Curriculum Learning

Reasoning distillation transfers complex reasoning abilities from large language models (LLMs) to smaller ones, yet its success depends on how well the training data align with the student model. This paper introduces the Data-Model Compatibility (DMC) metric, which can be used to assess the suitability of a dataset for reasoning distillation on a student model. DMC provides an assessment by jointly considering data quality, relative difficulty, and student capability. We validated the effectiveness of DMC from two perspectives: (1) DMC exhibits a strong correlation with reasoning distillation performance; and (2) using DMC as the criterion for data selection leads to improved reasoning distillation performance. Both findings are consistently demonstrated across multiple student models and tasks. Moreover, since the DMC of each dataset dynamically changes during training, our experiments demonstrate that dynamically selecting datasets based on DMC can further enhance performance.

Multimodal Emotion Recognition in Conversations (MERC) is a crucial task for understanding human interactions, where multimodal approaches integrating language, facial expressions, and vocal tone have achieved significant progress. However, modality misalignment and imbalanced learning remain major challenges, limiting the effective utilization of multimodal information. To address this issue, we propose a plug-and-play framework based on Self-Paced Curriculum Learning (SPCL) for MERC. We introduce a dual-level Difficulty Measurer that captures both utterance-level and conversation-level challenges. The utterance-level score models fine-grained modality-specific difficulty, while the conversation-level score captures broader dialogue structures, including emotional dependencies and modality coherence. Based on these scores, the Learning Scheduler dynamically guides training from easier to more difficult instances. By integrating SPCL into existing MERC architectures, our method alleviates modality imbalance and improves model robustness. Extensive experiments on the IEMOCAP and MELD datasets demonstrate consistent improvements across different architectures and modality settings. On IEMOCAP, SPCL improves weighted F1-score by approximately +1.2% to +6.6% over baseline models, while on MELD, gains reach up to +10.4%. These results highlight the effectiveness and generalizability of SPCL as a lightweight plug-and-play module for multimodal emotion recognition.

Recent advances in vision-language models (VLMs) emphasize long chain-of-thought reasoning; yet, we find that their performance on visual tasks is primarily limited by a lack of visual perception as opposed to reasoning itself. In this work, we systematically study the interplay between perception and reasoning in VLM post-training by decomposing their capabilities into three separate training stages: visual perception, visual reasoning, and textual reasoning, incorporating specialized training data. We demonstrate that visual perception (a) requires targeted optimization with specialized data; (b) serves as a fundamental scaffold that should be solidified through staged training before refining visual reasoning; and (c) is more effectively learned via RL than caption-based SFT. Our experiments across multiple VLMs demonstrate that staged training consistently improves both visual perception and reasoning performance over merged training. Notably, models trained with our approach achieve 1.5% higher reasoning accuracy with 20.8% shorter reasoning traces, suggesting that superior perception reduces the need for excessive reasoning. Furthermore, we show that this capability-based staging represents a new curriculum dimension orthogonal to traditional difficulty-based curricula, and combining both yields further additive gains. Our staged-training models achieve superior performance among open-weight VLMs, establishing advanced results on several visual math and perception (e.g., +5.2% on WeMath and +3.7% on RealWorldQA) tasks compared with the base counterpart.

Physics-informed neural networks (PINNs) offer a mesh-free framework for solving partial differential equations (PDEs), yet training often suffers from gradient pathologies, spectral bias, and poor convergence, especially for problems with strong nonlinearity, sharp gradients, or multiscale features. We propose the Curriculum-Guided Gaussian Mixture Physics-Informed Neural Network (CGMPINN), which integrates Gaussian mixture modeling with dynamic curriculum learning. Specifically, a GMM is periodically fitted to the PDE residual distribution to quantify spatially varying learning difficulty. A smooth curriculum schedule progressively shifts training focus from easy to harder regions, while precision-based variance modulation suppresses unreliable clusters during early optimization. This dual curriculum is governed by a shared curriculum parameter and can be combined with self-adaptive loss balancing. We further establish theoretical guarantees, including sublinear convergence of the gradient norm for the induced time-varying loss, uniform equivalence between the curriculum-weighted and standard PDE losses, and a generalization bound with an explicit weighting-induced bias characterization. Experiments on six benchmark PDEs spanning elliptic, parabolic, hyperbolic, advection-dominated, and nonlinear reaction-diffusion types show that CGMPINN consistently achieves the lowest relative $L_2$ and maximum absolute errors among all compared methods, reducing relative $L_2$ error by up to 97.8% over the standard PINN at comparable cost. Our code is publicly available at https://github.com/Mathematics-Yang/CGMPINN.

