic interpretability: reverse-engineering learned behaviors into their individual components. As a case study, we investigate the recently-discovered phenomenon of ``grokking'' exhibited by small transformers trained on modular addition tasks. We fully reverse engineer the algorithm learned by these networks, which uses discrete Fourier transforms and trigonometric identities to convert addition to rotation about a circle. We confirm the algorithm by analyzing the activations and weights and by performing ablations in Fourier space. Based on this understanding, we define progress measures that allow us to study the dynamics of training and split training into three continuous phases: memorization, circuit formation, and cleanup. Our results show that grokking, rather than being a sudden shift, arises from the gradual amplification of structured mechanisms encoded in the weights, followed by the later removal of memorizing components.

Reliable generalization lies at the heart of safe ML and AI. However, understanding when and how neural networks generalize remains one of the most important unsolved problems in the field. In this work, we conduct an extensive empirical study (20'910 models, 15 tasks) to investigate whether insights from the theory of computation can predict the limits of neural network generalization in practice. We demonstrate that grouping tasks according to the Chomsky hierarchy allows us to forecast whether certain architectures will be able to generalize to out-of-distribution inputs. This includes negative results where even extensive amounts of data and training time never lead to any non-trivial generalization, despite models having sufficient capacity to fit the training data perfectly. Our results show that, for our subset of tasks, RNNs and Transformers fail to generalize on non-regular tasks, LSTMs can solve regular and counter-language tasks, and only networks augmented with structured memory (such as a stack or memory tape) can successfully generalize on context-free and context-sensitive tasks.

This work investigates whether small-scale LMs can benefit from instruction tuning. We compare conversational and question-answering instruction tuning datasets, applied either in a merged or sequential curriculum, using decoder-only models with 100M and 140M parameters. Evaluation spans both fine-tuning (SuperGLUE) and zero-shot (BLiMP, EWoK, WUGs, entity tracking, and psycholinguistic correlation) settings. Results show that instruction tuning yields small but consistent gains in fine-tuning scenarios, with sequential curricula outperforming merged data; however, improvements do not consistently transfer to zero-shot tasks, suggesting a trade-off between interaction-focused adaptation and broad linguistic generalization. These results highlight both the potential and the constraints of adapting human-inspired learning strategies to low-resource LMs, and point toward hybrid, curriculum-based approaches for enhancing generalization under ecological training limits.

Large Language Models (LLMs) have shown significant promise as copilots in various tasks. Local deployment of LLMs on edge devices is necessary when handling privacy-sensitive data or latency-sensitive tasks. The computational constraints of such devices make direct deployment of powerful large-scale LLMs impractical, necessitating the Knowledge Distillation from large-scale models to lightweight models. Lots of work has been done to elicit diversity and quality training examples from LLMs, but little attention has been paid to aligning teacher instructional content based on student preferences, akin to "responsive teaching" in pedagogy. Thus, we propose ARTE, dubbed Aligning TeacheR with StudenT PreferencEs, a framework that aligns the teacher model with student preferences to generate tailored training examples for Knowledge Distillation. Specifically, we elicit draft questions and rationales from the teacher model, then collect student preferences on these questions and rationales using students' performance with in-context learning as a proxy, and finally align the teacher model with student preferences. In the end, we repeat the first step with the aligned teacher model to elicit tailored training examples for the student model on the target task. Extensive experiments on academic benchmarks demonstrate the superiority of ARTE over existing instruction-tuning datasets distilled from powerful LLMs. Moreover, we thoroughly investigate the generalization of ARTE, including the generalization of fine-tuned student models in reasoning ability and the generalization of aligned teacher models to generate tailored training data across tasks and students. In summary, our contributions lie in proposing a novel framework for tailored training example generation, demonstrating its efficacy in experiments, and investigating the generalization of both student & aligned teacher models in ARTE.

Artificial intelligence (AI) has undergone a renaissance recently, making major progress in key domains such as vision, language, control, and decision-making. This has been due, in part, to cheap data and cheap compute resources, which have fit the natural strengths of deep learning. However, many defining characteristics of human intelligence, which developed under much different pressures, remain out of reach for current approaches. In particular, generalizing beyond one's experiences--a hallmark of human intelligence from infancy--remains a formidable challenge for modern AI. The following is part position paper, part review, and part unification. We argue that combinatorial generalization must be a top priority for AI to achieve human-like abilities, and that structured representations and computations are key to realizing this objective. Just as biology uses nature and nurture cooperatively, we reject the false choice between "hand-engineering" and "end-to-end" learning, and instead advocate for an approach which benefits from their complementary strengths. We explore how using relational inductive biases within deep learning architectures can facilitate learning about entities, relations, and rules for composing them. We present a new building block for the AI toolkit with a strong relational inductive bias--the graph network--which generalizes and extends various approaches for neural networks that operate on graphs, and provides a straightforward interface for manipulating structured knowledge and producing structured behaviors. We discuss how graph networks can support relational reasoning and combinatorial generalization, laying the foundation for more sophisticated, interpretable, and flexible patterns of reasoning. As a companion to this paper, we have released an open-source software library for building graph networks, with demonstrations of how to use them in practice.

Many recent works have discussed the propensity, or lack thereof, for emergent languages to exhibit properties of natural languages. A favorite in the literature is learning compositionality. We note that most of those works have focused on communicative bandwidth as being of primary importance. While important, it is not the only contributing factor. In this paper, we investigate the learning biases that affect the efficacy and compositionality of emergent languages. Our foremost contribution is to explore how capacity of a neural network impacts its ability to learn a compositional language. We additionally introduce a set of evaluation metrics with which we analyze the learned languages. Our hypothesis is that there should be a specific range of model capacity and channel bandwidth that induces compositional structure in the resulting language and consequently encourages systematic generalization. While we empirically see evidence for the bottom of this range, we curiously do not find evidence for the top part of the range and believe that this is an open question for the community.

Large Reasoning Models (LRMs) demonstrate remarkable capabilities on complex tasks, exhibiting emergent, human-like thinking patterns. Despite their advances, we identify a fundamental limitation: current LRMs lack a dedicated meta-level cognitive system-an essential faculty in human cognition that enables "thinking about thinking". This absence leaves their emergent abilities uncontrollable (non-adaptive reasoning), unreliable (intermediate error), and inflexible (lack of a clear methodology). To address this gap, we introduce Meta-R1, a systematic and generic framework that endows LRMs with explicit metacognitive capabilities. Drawing on principles from cognitive science, Meta-R1 decomposes the reasoning process into distinct object-level and meta-level components, orchestrating proactive planning, online regulation, and adaptive early stopping within a cascaded framework. Experiments on three challenging benchmarks and against eight competitive baselines demonstrate that Meta-R1 is: (I) high-performing, surpassing state-of-the-art methods by up to 27.3%; (II) token-efficient, reducing token consumption to 15.7% ~ 32.7% and improving efficiency by up to 14.8% when compared to its vanilla counterparts; and (III) transferable, maintaining robust performance across datasets and model backbones.

Humans (e.g., crowdworkers) have a remarkable ability in solving different tasks, by simply reading textual instructions that define them and looking at a few examples. Despite the success of the conventional supervised learning on individual datasets, such models often struggle with generalization across tasks (e.g., a question-answering system cannot solve classification tasks). A long-standing challenge in AI is to build a model that learns a new task by understanding the human-readable instructions that define it. To study this, we introduce NATURAL INSTRUCTIONS, a dataset of 61 distinct tasks, their human-authored instructions, and 193k task instances (input-output pairs). The instructions are obtained from crowdsourcing instructions used to create existing NLP datasets and mapped to a unified schema. Using this meta-dataset, we measure cross-task generalization by training models on seen tasks and measuring generalization to the remaining unseen ones. We adopt generative pre-trained language models to encode task-specific instructions along with input and generate task output. Our results indicate that models benefit from instructions when evaluated in terms of generalization to unseen tasks (19% better for models utilizing instructions). These models, however, are far behind an estimated performance upperbound indicating significant room for more progress in this direction.

