Self-Training for Language Models

Multi-hop question answering (MHQA) enables accurate answers to complex queries by retrieving and reasoning over evidence dispersed across multiple documents. Existing MHQA approaches mainly rely on iterative retrieval-augmented generation, which suffer from the following two major issues. 1) Existing methods prematurely commit to surface-level entities rather than underlying reasoning structures, making question decomposition highly vulnerable to lexical ambiguity. 2) Existing methods overlook the logical dependencies among reasoning steps, resulting in uncoordinated execution. To address these issues, we propose STRIDE, a framework that separates strategic planning, dynamic control, and grounded execution. At its core, a Meta-Planner first constructs an entity-agnostic reasoning skeleton to capture the abstract logic of the query, thereby deferring entity grounding until after the reasoning structure is established, which mitigates disambiguation errors caused by premature lexical commitment. A Supervisor then orchestrates sub-question execution in a dependency-aware manner, enabling efficient parallelization where possible and sequential coordination when necessary. By dynamically deciding whether to retrieve new evidence or infer from existing facts, it avoids redundant queries and error propagation, while fusing cross-branch information and reformulating failed queries to enhance robustness. Grounded fact extraction and logical inference are delegated to specialized execution modules, ensuring faithfulness through explicit separation of retrieval and reasoning. We further propose STRIDE-FT, a modular fine-tuning framework that uses self-generated execution trajectories from STRIDE, requiring neither human annotations nor stronger teacher models. Experiments show that STRIDE achieves robust and accurate reasoning, while STRIDE-FT effectively enhances open-source LLMs.

Previous LLMs-based RL studies typically follow either supervised learning with high annotation costs, or unsupervised paradigms using voting or entropy-based rewards. However, their performance remains far from satisfactory due to the substantial annotation cost and issues such as model collapse or reward hacking. To address these issues, we introduce a new perspective inspired by cognitive learning theory and propose a novel approach called EasyRL. The core of EasyRL is to simulate the human cognitive acquisition curve by integrating reliable knowledge transfer from easy labeled data with a progressive divide-and-conquer strategy that tackles increasingly difficult unlabeled data. Specifically, we initialize a warm-up model using supervised RL with few-shot labeled data. This is followed by a divide-and-conquer pseudo-labeling strategy on difficult unlabeled data, combining consistency-based selection for low-uncertainty cases and reflection-based resolution for medium-uncertainty cases. Finally, difficulty-progressive self-training with iterative pseudo-labeling and RL further strengthens the model's reasoning capability. EasyRL provides a unified self-evolving framework that facilitates data-efficient post-training of LLMs. Experimental results on mathematical and scientific benchmarks demonstrate that EasyRL, using only 10% of easy labeled data, consistently outperforms state-of-the-art baselines.

Mechanisms for continued self-improvement of language models without external supervision remain an open challenge. We propose Peer-Predictive Self-Training (PST), a label-free fine-tuning framework in which multiple language models improve collaboratively by using a cross-model aggregate response as an internal training signal. Given a prompt, models generate responses sequentially; the final aggregated answer, which is often more reliable than individual responses in practice, serves as an internal reference for learning. We measure how informative each intermediate response is about the aggregate using pointwise mutual information (PMI), and use this signal to scale self-training updates: responses already aligned with the aggregate receive smaller updates, while less informative or misaligned responses receive larger ones. On mathematical reasoning benchmarks, including SimulEq, MATH-500-Numeric, and MultiArith, PST improves exact-match accuracy by 2.2--4.3 percentage points across Gemma-2-2B, LLaMA-3.2-1B, and Qwen2.5-1.5B, and reduces the average generator--verifier gap (GV-Gap) by 26--40%, while requiring no external supervision, no teacher--student hierarchy, and only cross-model interactions. These results suggest that peer-predictive feedback from cross-model generations can provide an effective mechanism for self-supervised language-model improvement.