Physics-Informed Neural Networks (PINNs) combine deep learning with physical constraints for solving partial differential equations (PDEs), and are widely applied in fluid mechanics, heat transfer, and solid mechanics. However, PINN training still suffers from high-dimensional non-convex loss landscapes, imbalanced multiobjective constraints, and ineffective information propagation. Existing curriculum learning and causality-guided strategies improve training stability, but mainly focus on temporal or parametric progression, lacking explicit treatment of spatial information propagation and inter-region consistency. Moreover, they are not directly applicable to boundary value problems (BVPs) with strong spatial coupling. To address this issue, we propose a spatially correlated curriculum learning framework for PINNs. To the best of our knowledge, this is the first work to address PINN training difficulties from the perspective of spatial coupling among subregions. First, spatial causal weights guide information from near-boundary regions inward, reducing optimization failures and spurious convergence. Second, a low-frequency information bridge enforces pseudo-label-based consistency across spatially separated regions, suppressing global low-frequency drift. Third, a region-adaptive reweighting strategy adjusts subregion losses to reduce local residuals and recover high-frequency details. Experiments on PDE benchmarks show that, under comparable computational cost, the proposed method alleviates training failures and improves solution accuracy. The code is available at https://github.com/pigofmomo/CurriculumLearningPINN.

We present VectraYX-Nano, a 41.95M-parameter decoder-only language model trained from scratch in Spanish for cybersecurity, with a Latin-American regional focus and native tool invocation via the Model Context Protocol (MCP). The model has four contributions. (i) Corpus: VectraYX-Sec-ES, a 170M-token Spanish corpus assembled by an eight-VM distributed pipeline at ~$25 USD of cloud compute and split into three curriculum phases (conversational 42M, cybersecurity 118M, offensive tooling 10M). (ii) Architecture: a 42M Transformer decoder with GQA, QK-Norm, RMSNorm, SwiGLU, RoPE and z-loss, paired with a domain-balanced 16,384-token byte-fallback BPE. (iii) Curriculum with replay across the three phases yields a monotonic loss descent (9.80 -> 3.17 -> 3.00 -> 2.16); after SFT (loss 1.74) the v2 bootstrap-ablation reference attains a conversational gate of 0.775 +/- 0.043 on B5 over N=4 seeds, and a controlled Phase-2 replay sweep over {0,5,10,25,50}% saturates B5 at >=25% replay. (iv) Two empirical findings, both N=4. A controlled bootstrap-corpus ablation across v2 (OpenSubs), v4 (mC4-ES), and v6 (60/25/15 OpenSubs/mC4/Wiki) exposes a loss-versus-register inversion: lower-perplexity bootstraps yield measurably worse conversational behavior (v2 > v4 > v6 on B5 at every paired seed). The B4 (tool-selection) floor of 0.000 is a corpus-density artifact, not a capacity gate: rebalancing the SFT mixture to tool-use ratio 1:21 yields VectraYX-Nano v7, the released headline configuration, reaching B4 = 0.230 +/- 0.052 at 42M while retaining B1 = 0.332 +/- 0.005 and B5 = 0.725 +/- 0.130; a LoRA replication on a 260M from-scratch mid-tier reaches 0.445 +/- 0.201. The released GGUF is 96 MB in F16, runs sub-second TTFT on commodity hardware under llama.cpp, and is, to our knowledge, the first published Spanish-native cybersecurity LLM with end-to-end MCP integration.

Fine-tuning multilingual ASR models like Whisper for low-resource languages often improves read speech but degrades spontaneous audio performance. To diagnose this mismatch, we introduce Vividh-ASR, a complexity-stratified benchmark for Hindi and Malayalam across four tiers: studio, broadcast, spontaneous, and synthetic noise. Through a controlled study of learning-rate timing and curriculum ordering, we find that early large parameter updates improve global WER by 12 absolute points, while a hard-to-easy curriculum adds gains for spontaneous speech. These findings motivate reverse multi-stage fine-tuning (R-MFT), a training recipe that enables a parameter-efficient 244M Whisper model to match or exceed conventionally fine-tuned 769M counterparts. Representational analysis via CKA and SVD reveals effective schedules concentrate adaptation in the decoder, preserving the pre-trained encoder's acoustic geometry. We release the benchmark and models.

