LLM Training

Modern language-model training is increasingly exposed to instability, degraded runs, and wasted compute, especially under aggressive learning-rate, scale, and runtime-stress conditions. This paper introduces Learn-by-Wire Guard (LBW-Guard), a bounded autonomous training-control governance layer that operates above AdamW. Rather than replacing the optimizer update rule, LBW-Guard observes training telemetry, interprets instability-sensitive regimes, and applies bounded control to optimizer execution while preserving fixed training objectives. We evaluate LBW-Guard in a Qwen2.5-centered stress-and-robustness suite using WikiText-103, with Qwen2.5-7B as the empirical anchor, model-size comparisons against Qwen2.5-3B and Qwen2.5-14B, learning-rate stress tests, gradient-clipping baselines, and a no-LoRA TinyLlama-1B full-parameter sanity check. In the 7B reference setting, LBW-Guard reduces final perplexity from 13.21 to 10.74, an 18.7% improvement, while reducing end-to-end time from 392.54s to 357.02s, a 1.10x speedup. Under stronger learning-rate stress, AdamW degrades to 1885.24 final perplexity at LR=3e-3 and 659.76 at LR=1e-3, whereas LBW-Guard remains trainable at 11.57 and 10.33, respectively. Gradient-clipping baselines do not reproduce this effect. These results support a scoped systems conclusion that stability-sensitive LLM training can benefit from a governance plane above the optimizer. LBW-Guard provides evidence that bounded runtime control can preserve productive compute under stress while remaining distinct from optimizer replacement and local gradient suppression.

Large Language Model (LLM) training is frequently interrupted by a heterogeneous spectrum of failures, from common GPU crashes to catastrophic cluster-wide outages. Existing checkpointing systems rely on monolithic, single-tier storage backend, forcing a trade-off between state-saving overhead and recovery speed. We propose TierCheck, a cluster-aware tiered checkpointing system that aligns storage placement with failure heterogeneity. TierCheck adopts a three-tier design that maintains lightweight differential checkpoints in local and peer memory for fast localized recovery, while asynchronously migrating heavyweight base checkpoints to remote persistent storage. It also ensures strict global consistency across tiers without stalling training, and achieves fast cluster-aware checkpoint restoration during recovery. Evaluations on models up to 40 billion parameters show that TierCheck achieves low training overhead, reduces end-to-end checkpointing time to under 10s, and supports high-frequency checkpointing, ultimately striking an optimal balance between low-overhead persistence and fast recovery.

Deploying large-scale LLM training and inference with optimal performance is exceptionally challenging due to a complex design space of parallelism strategies, system optimizations, and hardware configurations. Accurate and rapid performance simulation is critical for guiding optimization efforts and system studies by validating "what-if" Hooker Figure hypotheses. To address this, we introduce Charon, a unified, modular, and fine-grained simulator for accurately predicting LLM performance. Experiments show Charon achieves high accuracy across different models and configurations, with an overall prediction error consistently under 5.35%, and even under 3.74% for training with a large-scale GPU cluster. In a practical inference deployment case, Charon discovered a configuration that improved system throughput over an engineering-tuned baseline, demonstrating its significant real-world value.

Clinical decision support systems (CDSS) require scrutable, auditable pipelines that enable rigorous, reproducible validation. Yet current LLM-based CDSS remain largely opaque. Most "open" models are open-weight only, releasing parameters while withholding the data provenance, curation procedures, and generation pipelines that determine model behavior. Fully Open (FO) models, which expose the complete training stack end-to-end, do not currently exist in medicine. We introduce Fully Open Meditron, the first fully open pipeline for building LLM-CDSS, comprising a clinician-audited training corpus, a reproducible data construction and training framework, and a use-aligned evaluation protocol. The corpus unifies eight public medical QA datasets into a normalized conversational format and expands coverage with three clinician-vetted synthetic extensions: exam-style QA, guideline-grounded QA derived from 46,469 clinical practice guidelines, and clinical vignettes. The pipeline enforces system-wide decontamination, gold-label resampling of teacher generations, and end-to-end validation by a four-physician panel. We evaluate using an LLM-as-a-judge protocol over expert-written clinical vignettes, calibrated against 204 human raters. We apply the recipe to five FO base models (Apertus-70B/8B-Instruct, OLMo-2-32B-SFT, EuroLLM-22B/9B-Instruct). All MeditronFO variants are preferred over their bases. Apertus-70B-MeditronFO improves +6.6 points over its base (47.2% to 53.8%) on aggregate medical benchmarks, establishing a new FO SoTA. Gemma-3-27B-MeditronFO is preferred over MedGemma in 58.6% of LLM-as-a-judge comparisons and outperforms it on HealthBench (58% vs 55.9%). These results show that fully open pipelines can achieve state-of-the-art domain-specific performance without sacrificing auditability or reproducibility.