A widely held hypothesis for why generative recommendation (GR) models outperform conventional item ID-based models is that they generalize better. However, there is few systematic way to verify this hypothesis beyond a superficial comparison of overall performance. To address this gap, we categorize each data instance based on the specific capability required for a correct prediction: either memorization (reusing item transition patterns observed during training) or generalization (composing known patterns to predict unseen item transitions). Extensive experiments show that GR models perform better on instances that require generalization, whereas item ID-based models perform better when memorization is more important. To explain this divergence, we shift the analysis from the item level to the token level and show that what appears to be item-level generalization often reduces to token-level memorization for GR models. Finally, we show that the two paradigms are complementary. We propose a simple memorization-aware indicator that adaptively combines them on a per-instance basis, leading to improved overall recommendation performance.

Large Language Models (LLMs) exhibit remarkable capabilities, yet it remains unclear to what extent these reflect sophisticated recall (crystallized intelligence) or reasoning ability (fluid intelligence). We introduce chess as a controlled testbed for disentangling these faculties. Leveraging the game's structure and scalable engine evaluations, we construct a taxonomy of positions varying in training corpus proximity--ranging from common states solvable by memorization to novel ones requiring first-principles reasoning. We systematically evaluate multiple GPT generations under varying reasoning intensities. Our analysis reveals a clear gradient: performance consistently degrades as fluid intelligence demands increase. Notably, in out-of-distribution tasks, performance collapses to random levels. While newer models improve, progress slows significantly for tasks outside the training distribution. Furthermore, while reasoning-augmented inference improves performance, its marginal benefit per token decreases with distributional proximity. These results suggest current architectures remain limited in systematic generalization, highlighting the need for mechanisms beyond scale to achieve robust fluid intelligence.

Large language model agents trained with reinforcement learning (RL) often learn brittle, task-specific shortcuts. We hypothesize that agents generalize better when their successful trajectories are structurally compressible, decomposed into a small set of reusable abstract patterns. To formalize this, we introduce ReuseRL, which grounds agentic RL in the Minimum Description Length (MDL) principle. ReuseRL extracts a shared skill dictionary from successful trajectories and augments the RL objective with a segmentation cost, explicitly penalizing idiosyncratic behaviors that encode poorly. We prove a PAC-Bayes generalization bound for this compression penalty. Across ALFWorld, TextWorld-Cooking, and Countdown-Stepwise, ReuseRL improves in- and out-of-distribution success over vanilla GRPO and strong round-length baselines.

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-Adapting Improvement Loop (SAIL), where an in-domain video model iteratively updates itself on self-produced trajectories, collected through adaptation with an internet-scale pretrained video model, and steadily improves its performance for a specified task of interest. We apply SAIL 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 initially unseen during original in-domain video model training. Furthermore, we discover that SAIL is surprisingly robust regarding if and how the self-collected experience is filtered, and the quality of the initial in-domain demonstrations. Through adaptation with summarized internet-scale data, and learning through online experience, we thus demonstrate a way to iteratively bootstrap a high-performance video model for solving novel robotic tasks through self-improvement.

Adapting one's thought process based on corrective feedback is an essential ability in human learning, particularly in collaborative settings. In contrast, the current large language model training paradigm relies heavily on modeling vast, static corpora. While effective for knowledge acquisition, it overlooks the interactive feedback loops essential for models to adapt dynamically to their context. In this work, we propose a framework that treats this interactive in-context learning ability not as an emergent property, but as a distinct, trainable skill. We introduce a scalable method that transforms single-turn verifiable tasks into multi-turn didactic interactions driven by information asymmetry. We first show that current flagship models struggle to integrate corrective feedback on hard reasoning tasks. We then demonstrate that models trained with our approach dramatically improve the ability to interactively learn from language feedback. More specifically, the multi-turn performance of a smaller model nearly reaches that of a model an order of magnitude larger. We also observe robust out-of-distribution generalization: interactive training on math problems transfers to diverse domains like coding, puzzles and maze navigation. Our qualitative analysis suggests that this improvement is due to an enhanced in-context plasticity. Finally, we show that this paradigm offers a unified path to self-improvement. By training the model to predict the teacher's critiques, effectively modeling the feedback environment, we convert this external signal into an internal capability, allowing the model to self-correct even without a teacher.

State-of-the-art multimodal web agents, powered by Multimodal Large Language Models (MLLMs), can autonomously execute many web tasks by processing user instructions and interacting with graphical user interfaces (GUIs). Current strategies for building web agents rely on (i) the generalizability of underlying MLLMs and their steerability via prompting, and (ii) large-scale fine-tuning of MLLMs on web-related tasks. However, web agents still struggle to automate tasks on unseen websites and domains, limiting their applicability to enterprise-specific and proprietary platforms. Beyond generalization from large-scale pre-training and fine-tuning, we propose building agents for few-shot adaptability using human demonstrations. We introduce the AdaptAgent framework that enables both proprietary and open-weights multimodal web agents to adapt to new websites and domains using few human demonstrations (up to 2). Our experiments on two popular benchmarks -- Mind2Web & VisualWebArena -- show that using in-context demonstrations (for proprietary models) or meta-adaptation demonstrations (for meta-learned open-weights models) boosts task success rate by 3.36% to 7.21% over non-adapted state-of-the-art models, corresponding to a relative increase of 21.03% to 65.75%. Furthermore, our additional analyses (a) show the effectiveness of multimodal demonstrations over text-only ones, (b) shed light on the influence of different data selection strategies during meta-learning on the generalization of the agent, and (c) demonstrate the effect of number of few-shot examples on the web agent's success rate. Overall, our results unlock a complementary axis for developing widely applicable multimodal web agents beyond large-scale pre-training and fine-tuning, emphasizing few-shot adaptability.

Amidst the rapid advancements in generative language models, the investigation of how training data shapes the performance of GPT models is still emerging. This paper presents GPTfluence, a novel approach that leverages a featurized simulation to assess the impact of training examples on the training dynamics of GPT models. Our approach not only traces the influence of individual training instances on performance trajectories, such as loss and other key metrics, on targeted test points but also enables a comprehensive comparison with existing methods across various training scenarios in GPT models, ranging from 14 million to 2.8 billion parameters, across a range of downstream tasks. Contrary to earlier methods that struggle with generalization to new data, GPTfluence introduces a parameterized simulation of training dynamics, demonstrating robust generalization capabilities to unseen training data. This adaptability is evident across both fine-tuning and instruction-tuning scenarios, spanning tasks in natural language understanding and generation. We will make our code and data publicly available.

In this work we create agents that can perform well beyond a single, individual task, that exhibit much wider generalisation of behaviour to a massive, rich space of challenges. We define a universe of tasks within an environment domain and demonstrate the ability to train agents that are generally capable across this vast space and beyond. The environment is natively multi-agent, spanning the continuum of competitive, cooperative, and independent games, which are situated within procedurally generated physical 3D worlds. The resulting space is exceptionally diverse in terms of the challenges posed to agents, and as such, even measuring the learning progress of an agent is an open research problem. We propose an iterative notion of improvement between successive generations of agents, rather than seeking to maximise a singular objective, allowing us to quantify progress despite tasks being incomparable in terms of achievable rewards. We show that through constructing an open-ended learning process, which dynamically changes the training task distributions and training objectives such that the agent never stops learning, we achieve consistent learning of new behaviours. The resulting agent is able to score reward in every one of our humanly solvable evaluation levels, with behaviour generalising to many held-out points in the universe of tasks. Examples of this zero-shot generalisation include good performance on Hide and Seek, Capture the Flag, and Tag. Through analysis and hand-authored probe tasks we characterise the behaviour of our agent, and find interesting emergent heuristic behaviours such as trial-and-error experimentation, simple tool use, option switching, and cooperation. Finally, we demonstrate that the general capabilities of this agent could unlock larger scale transfer of behaviour through cheap finetuning.