The reasoning frontier of Large Language Models (LLMs) has advanced significantly through modern post-training paradigms (e.g., Reinforcement Learning from Verifiable Rewards (RLVR)). However, the efficacy of these methods remains fundamentally constrained by the diversity and complexity of the training data. One practical solution is data synthesis; yet, prevalent methods relying on unstructured mutation or exploration suffer from homogeneity collapse, failing to systematically expand the reasoning frontier. To overcome this, we propose Evoutionary Task Discovery (EvoTD), a framework that treats data synthesis as a directed search over a dual-axis manifold of Algorithmic Skills and Complexity Attributes. We introduce structured evolutionary operators to navigate this space: a Crossover operator that synthesizes novel skill compositions to enhance diversity, and a Parametric Mutation operator that scales structural constraints (e.g., input size, tree depth) to drive robust generalization. Crucially, we integrate a dynamic Zone of Proximal Development filter, ensuring tasks lie within the learnable region of the model. Empirically, EvoTD delivers substantial reasoning gains that generalize consistently across model architectures, pretraining regimes, and scales, demonstrating that structured evolutionary curricula can effectively support reasoning improvement. We release our code on https://github.com/liqinye/EvoTD.

Every molecule ever synthesised can be drawn as a 2D skeletal diagram, yet in modern property prediction this universally available representation has received less focus in favour of molecular graphs, 3D conformers, or billion-parameter language models, each imposing its own computational and data-engineering overhead. We present $\textbf{MolSight}$, the first systematic large-scale study of vision-based Molecular Property Prediction (MPP). Using 10 vision architectures, 7 pre-training strategies, and $2\,M$ molecule images, we evaluate performance across 10 downstream tasks spanning physical-property regression, drug-discovery classification, and quantum-chemistry prediction. To account for the wide variation in structural complexity across pre-training molecules, we further propose a $\textbf{chemistry-informed curriculum}$: five structural complexity descriptors partition the corpus into five tiers of increasing chemical difficulty, consistently outperforming non-curriculum baselines. We show that a single rendered bond-line image, processed by a vision encoder, is sufficient for competitive molecular property prediction, i.e. $\textit{chemical insight from sight alone}$. The best curriculum-trained configuration achieves the top result on $\textbf{5 of 10}$ benchmarks and top two on $\textbf{all 10}$, at \textbf{\textit{80$\times$ lower}} FLOPs than the nearest multi-modal competitor.

Learning dynamic whole-body motions for legged robots through reinforcement learning (RL) remains challenging due to the high risk of failure, which makes efficient exploration difficult and often leads to unstable learning. In this paper, we propose External Force Guided Curriculum Learning (EFGCL), a guided RL approach based on the principle of physical guidance, in which external assistive forces are introduced during training. Inspired by spotting in artistic gymnastics, EFGCL enables agents to physically experience successful motion executions without relying on task-specific reward shaping or reference trajectories. Experiments on a quadrupedal robot performing Jump, Backflip, and Lateral-Flip tasks demonstrate that EFGCL accelerates learning of the Jump task by approximately a factor of two and enables the acquisition of complex whole body motions that conventional RL methods fail to learn. We further show that the learned policies can be deployed on real robot, reproducing motions consistent with those observed in simulation. These results indicate that physically guided exploration, which allows agents to experience success early in training, is an effective and general strategy for improving learning efficiency in dynamic whole-body motion tasks.

Vision-language models (VLMs) enable text-guided object detection but degrade severely under cross-view scenarios where ground and aerial viewpoints differ in altitude, scale, and spatial layout. These geometric changes introduce systematic complexity variations between viewpoints, e.g., ground view images contain dense and highly occluded structures, while aerial images are sparse and globally organized. Fixed VLM fusion mechanisms cannot handle this discrepancy. We propose CrossVL, a framework combining Complexity-Aware Pathway Aggregation (CPA) and Paired Curriculum Learning (PCL) for enhanced cross-view detection for VLM. CPA estimates scene complexity from multimodal statistics and routes visual features through multiple pathways to obtain view-specific representations. PCL leverages semantic consistency of synchronized ground-aerial pairs to provide stable early supervision and then gradually shifts toward randomized sampling. On MAVREC, CrossVL improves Florence-2's aerial mAP from 58.66% to 61.03% and reduces the ground-aerial performance gap from 8.63pp to 6.65pp, while also achieving a 3.3x reduction in variance across random seeds. CPA provides stable complexity-aware feature aggregation, and PCL enhances optimization dynamics. Together, they demonstrate that coordinated architectural and training adaptations are crucial for robust cross-view VLM detection.