Extending LLM context windows is hindered by scarce high-quality long-context data. Recent methods synthesize data with genuine long-range dependencies via information-theoretic verification, selecting contexts that reduce a base model's predictive entropy. However, their single-pass offline construction with a fixed model creates a fundamental off-policy gap: the static screening landscape misaligns with the model's evolving capabilities, causing the training distribution to drift. We propose PolicyLong, shifting data construction towards a dynamic on-policy paradigm. By iteratively re-executing data screening (entropy computation, retrieval, and verification) using the current model, PolicyLong ensures the training distribution tracks evolving capabilities, yielding an emergent self-curriculum. Crucially, both positive and hard negative contexts derive from the current model's entropy landscape, co-evolving what the model learns to exploit and resist. Experiments on RULER, HELMET, and LongBench-v2 (Qwen2.5-3B) show PolicyLong consistently outperforms EntropyLong and NExtLong, with gains growing at longer contexts (e.g., +2.54 at 128K on RULER), confirming the value of on-policy data evolution.

Generative reward models (GRMs) have emerged as a promising approach for aligning Large Language Models (LLMs) with human preferences by offering greater representational capacity and flexibility than traditional scalar reward models. However, GRMs face two major challenges: reliance on costly human-annotated data restricts scalability, and self-training approaches often suffer from instability and vulnerability to reward hacking. To address these issues, we propose ConsistRM, a self-training framework that enables effective and stable GRM training without human annotations. ConsistRM incorporates the Consistency-Aware Answer Reward, which produces reliable pseudo-labels with temporal consistency, thereby providing more stable model optimization. Moreover, the Consistency-Aware Critique Reward is introduced to assess semantic consistency across multiple critiques and allocates fine-grained and differentiated rewards. Experiments on five benchmark datasets across four base models demonstrate that ConsistRM outperforms vanilla Reinforcement Fine-Tuning (RFT) by an average of 1.5%. Further analysis shows that ConsistRM enhances output consistency and mitigates position bias caused by input order, highlighting the effectiveness of consistency-aware rewards in improving GRMs. Our implementation is available at https://github.com/yuliangCarmelo/ConsistRM.

In the unsupervised self-evolution of Multimodal Large Language Models, the quality of feedback signals during post-training is pivotal for stable and effective learning. However, existing self-evolution methods predominantly rely on majority voting to select the most frequent output as the pseudo-golden answer, which may stem from the model's intrinsic biases rather than guaranteeing the objective correctness of the reasoning paths. To counteract the degradation, we propose Continuous Softened Retracing reSampling (CSRS) in MLLM self-evolution. Specifically, we introduce a Retracing Re-inference Mechanism (RRM) that the model re-inferences from anchor points to expand the exploration of long-tail reasoning paths. Simultaneously, we propose Softened Frequency Reward (SFR), which replaces binary rewards with continuous signals, calibrating reward based on the answers' frequency across sampled reasoning sets. Furthermore, incorporated with Visual Semantic Perturbation (VSP), CSRS ensures the model prioritizes mathematical logic over visual superficiality. Experimental results demonstrate that CSRS significantly enhances the reasoning performance of Qwen2.5-VL-7B on benchmarks such as MathVision. We achieve state-of-the-art (SOTA) results in unsupervised self-evolution on geometric tasks. Our code is avaible at https://github.com/yyy195/CSRS.

We propose Autolearn, a framework that enables language models to learn from documents they read, with no external supervision. Passages that produce anomalously high per-token loss are flagged, verified through a self-generated Q&A chain, and trained on with conviction-proportional $β_2$ adjustment. We introduce the perturbation gap (paraphrase-to-original perplexity ratio) as a metric that distinguishes memorization from understanding. The key mechanism is the training data format: Q&A-format training drives the perturbation gap below the pre-trained baseline (2.098 vs. 2.204, $Δ= -0.106$, $> 10σ$), suppressing token-sequence memorization, while standard fine-tuning's best attempt remains within noise ($Δ= -0.010$, $< 1σ$). Across four models spanning Qwen3 and Phi-4 families, Autolearn is the only method that enters this regime. Stochastic evaluation reveals passage-specific knowledge acquisition: the probability of generating a correct novel fact rises from 6% to 54% after training ($p < 10^{-4}$), and Q&A format outperforms standard fine-tuning on genuinely novel facts. The system is self-extinguishing: learned content reduces surprisal below threshold and is skipped on re-encounter.