We introduce LLM-in-Sandbox, enabling LLMs to explore within a code sandbox (i.e., a virtual computer), to elicit general intelligence in non-code domains. We first demonstrate that strong LLMs, without additional training, exhibit generalization capabilities to leverage the code sandbox for non-code tasks. For example, LLMs spontaneously access external resources to acquire new knowledge, leverage the file system to handle long contexts, and execute scripts to satisfy formatting requirements. We further show that these agentic capabilities can be enhanced through LLM-in-Sandbox Reinforcement Learning (LLM-in-Sandbox-RL), which uses only non-agentic data to train models for sandbox exploration. Experiments demonstrate that LLM-in-Sandbox, in both training-free and post-trained settings, achieves robust generalization spanning mathematics, physics, chemistry, biomedicine, long-context understanding, and instruction following. Finally, we analyze LLM-in-Sandbox's efficiency from computational and system perspectives, and open-source it as a Python package to facilitate real-world deployment.

Large Language Models trained on web-scale text acquire language generation abilities that can solve a wide range of tasks, particularly when task knowledge is refined into the generative prior using in-context examples. However, spurious features learned from noisy data hinder their generalizability. Supervised finetuning can introduce task specificity, but introduce data inefficiency. Prior studies indicate that (i) noisy neural circuitries coexist with generalizable ones within LLMs, and (ii) finetuning typically enhances (or suppresses) existing abilities without introducing newer ones. Building upon these, we propose TaRot, a novel method for task adaptation. TaRot intervenes in the neural circuitries using learnable rotation matrices that are optimized using Bayesian Optimization, on labelled samples in the order of standard few-shot prompting examples. Experiments on multiple classification and generation tasks using LLMs of varying sizes reveal the efficacy of TaRot, improving upon both zero- as well as few-shot performance, with average improvements (across models and tasks) of 23.81% and 11.15%, respectively. The source code is available at https://github.com/joykirat18/TaRot

Artificial intelligence (AI) systems, and Large Language Models (LLMs) in particular, are increasingly employed for creative tasks like scientific idea generation, constituting a form of generalization from training data unaddressed by existing conceptual frameworks. Despite its similarities to compositional generalization (CG), combinatorial creativity (CC) is an open-ended ability. Instead of evaluating for accuracy or correctness against fixed targets, which would contradict the open-ended nature of CC, we propose a theoretical framework and algorithmic task for evaluating outputs by their degrees of novelty and utility. From here, we make several important empirical contributions: (1) We obtain the first insights into the scaling behavior of creativity for LLMs. (2) We discover that, for fixed compute budgets, there exist optimal model depths and widths for creative ability. (3) We find that the ideation-execution gap, whereby LLMs excel at generating novel scientific ideas but struggle to ensure their practical feasibility, may be explained by a more fundamental novelty-utility tradeoff characteristic of creativity algorithms in general. Importantly, this tradeoff remains persistent even at scale, casting doubt on the long-term creative potential of LLMs in their current form. Together, our conceptual framework and empirical findings provide a foundation for understanding and improving creativity in modern AI models, bridging the gap between human and machine intelligence.

We investigate the use of transformer sequence models as dynamics models (TDMs) for control. In a number of experiments in the DeepMind control suite, we find that first, TDMs perform well in a single-environment learning setting when compared to baseline models. Second, TDMs exhibit strong generalization capabilities to unseen environments, both in a few-shot setting, where a generalist model is fine-tuned with small amounts of data from the target environment, and in a zero-shot setting, where a generalist model is applied to an unseen environment without any further training. We further demonstrate that generalizing system dynamics can work much better than generalizing optimal behavior directly as a policy. This makes TDMs a promising ingredient for a foundation model of control.

We consider the problem of eliciting compositional generalization capabilities in large language models (LLMs) with a novel type of prompting strategy. Compositional generalization empowers the LLMs to solve problems that are harder than the ones they have seen (i.e., easy-to-hard generalization), which is a critical reasoning capability of human-like intelligence. However, even the current state-of-the-art LLMs still struggle with this form of reasoning. To bridge this gap, we propose skills-in-context (SKiC) prompting, which instructs LLMs how to compose basic skills to resolve more complex problems. We find that it is crucial to demonstrate both the skills and the compositional examples within the same prompting context. With as few as two examplars, our SKiC prompting initiates strong synergies between skills and their composition capabilities. Notably, it empowers LLMs to solve unseen problems that require innovative skill compositions, achieving near-perfect generalization on a broad range of challenging compositionality tasks. Intriguingly, SKiC prompting unlocks the latent potential of LLMs, enabling them to leverage pre-existing internal skills acquired during earlier pre-training stages, even when these skills are not explicitly presented in the prompting context. This results in the capability of LLMs to solve unseen complex problems by activating and composing internal competencies. With such prominent features, SKiC prompting is able to achieve state-of-the-art performance on challenging mathematical reasoning benchmarks (e.g., MATH).

Supervised fine-tuning (SFT) and reinforcement learning (RL) are widely used post-training techniques for foundation models. However, their roles in enhancing model generalization capabilities remain unclear. This paper studies the difference between SFT and RL on generalization and memorization, focusing on text-based rule variants and visual variants. We introduce GeneralPoints, an arithmetic reasoning card game, and adopt V-IRL, a real-world navigation environment, to assess how models trained with SFT and RL generalize to unseen variants in both textual and visual domains. We show that RL, especially when trained with an outcome-based reward, generalizes across both rule-based textual and visual variants. SFT, in contrast, tends to memorize training data and struggles to generalize out-of-distribution scenarios. Further analysis reveals that RL improves the model's underlying visual recognition capabilities, contributing to its enhanced generalization in the visual domain. Despite RL's superior generalization, we show that SFT remains essential for effective RL training; SFT stabilizes the model's output format, enabling subsequent RL to achieve its performance gains. These findings demonstrates the capability of RL for acquiring generalizable knowledge in complex, multi-modal tasks.

Rote learning is a memorization technique based on repetition. It is commonly believed to hinder generalization by encouraging verbatim memorization rather than deeper understanding. This insight holds for even learning factual knowledge that inevitably requires a certain degree of memorization. In this work, we demonstrate that LLMs can be trained to generalize from rote memorized data. We introduce a two-phase memorize-then-generalize framework, where the model first rote memorizes factual subject-object associations using a semantically meaningless token and then learns to generalize by fine-tuning on a small set of semantically meaningful prompts. Extensive experiments over 8 LLMs show that the models can reinterpret rote memorized data through the semantically meaningful prompts, as evidenced by the emergence of structured, semantically aligned latent representations between the two. This surprising finding opens the door to both effective and efficient knowledge injection and possible risks of repurposing the memorized data for malicious usage.

Inspired by the success of DeepSeek R1 in reasoning via reinforcement learning without human feedback, we train a 3B language model using the Countdown Game with pure reinforcement learning. Our model outperforms baselines on four of five benchmarks, demonstrating improved generalization beyond its training data. Notably, response length does not correlate with reasoning quality, and while "aha moments" emerge, they do not always yield correct answers. These findings highlight the potential of RL-only training for reasoning enhancement and suggest future work on refining reward structures to bridge emergent insights with accuracy.

Useful social science theories predict behavior across settings. However, applying a theory to make predictions in new settings is challenging: rarely can it be done without ad hoc modifications to account for setting-specific factors. We argue that AI agents put in simulations of those novel settings offer an alternative for applying theory, requiring minimal or no modifications. We present an approach for building such "general" agents that use theory-grounded natural language instructions, existing empirical data, and knowledge acquired by the underlying AI during training. To demonstrate the approach in settings where no data from that data-generating process exists--as is often the case in applied prediction problems--we design a heterogeneous population of 883,320 novel games. AI agents are constructed using human data from a small set of conceptually related but structurally distinct "seed" games. In preregistered experiments, on average, agents predict initial human play in a random sample of 1,500 games from the population better than (i) a cognitive hierarchy model, (ii) game-theoretic equilibria, and (iii) out-of-the-box agents. For a small set of separate novel games, these simulations predict responses from a new sample of human subjects better even than the most plausibly relevant published human data.