LLM/VLM-based digital agents have advanced rapidly thanks to scalable sandboxes for coding, web navigation, and computer use, which provide rich interactive training grounds. In contrast, embodied agents still lack abundant, diverse, and automatically generated 3D environments for interactive learning. Existing embodied simulators rely on manually crafted scenes or procedural templates, while recent LLM-based 3D generation systems mainly produce static scenes rather than deployable environments with verifiable tasks and standard learning interfaces. We introduce SimWorld Studio, an open-source platform built on Unreal Engine 5 for generating evolving embodied learning environments. At its core is SimCoder, a tool/skill-augmented coding agent that writes and executes engine-level code to construct physically grounded 3D worlds from language/image instructions. SimCoder self-evolves by using verifier feedback (e.g., compilation errors, physics checks, VLM critiques) to revise environments and autonomously add reusable tools and skills to its library. Generated worlds are exported as Gym-style environments for embodied agent learning. SimWorld Studio further enables co-evolution between environment generation and embodied learning: agent performance feedback guides SimCoder to generate adaptive curricula near the learner's capability frontier, so that environments become increasingly challenging as the embodied agent improves. Three case studies on embodied navigation show that self-evolution improves generation reliability, generated environments substantially improve embodied agent performance that generalizes to unseen benchmarks, and co-evolution yields an 18-point success-rate gain over fixed-environment learning and a 40-point gain over an untrained agent.

Code generation, which aims to automatically generate source code from given programming requirements, has the potential to substantially improve software development efficiency. With the rapid advancement of large language models (LLMs), LLM-based code generation has attracted widespread attention from both academia and industry. However, as programming requirements become increasingly complex, existing LLMs still exhibit notable performance limitations. To address this challenge, recent studies have proposed training-based curriculum reinforcement learning (CRL) strategies to improve LLM code generation performance. Despite their effectiveness, existing CRL approaches suffer from several limitations, including misaligned requirement difficulty perception, the absence of requirement difficulty optimization, and suboptimal curriculum sampling strategies. In CRL-based code generation, programming requirements serve as the sole input to the model, making their quality and difficulty critical to training effectiveness. Motivated by insights from software requirements engineering, we propose RECRL, a novel requirement-aware curriculum reinforcement learning framework for enhancing LLM-based code generation. RECRL automatically perceives model-specific requirement difficulty, optimizes challenging requirements to improve training data utilization, and employs an adaptive curriculum sampling strategy to construct training batches with smoothly varying difficulty. Extensive experiments on five state-of-the-art LLMs across five widely-used code generation benchmarks by comparing with five state-of-the-art baselines, demonstrate the significant effectiveness of RECRL. For example, RECRL achieves an average Pass@1 improvement of 1.23%-5.62% over all state-of-the-art baselines.

We propose a paradigm shift toward open-ended curriculum self-play: rather than learning to answer on a fixed prompt set, a unified policy learns to question: generating verifiable problems, solving them, and turning verifier feedback into self-improvement without human-annotated solutions. We introduce ANCORA, in which the policy alternates between a Proposer that synthesizes novel specifications and a Solver that produces verified solutions, anchored by three load-bearing mechanisms: a two-level group-relative update coupling Proposer advantages across specifications with Solver advantages across solution attempts; iterative self-distilled SFT projecting the base model onto its valid-output manifold before RL; and a UCB-guided Curriculum DAG whose policy-induced problem set can provably expand under self-composition. Without these stabilizers, sparse verifier feedback drives Proposer collapse even under MLRL-aligned rewards; with them, ANCORA bootstraps a verifiable curriculum from zero human solutions. Instantiated in Verus, ANCORA lifts Dafny2Verus pass@1 from a 26.6% SFT baseline to 81.5% in test-time training (TTT, 0-shot), outperforming PSV self-play by 15.8 points despite PSV's 1-shot inference; in a transfer setting, training from Dafny2Verus seeds yields 36.2% and 17.2% pass@1 on held-out MBPP and HumanEval.