Improving the code generation capabilities of large language models (LLMs) typically relies on supervised fine-tuning or preference optimization, both of which require costly external resources such as powerful teacher models or reliable test units. However, in real-world scenarios, it is much harder to obtain reference solutions and test oracles than problem descriptions and test inputs. In this paper, we tackle a challenging yet realistic question: Can a code language model improve itself without access to a superior teacher and a test oracle? To answer this, we propose ConSelf, a self-improving approach built upon two key ideas. First, we introduce code semantic entropy, a novel metric that measures problem-level uncertainty by assessing the functional diversity of program behaviors, enabling a curriculum construction with the most learnable problems. Second, we present consensus-driven direct preference optimization (Con-DPO), a preference-based fine-tuning method that weights each preference pair by its behavioral consensus, thereby mitigating the impact of noisy self-generated supervision. Experiments on various benchmarks and backbone LLMs demonstrate that ConSelf significantly outperforms baselines, validating the effectiveness of semantic entropy-based curriculum construction and consensus-driven optimization in improving code generation without external supervision.

As large language models (LLMs) continue to advance, improving them solely through human supervision is becoming increasingly costly and limited in scalability. As models approach human-level capabilities in certain domains, human feedback may no longer provide sufficiently informative signals for further improvement. At the same time, the growing ability of models to make autonomous decisions and execute complex actions naturally enables abstractions in which components of the model development process can be progressively automated. Together, these challenges and opportunities have driven increasing interest in self-improvement, where models autonomously generate data, evaluate outputs, and iteratively refine their own capabilities. In this paper, we present a system-level perspective on self-improving language models and introduce a unified framework that organizes existing techniques. We conceptualize the self-improvement system as a closed-loop lifecycle, consisting of four tightly coupled processes: data acquisition, data selection, model optimization, and inference refinement, along with an autonomous evaluation layer throughout the process. Within this framework, the model itself plays a central role in driving each stage: collecting or generating data, selecting informative signals, updating its parameters, and refining outputs, while the autonomous evaluation layer continuously monitors progress and guides the improvement cycle across stages. Following this lifecycle perspective, we systematically review and analyze representative methods for each component from a technical standpoint. We further examine current limitations, potential risks, and prominent applications, and outline our vision for future research toward fully self-improving LLMs.

Self-improvement training, where models learn from self-generated solutions, promises sustained capability gains but suffers from a pervasive failure mode: across multiple rounds, compounding reasoning errors cause accuracy to stall or degrade. We trace this drift to standard filtering criteria that retain solutions based solely on final answer correctness, which lets lucky guesses (correct answers with flawed reasoning) contaminate the training data. We propose Verified Self-Improvement (VSI), a framework that conditions data retention on step-level structural integrity rather than just the final output. VSI validates solutions by recomputing arithmetic steps via a computer-algebra library (sympy), checking intermediate consistency, and enforcing domain constraints. Evaluating VSI on GSM8K with Qwen3-4B-Thinking across 5 rounds of self-improvement against four baselines (no verification, outcome verification, majority voting, and VSI with DPO) shows that VSI rejects approximately 34% of correct-answer solutions, successfully isolating lucky guesses. This cleaner training signal drives sustained accuracy gains across all rounds (80.5% to 91.0%), whereas outcome verification plateaus and unverified training collapses. Finally, converting VSI checks into DPO preference pairs trains the model to distinguish sound reasoning from lucky answers, boosting reward accuracy from 46% to 63%. VSI offers a simple, reproducible recipe for robust self-improvement whenever automated reasoning checks are available.

Recent progress in multimodal large language models has led to strong performance on reasoning tasks, but these improvements largely rely on high-quality annotated data or teacher-model distillation, both of which are costly and difficult to scale. To address this, we propose an unsupervised self-evolution training framework for multimodal reasoning that achieves stable performance improvements without using human-annotated answers or external reward models. For each input, we sample multiple reasoning trajectories and jointly model their within group structure. We use the Actor's self-consistency signal as a training prior, and introduce a bounded Judge based modulation to continuously reweight trajectories of different quality. We further model the modulated scores as a group level distribution and convert absolute scores into relative advantages within each group, enabling more robust policy updates. Trained with Group Relative Policy Optimization (GRPO) on unlabeled data, our method consistently improves reasoning performance and generalization on five mathematical reasoning benchmarks, offering a scalable path toward self-evolving multimodal models. The code are available at https://github.com/OPPO-Mente-Lab/LLM-Self-Judge.