The ability to extrapolate from short problem instances to longer ones is an important form of out-of-distribution generalization in reasoning tasks, and is crucial when learning from datasets where longer problem instances are rare. These include theorem proving, solving quantitative mathematics problems, and reading/summarizing novels. In this paper, we run careful empirical studies exploring the length generalization capabilities of transformer-based language models. We first establish that naively finetuning transformers on length generalization tasks shows significant generalization deficiencies independent of model scale. We then show that combining pretrained large language models' in-context learning abilities with scratchpad prompting (asking the model to output solution steps before producing an answer) results in a dramatic improvement in length generalization. We run careful failure analyses on each of the learning modalities and identify common sources of mistakes that highlight opportunities in equipping language models with the ability to generalize to longer problems.

Large Language Model (LLM) based agents have proved their ability to perform complex tasks like humans. However, there is still a large gap between open-sourced LLMs and commercial models like the GPT series. In this paper, we focus on improving the agent generalization capabilities of LLMs via instruction tuning. We first observe that the existing agent training corpus exhibits satisfactory results on held-in evaluation sets but fails to generalize to held-out sets. These agent-tuning works face severe formatting errors and are frequently stuck in the same mistake for a long while. We analyze that the poor generalization ability comes from overfitting to several manual agent environments and a lack of adaptation to new situations. They struggle with the wrong action steps and can not learn from the experience but just memorize existing observation-action relations. Inspired by the insight, we propose a novel AgentRefine framework for agent-tuning. The core idea is to enable the model to learn to correct its mistakes via observation in the trajectory. Specifically, we propose an agent synthesis framework to encompass a diverse array of environments and tasks and prompt a strong LLM to refine its error action according to the environment feedback. AgentRefine significantly outperforms state-of-the-art agent-tuning work in terms of generalization ability on diverse agent tasks. It also has better robustness facing perturbation and can generate diversified thought in inference. Our findings establish the correlation between agent generalization and self-refinement and provide a new paradigm for future research.

Even when massively overparameterized, deep neural networks show a remarkable ability to generalize. Research on this phenomenon has focused on generalization within distribution, via smooth interpolation. Yet in some settings neural networks also learn to extrapolate to data far beyond the bounds of the original training set, sometimes even allowing for infinite generalization, implying that an algorithm capable of solving the task has been learned. Here we undertake a case study of the learning dynamics of recurrent neural networks (RNNs) trained on the streaming parity task in order to develop an effective theory of algorithm development. The streaming parity task is a simple but nonlinear task defined on sequences up to arbitrary length. We show that, with sufficient finite training experience, RNNs exhibit a phase transition to perfect infinite generalization. Using an effective theory for the representational dynamics, we find an implicit representational merger effect which can be interpreted as the construction of a finite automaton that reproduces the task. Overall, our results disclose one mechanism by which neural networks can generalize infinitely from finite training experience.

The rapid advancements in large language models (LLMs) have demonstrated their potential to accelerate scientific discovery, particularly in automating the process of research ideation. LLM-based systems have shown promise in generating hypotheses and research ideas. However, current approaches predominantly rely on prompting-based pre-trained models, limiting their ability to optimize generated content effectively. Moreover, they also lack the capability to deal with the complex interdependence and inherent restrictions among novelty, feasibility, and effectiveness, which remains challenging due to the inherent trade-offs among these dimensions, such as the innovation-feasibility conflict. To address these limitations, we for the first time propose fine-tuning LLMs to be better idea proposers and introduce a novel framework that employs a two-stage approach combining Supervised Fine-Tuning (SFT) and controllable Reinforcement Learning (RL). In the SFT stage, the model learns foundational patterns from pairs of research papers and follow-up ideas. In the RL stage, multi-dimensional reward modeling, guided by fine-grained feedback, evaluates and optimizes the generated ideas across key metrics. Dimensional controllers enable dynamic adjustment of generation, while a sentence-level decoder ensures context-aware emphasis during inference. Our framework provides a balanced approach to research ideation, achieving high-quality outcomes by dynamically navigating the trade-offs among novelty, feasibility, and effectiveness.

We introduce HRMCR (HAE-RAE Multi-Step Commonsense Reasoning), a benchmark designed to evaluate large language models' ability to perform multi-step reasoning in culturally specific contexts, focusing on Korean. The questions are automatically generated via templates and algorithms, requiring LLMs to integrate Korean cultural knowledge into sequential reasoning steps. Consistent with prior observations on emergent abilities, our experiments reveal that models trained on fewer than \(2 \cdot 10^{25}\) training FLOPs struggle to solve any questions, showing near-zero performance. Beyond this threshold, performance improves sharply. State-of-the-art models (e.g., O1) still score under 50\%, underscoring the difficulty of our tasks. Notably, stepwise analysis suggests the observed emergent behavior may stem from compounding errors across multiple steps rather than reflecting a genuinely new capability. We publicly release the benchmark and commit to regularly updating the dataset to prevent contamination.

Conventional agent systems often struggle in open-ended environments where task distributions continuously drift and external supervision is scarce. Their reliance on static toolsets or offline training lags behind these dynamics, leaving the system's capability boundaries rigid and unknown. To address this, we propose the In-Situ Self-Evolving paradigm. This approach treats sequential task interactions as a continuous stream of experience, enabling the system to distill short-term execution feedback into long-term, reusable capabilities without access to ground-truth labels. Within this framework, we identify tool evolution as the critical pathway for capability expansion, which provides verifiable, binary feedback signals. Within this framework, we develop Yunjue Agent, a system that iteratively synthesizes, optimizes, and reuses tools to navigate emerging challenges. To optimize evolutionary efficiency, we further introduce a Parallel Batch Evolution strategy. Empirical evaluations across five diverse benchmarks under a zero-start setting demonstrate significant performance gains over proprietary baselines. Additionally, complementary warm-start evaluations confirm that the accumulated general knowledge can be seamlessly transferred to novel domains. Finally, we propose a novel metric to monitor evolution convergence, serving as a function analogous to training loss in conventional optimization. We open-source our codebase, system traces, and evolved tools to facilitate future research in resilient, self-evolving intelligence.

Generative artificial intelligence (AI) systems based on large-scale pretrained foundation models (PFMs) such as vision-language models, large language models (LLMs), diffusion models and vision-language-action (VLA) models have demonstrated the ability to solve complex and truly non-trivial AI problems in a wide variety of domains and contexts. Multimodal large language models (MLLMs), in particular, learn from vast and diverse data sources, allowing rich and nuanced representations of the world and, thereby, providing extensive capabilities, including the ability to reason, engage in meaningful dialog; collaborate with humans and other agents to jointly solve complex problems; and understand social and emotional aspects of humans. Despite this impressive feat, the cognitive abilities of state-of-the-art LLMs trained on large-scale datasets are still superficial and brittle. Consequently, generic LLMs are severely limited in their generalist capabilities. A number of foundational problems -- embodiment, symbol grounding, causality and memory -- are required to be addressed for LLMs to attain human-level general intelligence. These concepts are more aligned with human cognition and provide LLMs with inherent human-like cognitive properties that support the realization of physically-plausible, semantically meaningful, flexible and more generalizable knowledge and intelligence. In this work, we discuss the aforementioned foundational issues and survey state-of-the art approaches for implementing these concepts in LLMs. Specifically, we discuss how the principles of embodiment, symbol grounding, causality and memory can be leveraged toward the attainment of artificial general intelligence (AGI) in an organic manner.

The crystallization of modeling methods around the Transformer architecture has been a boon for practitioners. Simple, well-motivated architectural variations can transfer across tasks and scale, increasing the impact of modeling research. However, with the emergence of state-of-the-art 100B+ parameters models, large language models are increasingly expensive to accurately design and train. Notably, it can be difficult to evaluate how modeling decisions may impact emergent capabilities, given that these capabilities arise mainly from sheer scale alone. In the process of building BLOOM--the Big Science Large Open-science Open-access Multilingual language model--our goal is to identify an architecture and training setup that makes the best use of our 1,000,000 A100-GPU-hours budget. Specifically, we perform an ablation study at the billion-parameter scale comparing different modeling practices and their impact on zero-shot generalization. In addition, we study the impact of various popular pre-training corpora on zero-shot generalization. We also study the performance of a multilingual model and how it compares to the English-only one. Finally, we consider the scaling behaviour of Transformers to choose the target model size, shape, and training setup. All our models and code are open-sourced at https://huggingface.co/bigscience .