Vision-and-Language Navigation (VLN) aims to enable an embodied agent to follow natural-language instructions and navigate to a target location in unseen 3D environments. We argue that adapting VLMs to VLN requires endowing them with two complementary capabilities for acquiring such awareness, namely backward action reasoning (why) and forward transition prediction~(how). Based on this insight, we propose SpaAct, a simple yet effective training framework that activates the dynamic spatial awareness in VLMs. Specifically, SpaAct introduces two spatial activation tasks: Action Retrospection, which asks the model to infer the executed action sequence from visual transitions, and Future Frame Selection, which forces the model to predict the visual transitions conditioned on history and action. These two objectives provide lightweight supervision on both backward action reasoning and forward transition prediction, encouraging the model to build dynamic spatial awareness in a VLM-friendly way. To further stabilize adaptation, we design TriPA, a Tri-factor Progressive Adaptive curriculum learning method that organizes training samples from easy to hard, allowing the model to gradually acquire navigation skills from basic locomotion to long-horizon reasoning. Experiments on standard VLN-CE benchmarks show that SpaAct consistently improves VLM-based navigation and achieves state-of-the-art performance. We will release the code and models to support future research.

Many of the thousands of attested languages share common configurations of features, creating a spectrum from typologically very rare (e.g., object-verb-subject word order) or impossible languages to very common combinations of features (e.g., subject-object-verb word order). One central question is under what conditions such typological tendencies can be predicted, and specifically whether the learning bias of language models (LMs) is sufficient to reproduce such patterns. In this study, we add one dimensionality to such analysis -- the learning scenario for LMs -- to explore its interaction with the inductive bias of LMs. Specifically, as a first study, we examine the effect of curriculum learning (CL), as a developmentally motivated learning scenario, i.e., starting with simpler sentences rather than randomly-ordered input. We expand existing LM-based exploration (El-Naggar et al., 2025a,b) with a simple CL variant and find that CL substantially impacts the apparent inductive bias of LMs.

Recent advances in self-evolution video understanding frameworks have demonstrated the potential of autonomous learning without human annotations. However, existing methods often suffer from weakly controlled optimization and uncontrolled difficulty progression, as they lack structured guidance throughout the iterative learning process. To address these limitations, we propose CurEvo, a curriculum-guided self-evolution framework that introduces curriculum learning into self-evolution to achieve more structured and progressive model improvement. CurEvo dynamically regulates task difficulty, refines evaluation criteria, and balances data diversity according to model competence, forming a curriculum-guided feedback loop that aligns learning complexity with model capability. Built upon this principle, we develop a multi-dimensional adaptive QA framework that jointly evolves question generation and answer evaluation across perception, recognition, and understanding dimensions, ensuring coherent and measurable curriculum progression. Through this integration, CurEvo transforms weakly controlled self-evolution into a more structured learning process for autonomous video understanding. Across seven backbones, CurEvo consistently improves both benchmark accuracy and evaluator-based semantic score on four VideoQA benchmarks, validating the effectiveness of curriculum-guided self-evolution for video understanding.

Current visual text generation models struggle with the trade-off between text accuracy and overall image coherence. We find that achieving high text accuracy can reduce aesthetic quality and instruction-following capability. Although reinforcement learning approaches can alleviate the problem through aligning with multiple rewards, they are often unstable for text generation, as existing approaches normally optimize multiple rewards in a weighted-sum way. In addition, it is difficult to balance the weight of each reward. Moreover, reinforcement learning requires a set of training instructions. A large number of prompts require more training time and computing resources, while a small set leads to poor performance. Hence, how to select the prompts for efficient training is an unsolved problem. In this study, we propose Pareto-Optimal Curriculum Alignment (POCA), a framework that addresses this issue as a multi-objective problem by: 1) identifying the Pareto-optimal set to avoid simple scalarization and 2) designing an adaptive curriculum alignment strategy to manage a learning sequence of a multi-reward dataset using automatic difficulty assessment, which is crucial for optimal convergence as RL methods explore in a limited data environment. In synergy, POCA finds the Pareto-optimal set in a unified reward space, which eliminates inconsistent signals to find the best trade-off solution from different rewards under an easy-to-hard optimization landscape. The experimental results show that POCA significantly improves all metrics such as CLIP, HPS scores and sentence accuracy.