Label-free reinforcement learning enables large language models to improve reasoning capabilities without ground-truth supervision, typically by treating majority-voted answers as pseudo-labels. However, we identify a critical failure mode: as training maximizes self-consistency, output diversity collapses, causing the model to confidently reinforce systematic errors that evade detection. We term this the consensus trap. To escape it, we propose CoVerRL, a framework where a single model alternates between generator and verifier roles, with each capability bootstrapping the other. Majority voting provides noisy but informative supervision for training the verifier, while the improving verifier progressively filters self-consistent errors from pseudo-labels. This co-evolution creates a virtuous cycle that maintains high reward accuracy throughout training. Experiments across Qwen and Llama model families demonstrate that CoVerRL outperforms label-free baselines by 4.7-5.9% on mathematical reasoning benchmarks. Moreover, self-verification accuracy improves from around 55% to over 85%, confirming that both capabilities genuinely co-evolve.

Large language models (LLMs) are systematically overconfident: they routinely express high certainty on questions they often answer incorrectly. Existing calibration methods either require labeled validation data, degrade under distribution shifts, or incur substantial inference costs. Recent work has shown that LLMs already contain a better-calibrated signal than the one they verbalize: the token probability of "True" when the model is asked "Is this answer correct?" ($P(\text{True})$) consistently outperforms their stated confidence, a gap that is theoretically grounded as generative error is lower-bounded by roughly twice the corresponding discriminative error. We introduce $\textbf{SECL}$ ($\textbf{SE}$lf-$\textbf{C}$alibrating $\textbf{L}$anguage Models), a test-time training (TTT) pipeline that exploits this gap as label-free self-supervision, requiring no labeled data or human supervision. SECL adapts only when the input distribution shifts, training on just 6--26% of the question stream at lower cost than the baseline it distills from. Across four small language models from three model families and four diverse domains, SECL reduces Expected Calibration Error (ECE) by 56--78%, outperforming its own supervision signal and matching or outperforming recent inference-time methods. SECL is the first method to apply TTT to calibration; seven ablations covering signal quality, gating strategy, weight accumulation, loss design, domain ordering, hyperparameter sensitivity, and layer selection confirm that each component is crucial and robust across configurations. Code: https://anonymous.4open.science/r/secl-emnlp26-submission-C890

Modern language model-based AI systems are remarkably powerful, yet their capabilities remain fundamentally capped by their human creators in three key ways. First, although a model's weights can be updated via fine-tuning, acquiring new knowledge from small, specialized corpora after pretraining remains highly data-inefficient. Second, the training of these systems relies heavily on finite, human-generated data from across history. Third, the pipelines used to train AI models are confined by the algorithms that human researchers can discover and explore. This thesis takes a small step toward overcoming these inherent limitations, presenting three chapters aimed at breaking these dependencies to create continually self-improving AI. First, to overcome this data-efficiency barrier in knowledge acquisition, we propose a synthetic data approach that diversifies and amplifies small corpora into rich knowledge representations, enabling a model to effectively update its parameters from limited source material. Second, to reduce reliance on human data, we show that given a fixed amount of such data, the model can self-generate synthetic data to bootstrap its fundamental pretraining capabilities without distillation from any off-the-shelf, instruction-tuned LM. Finally, to transcend human-engineered training paradigms, we demonstrate that by scaling search during test time over the space of algorithms, AI can search over a larger space of learning algorithm configurations than human researchers can explore manually.

Current label-free RLVR approaches for large language models (LLMs), such as TTRL and Self-reward, have demonstrated effectiveness in improving the performance of LLMs on complex reasoning tasks. However, these methods rely heavily on accurate pseudo-label estimation and converge on spurious yet popular answers, thereby trapping in a dominant mode and limiting further improvements. Building on this, we propose Dual Consensus Reinforcement Learning (DCRL), a novel self-supervised training method which is capable of generating more reliable learning signals through a two-stage consensus mechanism. The model initially acts as an anchor, producing dominant responses; then it serves as an explorer, generating diverse auxiliary signals via a temporary unlearning process. The final training target is derived from the harmonic mean of these two signal sets. Notably, the process operates entirely without external models or supervision. Across eight benchmarks and diverse domains, DCRL consistently improves Pass@1 over majority vote while yielding more stable training dynamics. These results demonstrate that DCRL establishes a scalable path toward stronger reasoning without labels.