Recent diagnostic datasets on compositional generalization, such as SCAN (Lake and Baroni, 2018) and COGS (Kim and Linzen, 2020), expose severe problems in models trained from scratch on these datasets. However, in contrast to this poor performance, state-of-the-art models trained on larger and more general datasets show better generalization ability. In this work, to reconcile this inconsistency, we conduct an empirical analysis by training Transformer models on a variety of training sets with different data factors, including dataset scale, pattern complexity, example difficulty, etc. First, we show that increased dataset complexity can lead to better generalization behavior on multiple different generalization challenges. To further understand this improvement, we show two axes of the benefit from more complex datasets: they provide more diverse examples so compositional understanding becomes more effective, and they also prevent ungeneralizable memorization of the examples due to reduced example repetition frequency. Finally, we explore how training examples of different difficulty levels influence generalization differently. On synthetic datasets, simple examples invoke stronger compositionality than hard examples do. On larger-scale real language datasets, while hard examples become more important potentially to ensure decent data coverage, a balanced mixture of simple and hard examples manages to induce the strongest generalizability. The code and data for this work are available at https://github.com/owenzx/data4comp

Neural networks adapt very well to distributed and continuous representations, but struggle to generalize from small amounts of data. Symbolic systems commonly achieve data efficient generalization by exploiting modularity to benefit from local and discrete features of a representation. These features allow symbolic programs to be improved one module at a time and to experience combinatorial growth in the values they can successfully process. However, it is difficult to design a component that can be used to form symbolic abstractions and which is adequately overparametrized to learn arbitrary high-dimensional transformations. I present Graph-based Symbolically Synthesized Neural Networks (G-SSNNs), a class of neural modules that operate on representations modified with synthesized symbolic programs to include a fixed set of local and discrete features. I demonstrate that the choice of injected features within a G-SSNN module modulates the data efficiency and generalization of baseline neural models, creating predictable patterns of both heightened and curtailed generalization. By training G-SSNNs, we also derive information about desirable semantics of symbolic programs without manual engineering. This information is compact and amenable to abstraction, but can also be flexibly recontextualized for other high-dimensional settings. In future work, I will investigate data efficient generalization and the transferability of learned symbolic representations in more complex G-SSNN designs based on more complex classes of symbolic programs. Experimental code and data are available at https://github.com/shlomenu/symbolically_synthesized_networks .

The advent of the Transformer has led to the development of large language models (LLM), which appear to demonstrate human-like capabilities. To assess the generality of this class of models and a variety of other base neural network architectures to multimodal domains, we evaluated and compared their capacity for multimodal generalization. We introduce a multimodal question-answer benchmark to evaluate three specific types of out-of-distribution (OOD) generalization performance: distractor generalization (generalization in the presence of distractors), systematic compositional generalization (generalization to new task permutations), and productive compositional generalization (generalization to more complex tasks structures). We found that across model architectures (e.g., RNNs, Transformers, Perceivers, etc.), models with multiple attention layers, or models that leveraged cross-attention mechanisms between input domains, fared better. Our positive results demonstrate that for multimodal distractor and systematic generalization, either cross-modal attention or models with deeper attention layers are key architectural features required to integrate multimodal inputs. On the other hand, neither of these architectural features led to productive generalization, suggesting fundamental limitations of existing architectures for specific types of multimodal generalization. These results demonstrate the strengths and limitations of specific architectural components underlying modern neural models for multimodal reasoning. Finally, we provide Generic COG (gCOG), a configurable benchmark with several multimodal generalization splits, for future studies to explore.

While the phenomenon of grokking, i.e., delayed generalization, has been studied extensively, it remains an open problem whether there is a mathematical framework that characterizes what kind of features will emerge, how and in which conditions it happens, and is closely related to the gradient dynamics of the training, for complex structured inputs. We propose a novel framework, named Li_2, that captures three key stages for the grokking behavior of 2-layer nonlinear networks: (I) \textbf{L}azy learning, (II) \textbf{i}ndependent feature learning and (III) \textbf{i}nteractive feature learning. At the lazy learning stage, top layer overfits to random hidden representation and the model appears to memorize. Thanks to lazy learning and weight decay, the backpropagated gradient G_F from the top layer now carries information about the target label, with a specific structure that enables each hidden node to learn their representation independently. Interestingly, the independent dynamics follows exactly the gradient ascent of an energy function E, and its local maxima are precisely the emerging features. We study whether these local-optima induced features are generalizable, their representation power, and how they change on sample size, in group arithmetic tasks. When hidden nodes start to interact in the later stage of learning, we provably show how G_F changes to focus on missing features that need to be learned. Our study sheds lights on roles played by key hyperparameters such as weight decay, learning rate and sample sizes in grokking, leads to provable scaling laws of feature emergence, memorization and generalization, and reveals the underlying cause why recent optimizers such as Muon can be effective, from the first principles of gradient dynamics. Our analysis can be extended to multi-layer architectures.

There is a concerted effort to build domain-general artificial intelligence in the form of universal neural network models with sufficient computational flexibility to solve a wide variety of cognitive tasks but without requiring fine-tuning on individual problem spaces and domains. To do this, models need appropriate priors and inductive biases, such that trained models can generalise to out-of-distribution examples and new problem sets. Here we provide an overview of the hallmarks endowing biological neural networks with the functionality needed for flexible cognition, in order to establish which features might also be important to achieve similar functionality in artificial systems. We specifically discuss the role of system-level distribution of network communication and recurrence, in addition to the role of short-term topological changes for efficient local computation. As machine learning models become more complex, these principles may provide valuable directions in an otherwise vast space of possible architectures. In addition, testing these inductive biases within artificial systems may help us to understand the biological principles underlying domain-general cognition.

A modular design encourages neural models to disentangle and recombine different facets of knowledge to generalise more systematically to new tasks. In this work, we assume that each task is associated with a subset of latent discrete skills from a (potentially small) inventory. In turn, skills correspond to parameter-efficient (sparse / low-rank) model parameterisations. By jointly learning these and a task-skill allocation matrix, the network for each task is instantiated as the average of the parameters of active skills. To favour non-trivial soft partitions of skills across tasks, we experiment with a series of inductive biases, such as an Indian Buffet Process prior and a two-speed learning rate. We evaluate our latent-skill model on two main settings: 1) multitask reinforcement learning for grounded instruction following on 8 levels of the BabyAI platform; and 2) few-shot adaptation of pre-trained text-to-text generative models on CrossFit, a benchmark comprising 160 NLP tasks. We find that the modular design of a network significantly increases sample efficiency in reinforcement learning and few-shot generalisation in supervised learning, compared to baselines with fully shared, task-specific, or conditionally generated parameters where knowledge is entangled across tasks. In addition, we show how discrete skills help interpretability, as they yield an explicit hierarchy of tasks.

We introduce and train distributed neural architectures (DNA) in vision and language domains. DNAs are initialized with a proto-architecture that consists of (transformer, MLP, attention, etc.) modules and routers. Any token (or patch) can traverse any series of modules in any order. DNAs are a natural generalization of the sparse methods such as Mixture-of-Experts, Mixture-of-Depths, parameter sharing, etc. Computation and communication patterns of DNA modules are learnt end-to-end during training and depend on the content and context of each token (or patch). These patterns can be shaped by further requirements added to the optimization objective such as compute/memory efficiency or load balancing. We empirically show that (i) trained DNAs are competitive with the dense baselines in both domains and (ii) compute efficiency/parameter sharing can be learnt from data. Next, we analyze the emergent connectivity and computation patterns in the trained DNAs. We find that the paths that tokens take through the models are themselves distributed according to a power-law. We show that some paths (or, equivalently, groups of modules) show emergent specialization. Finally, we demonstrate that models learn to allocate compute and active parameters in an interpretable way.