Curriculum learning helps language models tackle complex reasoning by gradually increasing task difficulty. However, it often fails to generate consistent step-by-step reasoning, especially in multilingual and low-resource settings where cross-lingual transfer from English to Indian languages remains limited. We propose IRIS: Interleaved Reinforcement with Incremental Staged Curriculum, a two-axis framework that combines Supervised Fine-Tuning on progressively harder problems (vertical axis) with Reverse Curriculum Reinforcement Learning to reduce reliance on step-by-step guidance (horizontal axis). We design a composite reward combining correctness, step-wise alignment, continuity, and numeric incentives, optimized via Group Relative Policy Optimization (GRPO). We release CL-Math, a dataset of 29k problems with step-level annotations in English, Hindi, and Marathi. Across standard benchmarks and curated multilingual test sets, IRIS consistently improves performance, with strong results on math reasoning tasks and substantial gains in low-resource and bilingual settings, alongside modest improvements in high-resource languages.

On-policy distillation (OPD) has shown strong potential for transferring reasoning ability from frontier or domain-specific models to smaller students. While effective on static single-turn tasks, its behavior in multi-turn agent settings remains underexplored. In this work, we identify a key limitation of vanilla OPD in such settings, which we term Trajectory-Level KL Instability. Specifically, we observe that KL divergence increases together with a drop in success rate, and even after convergence, the KL remains high, leading to unstable training. This instability arises from inter-turn error compounding: as errors accumulate, the student is driven beyond the teacher's effective support, rendering the supervision signal unreliable. To address this, we propose TCOD (Temporal Curriculum On-Policy Distillation), a simple yet effective framework that controls the trajectory depth exposed to the student and progressively expands it from short to long with a curriculum schedule. Experimental results across four student-teacher pairs on three multi-turn agent benchmarks (ALFWorld, WebShop, ScienceWorld) show that TCOD mitigates KL escalation and enhances KL stability throughout training, improving agent performance by up to 18 points over vanilla OPD. Further evaluations show that TCOD can even surpass the teacher's performance and generalize to tasks on which the teacher fails. Our code is available at https://github.com/kokolerk/TCOD.

We show that pre-training a Transformer on music before language significantly accelerates language acquisition. Using piano performances (MAESTRO dataset), a developmental pipeline -- music $\to$ poetry $\to$ prose -- yields a $17.5\%$ perplexity improvement over random initialization ($p < 0.001$, 5 seeds), with music and poetry improving orthogonal model components (internal computation and embeddings, respectively). Convergence tests confirm that this is not a transient head start: at $d\!=\!64$, multi-seed validation (5 seeds) shows a persistent 5.5% gap at plateau ($p = 0.017$), with the pipeline converging faster and to a lower loss in every run. Real music matches the transfer ceiling of synthetic patterns with one-third the data, and scaling experiments reveal that optimal pre-training data volume shifts with model capacity ($-3\% \to +3\% \to +6\%$ advantage of larger datasets from $d\!=\!16$ to $d\!=\!64$). Across the scales we study ($d\!\in\!\{16,32,64\}$, up to ${\sim}400$K parameters), these results suggest a capacity-dependent data curation principle and indicate that structured human creative outputs can provide an efficient pre-training substrate for small language models; stronger conclusions at modern pre-training scale will require substantially larger experiments.

Vision-Language Models (VLMs) have demonstrated remarkable progress in single-image understanding, yet effective reasoning across multiple images remains challenging. We identify a critical capability gap in existing multi-image alignment approaches: current methods focus primarily on localized reasoning with pre-specified image indices (``Look at Image 3 and...''), bypassing the essential skills of global visual search and autonomous cross-image comparison. To address this limitation, we introduce a Simple-to-Hard (S2H) learning framework that systematically constructs multi-image preference data across three hierarchical reasoning levels requiring an increasing level of capabilities: (1) single-image localized reasoning, (2) multi-image localized comparison, and (3) global visual search. Unlike prior work that relies on model-specific attributes, such as hallucinations or attention heuristics, to generate preference pairs, our approach leverages prompt-driven complexity to create chosen/rejected pairs that are applicable across different models. Through extensive evaluations on LLaVA and Qwen-VL models, we show that our diverse multi-image reasoning data significantly enhances multi-image reasoning performance, yielding significant improvements over baseline methods across benchmarks. Importantly, our approach maintains strong single-image reasoning performance while simultaneously strengthening multi-image understanding capabilities, thus advancing the state of the art for holistic visual preference alignment.