Reinforcement learning with verifiable rewards improves reasoning in large language models (LLMs), but many methods still rely on large human-labeled datasets. While self-play reduces this dependency, it often lacks explicit planning and strong quality control, limiting stability in long-horizon multi-step reasoning. We present SAGE (Self-evolving Agents for Generalized reasoning Evolution), a closed-loop framework where four agents: Challenger, Planner, Solver, and Critic, co-evolve from a shared LLM backbone using only a small seed set. The Challenger continuously generates increasingly difficult tasks; the Planner converts each task into a structured multi-step plan; and the Solver follows the plan to produce an answer, whose correctness is determined by external verifiers. The Critic scores and filters both generated questions and plans to prevent curriculum drift and maintain training signal quality, enabling stable self-training. Across mathematics and code-generation benchmarks, SAGE delivers consistent gains across model scales, improving the Qwen-2.5-7B model by 8.9% on LiveCodeBench and 10.7% on OlympiadBench.

Cyberbullying on social media is inherently multilingual and multi-faceted, where abusive behaviors often overlap across multiple categories. Existing methods are commonly limited by monolingual assumptions or single-task formulations, which restrict their effectiveness in realistic multilingual and multi-label scenarios. In this paper, we propose HMS-BERT, a hybrid multi-task self-training framework for multilingual and multi-label cyberbullying detection. Built upon a pretrained multilingual BERT backbone, HMS-BERT integrates contextual representations with handcrafted linguistic features and jointly optimizes a fine-grained multi-label abuse classification task and a three-class main classification task. To address labeled data scarcity in low-resource languages, an iterative self-training strategy with confidence-based pseudo-labeling is introduced to facilitate cross-lingual knowledge transfer. Experiments on four public datasets demonstrate that HMS-BERT achieves strong performance, attaining a macro F1-score of up to 0.9847 on the multi-label task and an accuracy of 0.6775 on the main classification task. Ablation studies further verify the effectiveness of the proposed components.

Large audio language models (ALMs) extend LLMs with auditory understanding. A common approach freezes the LLM and trains only an adapter on self-generated targets. However, this fails for reasoning LLMs (RLMs) whose built-in chain-of-thought traces expose the textual surrogate input, yielding unnatural responses. We propose self-rephrasing, converting self-generated responses into audio-understanding variants compatible with RLMs while preserving distributional alignment. We further fuse and compress multiple audio encoders for stronger representations. For training, we construct a 6M-instance multi-task corpus (2.5M unique prompts) spanning 19K hours of speech, music, and sound. Our 4B-parameter ALM outperforms similarly sized models and surpasses most larger ALMs on related audio-reasoning benchmarks, while preserving textual capabilities with a low training cost. Notably, we achieve the best open-source result on the MMAU-speech and MMSU benchmarks and rank third among all the models.

Medical Multimodal Large Language Models (MLLMs) have demonstrated remarkable capabilities across diverse healthcare tasks. However, current post-training strategies, such as supervised fine-tuning and reinforcement learning, heavily depend on substantial annotated data while overlooking the potential of unlabeled test data for model enhancement. This limitation becomes particularly pronounced in medical domains, where acquiring extensive labeled medical data is difficult due to the strict data sensitivity and annotation complexity. Moreover, leveraging test data poses challenges in generating reliable supervision signals from unlabeled samples and maintaining stable self-evolution. To address these limitations, we propose Med-Evo, the first self-evolution framework for medical MLLMs that utilizes label-free reinforcement learning to promote model performance without requiring additional labeled data. Our framework introduces two key innovations: $1)$ Feature-driven Pseudo Labeling (FPL) that identifies semantic centroids from all heterogeneous candidate responses to select pseudo labels in each rollout, and $2)$ Hard-Soft Reward (HSR) that combines exact match with token-level assessment and semantic similarity to provide hierarchical reward. Experiments on three medical VQA benchmarks and two base MLLMs show clear advantages of our approach over SOTA methods, with significant improvements of 10.43% accuracy and 4.68% recall on the SLAKE dataset using Qwen2.5-VL, showing the effectiveness of our method.