Understanding how language model performance varies with scale is critical to benchmark and algorithm development. Scaling laws are one approach to building this understanding, but the requirement of training models across many different scales has limited their use. We propose an alternative, observational approach that bypasses model training and instead builds scaling laws from ~80 publically available models. Building a single scaling law from multiple model families is challenging due to large variations in their training compute efficiencies and capabilities. However, we show that these variations are consistent with a simple, generalized scaling law where language model performance is a function of a low-dimensional capability space, and model families only vary in their efficiency in converting training compute to capabilities. Using this approach, we show the surprising predictability of complex scaling phenomena: we show that several emergent phenomena follow a smooth, sigmoidal behavior and are predictable from small models; we show that the agent performance of models such as GPT-4 can be precisely predicted from simpler non-agentic benchmarks; and we show how to predict the impact of post-training interventions like Chain-of-Thought and Self-Consistency as language model capabilities continue to improve.

Modern LLMs show mastery over an ever-growing range of skills, as well as the ability to compose them flexibly. However, extending model capabilities to new skills in a scalable manner is an open-problem: fine-tuning and parameter-efficient variants risk catastrophic forgetting, while context-based approaches have limited expressiveness and are constrained by the model's effective context. We explore skill neologisms--i.e., soft tokens integrated in the model's vocabulary and optimized to improve capabilities over a specific skill--as a way to selectively extend model capabilities to new skills without weight updates. We first observe that off-the-shelf pre-trained LLMs already demonstrate tokens associated with procedural knowledge. We then show that skill neologisms can be learned to improve model capabilities on specific skills while being composable with out-of-distribution skills, and that independently trained skill neologisms can be composed zero-shot. These results suggest that skill neologisms may provide a scalable path towards skill-based continual learning.

Recently an influx of studies claim emergent cognitive abilities in large language models (LLMs). Yet, most rely on anecdotes, overlook contamination of training sets, or lack systematic Evaluation involving multiple tasks, control conditions, multiple iterations, and statistical robustness tests. Here we make two major contributions. First, we propose CogEval, a cognitive science-inspired protocol for the systematic evaluation of cognitive capacities in Large Language Models. The CogEval protocol can be followed for the evaluation of various abilities. Second, here we follow CogEval to systematically evaluate cognitive maps and planning ability across eight LLMs (OpenAI GPT-4, GPT-3.5-turbo-175B, davinci-003-175B, Google Bard, Cohere-xlarge-52.4B, Anthropic Claude-1-52B, LLaMA-13B, and Alpaca-7B). We base our task prompts on human experiments, which offer both established construct validity for evaluating planning, and are absent from LLM training sets. We find that, while LLMs show apparent competence in a few planning tasks with simpler structures, systematic evaluation reveals striking failure modes in planning tasks, including hallucinations of invalid trajectories and getting trapped in loops. These findings do not support the idea of emergent out-of-the-box planning ability in LLMs. This could be because LLMs do not understand the latent relational structures underlying planning problems, known as cognitive maps, and fail at unrolling goal-directed trajectories based on the underlying structure. Implications for application and future directions are discussed.

The rise of Large Reasoning Models (LRMs) promises a significant leap forward in language model capabilities, aiming to tackle increasingly sophisticated tasks with unprecedented efficiency and accuracy. However, despite their impressive performance, recent studies have highlighted how current reasoning models frequently fail to generalize to novel, unseen problems, often resorting to memorized solutions rather than genuine inferential reasoning. Such behavior underscores a critical limitation in modern LRMs, i.e., their tendency toward overfitting, which in turn results in poor generalization in problem-solving capabilities. In this paper, we introduce Nexus Architect, an enhanced iteration of our multi-agent system framework, Nexus, equipped with a novel automated workflow synthesis mechanism. Given a user's prompt and a small set of representative examples, the Architect autonomously generates a tailored reasoning workflow by selecting suitable strategies, tool integrations, and adversarial techniques for a specific problem class. Furthermore, the Architect includes an iterative prompt refinement mechanism that fine-tunes agents' system prompts to maximize performance and improve the generalization capabilities of the system. We empirically evaluate Nexus Architect by employing an off-the-shelf, non-reasoning model on a custom dataset of challenging logical questions and compare its performance against state-of-the-art LRMs. Results show that Nexus Architect consistently outperforms existing solutions, achieving up to a 66% increase in pass rate over Gemini 2.5 Flash Preview, nearly 2.5times against Claude Sonnet 4 and DeepSeek-R1, and over 3times w.r.t. Llama 4 Scout.

While Large Language Models (LLMs) have emerged with remarkable capabilities in complex tasks through Chain-of-Thought reasoning, practical resource constraints have sparked interest in transferring these abilities to smaller models. However, achieving both domain performance and cross-domain generalization remains challenging. Existing approaches typically restrict students to following a single golden rationale and treat different reasoning paths independently. Due to distinct inductive biases and intrinsic preferences, alongside the student's evolving capacity and reasoning preferences during training, a teacher's "optimal" rationale could act as out-of-distribution noise. This misalignment leads to a degeneration of the student's latent reasoning distribution, causing suboptimal performance. To bridge this gap, we propose MIND, a capability-adaptive framework that transitions distillation from passive mimicry to active cognitive construction. We synthesize diverse teacher perspectives through a novel "Teaching Assistant" network. By employing a Feedback-Driven Inertia Calibration mechanism, this network utilizes inertia-filtered training loss to align supervision with the student's current adaptability, effectively enhancing performance while mitigating catastrophic forgetting. Extensive experiments demonstrate that MIND achieves state-of-the-art performance on both in-distribution and out-of-distribution benchmarks, and our sophisticated latent space analysis further confirms the mechanism of reasoning ability internalization.

Reinforcement learning (RL)-based post-training often improves the reasoning performance of large language models (LLMs) beyond the training domain, while supervised fine-tuning (SFT) frequently leads to general capabilities forgetting. However, the mechanisms underlying this contrast remain unclear. To bridge this gap, we present a feature-level mechanistic analysis methodology to probe RL generalization using a controlled experimental setup, where RL- and SFT-tuned models are trained from the same base model on identical data. Leveraging our interpretability framework, we align internal activations across models within a shared feature space and analyze how features evolve during post-training. We find that SFT rapidly introduces many highly specialized features that stabilize early in training, whereas RL induces more restrained and continually evolving feature changes that largely preserve base models' representations. Focusing on samples where RL succeeds but the base model fails, we identify a compact, task-agnostic set of features that directly mediate generalization across diverse tasks. Feature-level interventions confirm their causal role: disabling these features significantly degrades RL models' generalization performance, while amplifying them improves base models' performance. The code is available at https://github.com/danshi777/RL-generalization.

Transformer models pre-trained with a masked-language-modeling objective (e.g., BERT) encode commonsense knowledge as evidenced by behavioral probes; however, the extent to which this knowledge is acquired by systematic inference over the semantics of the pre-training corpora is an open question. To answer this question, we selectively inject verbalized knowledge into the minibatches of a BERT model during pre-training and evaluate how well the model generalizes to supported inferences. We find generalization does not improve over the course of pre-training, suggesting that commonsense knowledge is acquired from surface-level, co-occurrence patterns rather than induced, systematic reasoning.

In this paper we propose to study generalization of neural networks on small algorithmically generated datasets. In this setting, questions about data efficiency, memorization, generalization, and speed of learning can be studied in great detail. In some situations we show that neural networks learn through a process of "grokking" a pattern in the data, improving generalization performance from random chance level to perfect generalization, and that this improvement in generalization can happen well past the point of overfitting. We also study generalization as a function of dataset size and find that smaller datasets require increasing amounts of optimization for generalization. We argue that these datasets provide a fertile ground for studying a poorly understood aspect of deep learning: generalization of overparametrized neural networks beyond memorization of the finite training dataset.