What does it mean to give an AI agent a complete education? Current agent development produces specialists systems optimized for a single capability dimension, whether tool use, code generation, or security awareness that exhibit predictable deficits wherever they were not trained. We argue this pattern reflects a structural absence: there is no curriculum theory for agents, no principled account of what a fully developed agent should know, be, and be able to do across the full scope of intelligent behavior. This paper introduces the AIT Academy (Agents Institute of Technology Academy), a curriculum framework for cultivating AI agents across the tripartite structure of human knowledge. Grounded in Kagan's Three Cultures and UNESCO ISCED-F 2013, AIT organizes agent capability development into three domains: Natural Science and Technical Reasoning (Domain I), Humanities and Creative Expression (Domain II), and Social Science and Ethical Reasoning (Domain III). The Confucian Six Arts (liuyi) a 2,500-year-old holistic education system are reinterpreted as behavioral archetypes that map directly onto trainable agent capabilities within each domain. Three representative training grounds instantiate the framework across multiple backbone LLMs: the ClawdGO Security Dojo (Domain I), Athen's Academy (Domain II), and the Alt Mirage Stage (Domain III). Experiments demonstrate a 15.9-point improvement in security capability scores under weakest-first curriculum scheduling, and a 7-percentage-point gain in social reasoning performance under principled attribution modeling. A cross-domain finding Security Awareness Calibration Pathology (SACP), in which over-trained Domain I agents fail on out-of-distribution evaluation illustrates the diagnostic value of a multi-domain perspective unavailable to any single-domain framework.

The King Wen sequence of the I-Ching (c. 1000 BC) orders 64 hexagrams -- states of a six-dimensional binary space -- in a pattern that has puzzled scholars for three millennia. We present a rigorous statistical characterization of this ordering using Monte Carlo permutation analysis against 100,000 random baselines. We find that the sequence has four statistically significant properties: higher-than-random transition distance (98.2nd percentile), negative lag-1 autocorrelation (p=0.037), yang-balanced groups of four (p=0.002), and asymmetric within-pair vs. between-pair distances (99.2nd percentile). These properties superficially resemble principles from curriculum learning and curiosity-driven exploration, motivating the hypothesis that they might benefit neural network training. We test this hypothesis through three experiments: learning rate schedule modulation, curriculum ordering, and seed sensitivity analysis, conducted across two hardware platforms (NVIDIA RTX 2060 with PyTorch and Apple Silicon with MLX). The results are uniformly negative. King Wen LR modulation degrades performance at all tested amplitudes. As curriculum ordering, King Wen is the worst non-sequential ordering on one platform and within noise on the other. A 30-seed sweep confirms that only King Wen's degradation exceeds natural seed variance. We explain why: the sequence's high variance -- the very property that makes it statistically distinctive -- destabilizes gradient-based optimization. Anti-habituation in a fixed combinatorial sequence is not the same as effective training dynamics.

Reinforcement learning with verifiable rewards (RLVR) has been a main driver of recent breakthroughs in large reasoning models. Yet it remains a mystery how rewards based solely on final outcomes can help overcome the long-horizon barrier to extended reasoning. To understand this, we develop a theory of the training dynamics of RLVR for transformers on compositional reasoning tasks. Our theory shows that mixed-difficulty training naturally induces an implicit curriculum: without any explicit schedule, easier problems become learnable first and shape the frontier for harder ones, creating a learning progression from easy to hard during optimization. The effectiveness of this curriculum is governed by the smoothness of the difficulty spectrum. When the spectrum is smooth, training dynamics enter a well-behaved relay regime, in which persistent gradient signals on easier problems make slightly harder ones tractable and keep training at the edge of competence. When the spectrum contains abrupt discontinuities, training undergoes grokking-type phase transitions with prolonged plateaus before progress recurs. As a technical contribution, our analysis develops and adapts techniques from Fourier analysis on finite groups to our setting. We validate the predicted mechanisms empirically via controlled synthetic experiments and real-model RLVR runs.