Safety alignment is critical for deploying large language models (LLMs) in real-world applications, yet most existing approaches rely on large human-annotated datasets and static red-teaming benchmarks that are costly, difficult to scale, and slow to adapt to evolving model behaviors. Moreover, overly conservative safety mechanisms can reduce model usefulness by rejecting sensitive but legitimate queries. We introduce Self-MOA (Self Multi-Objective Alignment), a fully automated framework for aligning small language models using weak supervision from automated evaluator models. Self-MOA operates as a closed loop that dynamically generates model-specific red team prompts, constructs preference data from model-generated responses, and aligns models via multi-objective preference optimization to jointly optimize for safety and helpfulness. Across multiple small language models and safety benchmarks, Self-MOA achieves a 12.41% improvement in safety while preserving helpfulness, using as little as 11 times less training data than human-supervised alignment baselines. These results demonstrate that adaptive, automated alignment can reduce the dependence on static, human-curated safety pipelines in resource-constrained settings.

Test-time adaptation offers a promising avenue for improving reasoning performance in large language models without additional supervision, but existing approaches often apply a uniform optimization objective across all inputs, leading to inefficient or unstable adaptation on heterogeneous reasoning problems. We propose DiSCTT, a difficulty-aware, consensus-guided self-curriculum framework that dynamically allocates test-time optimization strategies based on instance-level epistemic uncertainty estimated from agreement among sampled reasoning trajectories. Inputs with high consensus are consolidated via supervised fine-tuning using majority-agreed solutions as pseudo-labels, while low-consensus inputs are optimized via reinforcement learning with a consensus-regularized objective that encourages diversity under relevance constraints. Across a broad suite of mathematical and general reasoning benchmarks, DiSCTT consistently outperforms strong test-time adaptation baselines, achieving higher accuracy with reduced variance and substantially lower computation and wall-clock training times. These results demonstrate that explicitly accounting for instance difficulty and uncertainty enables more stable, efficient, and effective test-time adaptation for reasoning models.

Multimodal Large Language Models (MLLMs) have achieved notable success in enhancing translation performance by integrating multimodal information. However, existing research primarily focuses on image-guided methods, whose applicability is constrained by the scarcity of multilingual image-text pairs. The speech modality overcomes this limitation due to its natural alignment with text and the abundance of existing speech datasets, which enable scalable language coverage. In this paper, we propose a Speech-guided Machine Translation (SMT) framework that integrates speech and text as fused inputs into an MLLM to improve translation quality. To mitigate reliance on low-resource data, we introduce a Self-Evolution Mechanism. The core components of this framework include a text-to-speech model, responsible for generating synthetic speech, and an MLLM capable of classifying synthetic speech samples and iteratively optimizing itself using positive samples. Experimental results demonstrate that our framework surpasses all existing methods on the Multi30K multimodal machine translation benchmark, achieving new state-of-the-art results. Furthermore, on general machine translation datasets, particularly the FLORES-200, it achieves average state-of-the-art performance in 108 translation directions. Ablation studies on CoVoST-2 confirms that differences between synthetic and authentic speech have negligible impact on translation quality. The code and models are released at https://github.com/yxduir/LLM-SRT.

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

Can a language model improve reasoning by learning from its own imperfect responses, without rewards or teacher-provided solutions? We present Self-evolving Post-Training (SePT), a simple method that alternates temperature-controlled self-generation with next-token likelihood training. Each round uses the updated model to generate new training responses, with one response per prompt by default and no correctness filtering. Across six mathematical benchmarks, SePT improves a temperature-selected no-training baseline by 11.4 and 6.7 AVG points on Qwen2.5-Math-7B and Qwen2.5-7B, respectively, where AVG averages Pass@1, Pass@8 and Pass@32 across benchmarks. We analyze how sampling temperature shapes the learning signal and investigate the value of the resulting responses. Responses from a SePT-trained model improve a student initialized from the original weights, while their reasoning prefixes help an unchanged model complete solutions, even when matched in length to prefixes from a colder initial model. Comparing next-token predictions at identical contexts also reveals changes in token rankings that decoding-temperature adjustment cannot reproduce. Further evaluations across nine starting models, general reasoning and code generation examine broader applicability. Together, these results show that reward-free self-training can improve both a model's predictions and the supervision it provides. Our code is available at https://github.com/ElementQi/SePT.