Large language models often struggle with zero-shot generalization, and several modular approaches have been proposed to address this challenge. Yet, we hypothesize that a key limitation remains: the entanglement of general knowledge and task-specific adaptations. To overcome this, we propose a modular framework that disentangles these components by constructing a library of task-specific LoRA modules alongside a general-domain LoRA. By subtracting this general knowledge component from each task-specific module, we obtain residual modules that focus more exclusively on task-relevant information, a method we call general knowledge subtraction (GenKnowSub). Leveraging the refined task-specific modules and the Arrow routing algorithm ostapenko2024towards, we dynamically select and combine modules for new inputs without additional training. Our studies on the Phi-3 model and standard Arrow as baselines reveal that using general knowledge LoRAs derived from diverse languages, including English, French, and German, yields consistent performance gains in both monolingual and cross-lingual settings across a wide set of benchmarks. Further experiments on Phi-2 demonstrate how GenKnowSub generalizes to weaker LLMs. The complete code and data are available at https://github.com/saharsamr/Modular-LLM.

Finetuning large language models on narrowly harmful datasets can cause them to become emergently misaligned, giving stereotypically `evil' responses across diverse unrelated settings. Concerningly, a pre-registered survey of experts failed to predict this result, highlighting our poor understanding of the inductive biases governing learning and generalisation in LLMs. We use emergent misalignment (EM) as a case study to investigate these inductive biases and find that models can just learn the narrow dataset task, but that the general solution appears to be more stable and more efficient. To establish this, we build on the result that different EM finetunes converge to the same linear representation of general misalignment, which can be used to mediate misaligned behaviour. We find a linear representation of the narrow solution also exists, and can be learned by introducing a KL divergence loss. Comparing these representations reveals that general misalignment achieves lower loss, is more robust to perturbations, and is more influential in the pre-training distribution. This work isolates a concrete representation of general misalignment for monitoring and mitigation. More broadly, it offers a detailed case study and preliminary metrics for investigating how inductive biases shape generalisation in LLMs. We open-source all code, datasets and model finetunes.

We address a fundamental challenge in Reinforcement Learning from Interaction Demonstration (RLID): demonstration noise and coverage limitations. While existing data collection approaches provide valuable interaction demonstrations, they often yield sparse, disconnected, and noisy trajectories that fail to capture the full spectrum of possible skill variations and transitions. Our key insight is that despite noisy and sparse demonstrations, there exist infinite physically feasible trajectories that naturally bridge between demonstrated skills or emerge from their neighboring states, forming a continuous space of possible skill variations and transitions. Building upon this insight, we present two data augmentation techniques: a Stitched Trajectory Graph (STG) that discovers potential transitions between demonstration skills, and a State Transition Field (STF) that establishes unique connections for arbitrary states within the demonstration neighborhood. To enable effective RLID with augmented data, we develop an Adaptive Trajectory Sampling (ATS) strategy for dynamic curriculum generation and a historical encoding mechanism for memory-dependent skill learning. Our approach enables robust skill acquisition that significantly generalizes beyond the reference demonstrations. Extensive experiments across diverse interaction tasks demonstrate substantial improvements over state-of-the-art methods in terms of convergence stability, generalization capability, and recovery robustness.

The development of native computer-use agents (CUA) represents a significant leap in multimodal AI. However, their potential is currently bottlenecked by the constraints of static data scaling. Existing paradigms relying primarily on passive imitation of static datasets struggle to capture the intricate causal dynamics inherent in long-horizon computer tasks. In this work, we introduce EvoCUA, a native computer use agentic model. Unlike static imitation, EvoCUA integrates data generation and policy optimization into a self-sustaining evolutionary cycle. To mitigate data scarcity, we develop a verifiable synthesis engine that autonomously generates diverse tasks coupled with executable validators. To enable large-scale experience acquisition, we design a scalable infrastructure orchestrating tens of thousands of asynchronous sandbox rollouts. Building on these massive trajectories, we propose an iterative evolving learning strategy to efficiently internalize this experience. This mechanism dynamically regulates policy updates by identifying capability boundaries -- reinforcing successful routines while transforming failure trajectories into rich supervision through error analysis and self-correction. Empirical evaluations on the OSWorld benchmark demonstrate that EvoCUA achieves a success rate of 56.7%, establishing a new open-source state-of-the-art. Notably, EvoCUA significantly outperforms the previous best open-source model, OpenCUA-72B (45.0%), and surpasses leading closed-weights models such as UI-TARS-2 (53.1%). Crucially, our results underscore the generalizability of this approach: the evolving paradigm driven by learning from experience yields consistent performance gains across foundation models of varying scales, establishing a robust and scalable path for advancing native agent capabilities.

Abstract reasoning ability reflects the intelligence and generalization capacity of LLMs to extract and apply abstract rules. However, accurately measuring this ability remains challenging: existing benchmarks either rely on expensive manual annotation, limiting their scale, or risk measuring memorization rather than genuine reasoning. To address this, we introduce an automated pipeline named A2RBench, encompassing generation, expansion, evaluation, and analysis. Specifically, in the generation stage, LLMs create diverse tasks demanding genuine reasoning; in the expansion stage, LLMs reuse validated rules and expand new input spaces to generate task variations, achieving scaling. However, such a process may cause hallucinations. To eliminate it, we further establish a theoretical framework and prove that programmatic verification--testing whether the inverse operation perfectly reverses the forward operation (cycle consistency)--guarantees a unique solution. Through extensive evaluations on mainstream LLMs, we find: (1) Current LLMs exhibit fundamental deficiencies in abstract reasoning, with top models significantly underperforming humans on a representative subset (39.8% vs. 68.5%). (2) Current LLMs fall far short of 2D and 1D in the complexity of generated 3D tasks, revealing their lack of understanding of high-dimensional tasks. (3) Counterintuitively, inputs with higher information complexity can simplify the reasoning process.

We developed a benchmark set to assess the generalization of state-of-the-art large language models on problems beyond linguistic tasks and evaluate it on a systematic progression of GPT models (GPT-3.5, GPT-4, GPT-4o, GPT-4o-mini). Using simple games like Tic-Tac-Toe, Connect Four, Battleship, and a Shape Recognition Game, all encoded in ASCII, we test strategic capabilities and spatial reasoning, core abilities any artificial intelligence would need to master for solving problems in chemistry. To probe generalization, we introduce two new games for spatial logic: LEGO Connect Language (LCL) and Guess-the-SMILES (GtS), a operationally simple chemistry benchmark. Our results show that GPT models provide meaningful responses for several tasks but, generally, perform poorly. A systematic performance progression with increased model capabilities (GPT-3.5, GPT-4, GPT-4o) is only observed for 4 out of the 7 benchmark tasks. All models consistently struggle with Battleship, LCL, and GtS. This suggests that while GPT models can emulate conversational proficiency and basic rule comprehension, they have limited generalization with respect to strategy and spatial reasoning. Particularly poor performance is observed for interpreting molecular graphs when encoded in ASCII. The results provided by our open-source benchmark suite (https://github.com/BlueVelvetSackOfGoldPotatoes/child-play{ChildPlay GitHub Repository}) caution against claims of emergent intelligence in GPT models, which appear more specialized than general.