RL methods for scaling large reasoning models stall on datasets with low initial success rates, and thus little training signal. We investigate a fundamental question: Can a pretrained LLM leverage latent knowledge to generate an automated curriculum for problems it cannot solve? We explore this with SOAR: An asymmetric self-play framework that uses meta-RL to surface these pedagogical signals. A teacher model proposes synthetic problems for a student model, and is rewarded with its improvement on a subset of hard problems, thus grounding the curriculum in real student progress rather than intrinsic proxy rewards. Our study on the hardest subsets of math benchmarks (0/128 success) reveals three core findings. First, it is possible to realize bilevel meta-RL that unlocks learning under sparse, binary rewards by sharpening a latent capacity of pretrained models to generate useful problems. Second, grounded rewards outperform intrinsic learnability rewards used in prior LLM self-play, reliably avoiding typical instability and diversity collapse modes. Third, the structure and well-posedness of questions are more critical for learning progress than solution correctness. Our results suggest that the ability to generate useful stepping stones does not require the preexisting ability to solve the hard problems, paving a principled path to escape reasoning plateaus without additional curated data

Curriculum learning (CL) structures training from simple to complex samples, facilitating progressive learning. However, existing CL approaches for emotion recognition often rely on heuristic, data-driven, or model-based definitions of sample difficulty, neglecting the difficulty for human perception, a critical factor in subjective tasks like emotion recognition. We propose CHUCKLE (Crowdsourced Human Understanding Curriculum for Knowledge Led Emotion Recognition), a perception-driven CL framework that leverages annotator agreement and alignment in crowd-sourced datasets to define sample difficulty, under the assumption that clips challenging for humans are similarly hard for neural networks. Experimental results suggest that CHUCKLE enhances the performance of LSTMs and Transformers over non-curriculum baselines, while reducing the number of gradient updates, thereby enhancing both training efficiency and model robustness in both subject-dependent and subject-independent settings.

As the cost of pretraining large language models grows, there is continued interest in strategies to improve learning efficiency during this core training stage. Motivated by cognitive development, where humans gradually build knowledge as their brains mature, we propose Curriculum-Guided Layer Scaling (CGLS), a framework for compute-efficient pretraining that synchronizes increasing data difficulty with model growth through progressive layer stacking (i.e. gradually adding layers during training). At the 100M parameter scale, using a curriculum transitioning from synthetic short stories to general web data, CGLS outperforms baseline methods on the question-answering benchmarks PIQA and ARC. Pretraining at the 1.2B scale, we stratify the DataComp-LM corpus with a DistilBERT-based classifier and progress from general text to highly technical or specialized content. Our results show that progressively increasing model depth alongside sample difficulty leads to better generalization and zero-shot performance on various downstream benchmarks. Altogether, our findings demonstrate that CGLS unlocks the potential of progressive stacking, offering a simple yet effective strategy for improving generalization on knowledge-intensive and reasoning tasks.

Curriculum learning enhances Direct Preference Optimization (DPO) for aligning Large Language Models (LLMs), yet existing methods rely on a one-dimensional view of difficulty. In this work, we reframe alignment difficulty as a two-dimensional space spanned by Prompt Complexity (PC) and Pairwise Distinguishability (PD), providing a more principled foundation for alignment. We first demonstrate the efficacy of this space by developing DM-Curri-DPO, a framework of static curricula that already achieves significant gains over baseline methods. Moving beyond these handcrafted paths, we introduce our primary contribution: GSP-Curri-DPO, a novel Group-wise Self-Paced Learning framework. This advanced method empowers the model to navigate the difficulty grid, discovering an optimal learning trajectory based on its own evolving capabilities. Extensive experiments show our self-paced approach not only sets a new state-of-the-art on key benchmarks but, more importantly, demonstrates superior data efficiency and robustness to preference noise. Our work establishes a new paradigm for LLM alignment, offering both a structured difficulty space and an intelligent, model-driven methodology for navigating it.

Reinforcement finetuning (RFT) has shown great potential for enhancing the mathematical reasoning capabilities of large language models (LLMs), but it is often sample- and compute-inefficient, requiring extensive training. In this work, we introduce AdaRFT (Adaptive Curriculum Reinforcement Finetuning), a method that significantly improves the efficiency of RFT through adaptive curriculum learning. AdaRFT dynamically adjusts the difficulty of training problems based on the model's recent reward signals, ensuring that the model consistently trains on tasks that are challenging but solvable. This adaptive sampling strategy accelerates learning by maintaining an optimal difficulty range, avoiding wasted computation on problems that are too easy or too hard. AdaRFT requires only a lightweight extension to standard RFT algorithms like Proximal Policy Optimization (PPO), without modifying the reward function or model architecture. Experiments on competition-level math datasets demonstrate that AdaRFT improves convergence efficiency and reasoning performance. Given problem-level difficulty annotations, AdaRFT reduces RFT training time by up to 2 times across data distributions and model scales, offering a more scalable and effective RFT framework.