Recent advances in Large Reasoning Models (LRMs) trained with Long Chain-of-Thought (Long CoT) reasoning have demonstrated remarkable cross-domain generalization capabilities. However, the underlying mechanisms supporting such transfer remain poorly understood. We hypothesize that cross-domain generalization arises from shared abstract reasoning prototypes -- fundamental reasoning patterns that capture the essence of problems across domains. These prototypes minimize the nuances of the representation, revealing that seemingly diverse tasks are grounded in shared reasoning structures.Based on this hypothesis, we propose ProtoReasoning, a framework that enhances the reasoning ability of LLMs by leveraging scalable and verifiable prototypical representations (Prolog for logical reasoning, PDDL for planning).ProtoReasoning features: (1) an automated prototype construction pipeline that transforms problems into corresponding prototype representations; (2) a comprehensive verification system providing reliable feedback through Prolog/PDDL interpreters; (3) the scalability to synthesize problems arbitrarily within prototype space while ensuring correctness. Extensive experiments show that ProtoReasoning achieves 4.7% improvement over baseline models on logical reasoning (Enigmata-Eval), 6.3% improvement on planning tasks, 4.0% improvement on general reasoning (MMLU) and 1.0% on mathematics (AIME24). Significantly, our ablation studies confirm that learning in prototype space also demonstrates enhanced generalization to structurally similar problems compared to training solely on natural language representations, validating our hypothesis that reasoning prototypes serve as the foundation for generalizable reasoning in large language models.

Understanding and accurately following instructions is critical for large language models (LLMs) to be effective across diverse tasks. In this work, we rigorously examine the key factors that enable models to generalize to unseen instructions, providing insights to guide the collection of data for instruction-tuning. Through controlled experiments, inspired by the Turing-complete Markov algorithm, we demonstrate that such generalization only emerges when training data is diversified enough across semantic domains. Our findings also reveal that merely diversifying within limited domains fails to ensure robust generalization. In contrast, cross-domain data diversification, even under constrained data budgets, significantly enhances a model's adaptability. We further extend our analysis to real-world scenarios, including fine-tuning of $textbf{specialist} and textbf{generalist}$ models. In both cases, we demonstrate that 1) better performance can be achieved by increasing the diversity of an established dataset while keeping the data size constant, and 2) when scaling up the data, diversifying the semantics of instructions is more effective than simply increasing the quantity of similar data. Our research provides important insights for dataset collation, particularly when optimizing model performance by expanding training data for both specialist and generalist scenarios. We show that careful consideration of data diversification is key: training specialist models with data extending beyond their core domain leads to significant performance improvements, while generalist models benefit from diverse data mixtures that enhance their overall instruction-following capabilities across a wide range of applications. Our results highlight the critical role of strategic diversification and offer clear guidelines for improving data quality.

Large Language Models (LLMs) exhibit a troubling duality, capable of both remarkable generalization and brittle, verbatim memorization of their training data. This unpredictability undermines their reliability in high-stakes applications. In this work, we propose a unified framework to understand, identify, and control these distinct reasoning modes. First, we introduce a theoretical model based on the Information Bottleneck (IB) principle, formalizing generalization as the learning of a compressed, task-relevant representation and memorization as a failure to compress. Building on this theory, we develop Dynamic Mode Steering (DMS), a novel inference-time algorithm which comprises two components: (1) a lightweight, causally-grounded linear probe that identifies the model's instantaneous reliance on memorization, and (2) a dynamic activation steering mechanism that nudges the model's computation towards pre-identified generalization circuits. We frame DMS as a form of adaptive, self-contrastive decoding. Experiments on reasoning and faithfulness tasks demonstrate that DMS significantly improves logical consistency and factual accuracy, thereby offering a principled approach to enhancing LLM reliability.

The prevailing video retrieval paradigm is structurally misaligned, as narrow benchmarks incentivize correspondingly limited data and single-task training. Therefore, universal capability is suppressed due to the absence of a diagnostic evaluation that defines and demands multi-dimensional generalization. To break this cycle, we introduce a framework built on the co-design of evaluation, data, and modeling. First, we establish the Universal Video Retrieval Benchmark (UVRB), a suite of 16 datasets designed not only to measure performance but also to diagnose critical capability gaps across tasks and domains. Second, guided by UVRB's diagnostics, we introduce a scalable synthesis workflow that generates 1.55 million high-quality pairs to populate the semantic space required for universality. Finally, we devise the Modality Pyramid, a curriculum that trains our General Video Embedder (GVE) by explicitly leveraging the latent interconnections within our diverse data. Extensive experiments show GVE achieves state-of-the-art zero-shot generalization on UVRB. In particular, our analysis reveals that popular benchmarks are poor predictors of general ability and that partially relevant retrieval is a dominant but overlooked scenario. Overall, our co-designed framework provides a practical path to escape the limited scope and advance toward truly universal video retrieval.

Training tool-augmented LLMs has emerged as a promising approach to enhancing language models' capabilities for complex tasks. The current supervised fine-tuning paradigm relies on constructing extensive domain-specific datasets to train models. However, this approach often struggles to generalize effectively to unfamiliar or intricate tool-use scenarios. Recently, reinforcement learning (RL) paradigm can endow LLMs with superior reasoning and generalization abilities. In this work, we address a key question: Can the pure RL be used to effectively elicit a model's intrinsic reasoning capabilities and enhance the tool-agnostic generalization? We propose a dynamic generalization-guided reward design for rule-based RL, which progressively shifts rewards from exploratory to exploitative tool-use patterns. Based on this design, we introduce the Tool-Zero series models. These models are trained to enable LLMs to autonomously utilize general tools by directly scaling up RL from Zero models (i.e., base models without post-training). Experimental results demonstrate that our models achieve over 7% performance improvement compared to both SFT and RL-with-SFT models under the same experimental settings. These gains are consistently replicated across cross-dataset and intra-dataset evaluations, validating the effectiveness and robustness of our methods.

The study of language emergence aims to understand how human languages are shaped by perceptual grounding and communicative intent. Computational approaches to emergent communication (EC) predominantly consider referential games in limited domains and analyze the learned protocol within the game framework. As a result, it remains unclear how the emergent languages from these settings connect to natural languages or provide benefits in real-world language processing tasks, where statistical models trained on large text corpora dominate. In this work, we propose a novel way to establish such a link by corpus transfer, i.e. pretraining on a corpus of emergent language for downstream natural language tasks, which is in contrast to prior work that directly transfers speaker and listener parameters. Our approach showcases non-trivial transfer benefits for two different tasks -- language modeling and image captioning. For example, in a low-resource setup (modeling 2 million natural language tokens), pre-training on an emergent language corpus with just 2 million tokens reduces model perplexity by 24.6% on average across ten natural languages. We also introduce a novel metric to predict the transferability of an emergent language by translating emergent messages to natural language captions grounded on the same images. We find that our translation-based metric highly correlates with the downstream performance on modeling natural languages (for instance rho=0.83 on Hebrew), while topographic similarity, a popular metric in previous work, shows surprisingly low correlation (rho=0.003), hinting that simple properties like attribute disentanglement from synthetic domains might not capture the full complexities of natural language. Our findings also indicate potential benefits of moving language emergence forward with natural language resources and models.

Neural networks often learn simple explanations that fit the majority of the data while memorizing exceptions that deviate from these explanations.This behavior leads to poor generalization when the learned explanations rely on spurious correlations. In this work, we formalize the interplay between memorization and generalization, showing that spurious correlations would particularly lead to poor generalization when are combined with memorization. Memorization can reduce training loss to zero, leaving no incentive to learn robust, generalizable patterns. To address this, we propose memorization-aware training (MAT), which uses held-out predictions as a signal of memorization to shift a model's logits. MAT encourages learning robust patterns invariant across distributions, improving generalization under distribution shifts.

Our understanding of the generalization capabilities of neural networks (NNs) is still incomplete. Prevailing explanations are based on implicit biases of gradient descent (GD) but they cannot account for the capabilities of models from gradient-free methods nor the simplicity bias recently observed in untrained networks. This paper seeks other sources of generalization in NNs. Findings. To understand the inductive biases provided by architectures independently from GD, we examine untrained, random-weight networks. Even simple MLPs show strong inductive biases: uniform sampling in weight space yields a very biased distribution of functions in terms of complexity. But unlike common wisdom, NNs do not have an inherent "simplicity bias". This property depends on components such as ReLUs, residual connections, and layer normalizations. Alternative architectures can be built with a bias for any level of complexity. Transformers also inherit all these properties from their building blocks. Implications. We provide a fresh explanation for the success of deep learning independent from gradient-based training. It points at promising avenues for controlling the solutions implemented by trained models.