Second-order methods offer an attractive path toward more sample-efficient LLM training, but their practical use is often blocked by the systems cost of maintaining and updating large matrix-based optimizer states. We introduce \textbf{Asteria}, a runtime system designed to remove this bottleneck by separating second-order optimization logic from the critical GPU training path. Rather than keeping all preconditioner state on the accelerator, Asteria dynamically distributes optimizer state across GPU memory, CPU memory, and optional NVMe storage according to architectural constraints and runtime pressure. It further uses training hooks to prepare shadow states in advance, allowing expensive inverse-root computations to proceed asynchronously on the host while GPU computation continues. For distributed training, Asteria employs a bounded-staleness protocol that limits synchronization frequency while preserving optimizer effectiveness through topology-aware coordination. We evaluate Asteria on both memory-constrained and distributed training settings. On a DGX Spark platform with a single GB10 GPU and 128GB unified memory, Asteria supports second-order training for a 1B-parameter language model. On multi-node GH200 systems, it lowers visible optimizer overhead, reduces recurring latency spikes, accelerates convergence in wall-clock time, and maintains the optimization advantages of SOAP and KL-Shampoo in a 7B-parameter language model. Our results suggest that second-order LLM training can be made practical not by simplifying the optimizer alone, but by rethinking how optimizer state, background computation, and distributed synchronization are managed at the runtime level.

Large language model (LLM) training today runs on clusters spanning thousands of GPUs. While this scale enables rapid model advances, developing, debugging, and performance-tuning the training framework inevitably becomes complex and costly. This is because engineers often need to reproduce production behaviors to diagnose failures or evaluate optimizations, thereby demanding frequent and even exclusive access to production-scale clusters -- which becomes increasingly hard given that the majority of GPUs are already committed to production workloads. Simulation relies on complex performance models that are difficult to maintain, and downscaled experiments often fail to capture scale-dependent behaviors. We present PrismLLM to decouple large-scale execution from the need to access large clusters, enabling engineers to run and observe ranks of interest under faithful large-scale behavior using only a few GPUs. PrismLLM constructs a high-fidelity execution graph via a slicing-based approach that captures computation, communication, and dependencies of the target scale. Then, PrismLLM performs hybrid emulation where selected ranks execute the original program while the remaining ranks are replayed as virtual participants. Experiments on large-scale LLM training workloads show that PrismLLM accurately reproduces performance and memory behavior, achieving only 0.58% average error in iteration time and less than 0.01% error in peak GPU memory usage. PrismLLM can emulate clusters of up to 8192 GPUs using fewer than 1% of the physical GPUs required by the original deployment.

Scaling LLMs requires tremendous computational resources, and recent advances in AI have gone hand in hand with massive amounts of capital expenditure. While it is established that scaling up LLMs reliably increases model quality (quantified in terms of loss or downstream evaluations), it is unclear how these quality improvements translate to potential revenue, and whether revenue increases would offset costs of larger-scale training and inference. In this work, we develop an economic model for characterizing the rational behavior of an LLM training firm by combining scaling laws with microeconomic theory. Under our model of firm behavior, LLM quality can be increased with more parameters and training tokens, leading to more potential adoption by consumers, who each have a quality threshold for using the LLM. On the other hand, additional parameters and training tokens both incur additional costs. We analyze the profit maximization problem for this model under compute-bound and data-bound regimes. In the compute-bound regime, optimal model size and token budget track hardware efficiency $E$ (FLOPs/$) at a near-linear rate; total training cost then scales sub-quadratically in $E$. Data efficiency improvements incentivize larger models and training expenditure. When we are limited to $D$ data, profit-optimal training expenditure scales as $D^2/E$, i.e, increase with data and decreases with hardware efficiency (as well as data efficiency). Finally, we analyze practical trends in training expenditure: current trends are consistent with our most permissive model variants in the compute-bound regime, but are not profit-optimal in the data-bound regime or assuming hardware advances will stall. Overall, our results provide a theory of profit-optimal LLM training, providing a foundation for engaging critically with industry statements and supporting long-term economic decision making.

Many real-world coding challenges are open-ended and admit no known optimal solution. Yet, recent progress in LLM coding has focused on well-defined tasks such as feature implementation, bug fixing, and competitive programming. Open-ended coding remains a weak spot for LLMs, largely because open-ended training problems are scarce and expensive to construct. Our goal is to synthesize open-ended coding problems at scale to train stronger LLM coders. We introduce FrontierSmith, an automated system for iteratively evolving open-ended problems from existing closed-ended coding tasks. Starting from competitive programming problems, FrontierSmith generates candidate open-ended variants by changing the problems'goals, restricting outputs, and generalizing inputs. It then uses a quantitative idea divergence metric to select problems that elicit genuinely diverse approaches from different solvers. Agents then generate test cases and verifiers for the surviving candidates. On two open-ended coding benchmarks, training on our synthesized data yields substantial gains over the base models: Qwen3.5-9B improves by +8.82 score on FrontierCS and +306.36 (Elo-rating-based performance) on ALE-bench; Qwen3.5-27B improves by +12.12 and +309.12, respectively. The synthesized problems also make agents take more turns and use more tokens, similar to human-curated ones, suggesting that closed-ended seeds can be a practical starting point for long-horizon coding data.

Data mixing decides how to combine different sources or types of data and is a consequential problem throughout language model training. In pretraining, data composition is a key determinant of model quality; in continual learning and adaptation, it governs what is retained and acquired. Yet existing data mixing methods address only one phase of this lifecycle at a time: some require smaller proxy models tied to a single training phase, others assume a fixed domain set, and continual learning lacks principled guidance altogether. We argue that data mixing is fundamentally an online decision making problem -- one that recurs throughout training and demands a single, unified solution. We introduce OP-Mix (On-Policy Mix), a data mixing algorithm that operates across the entire language model training lifecycle. Our main insight is that candidate data mixtures can be cheaply simulated by interpolating between low-rank adapters trained directly on the current model, eliminating separate proxy models and ensuring the search is always grounded in the model's actual learning dynamics. Across pretraining, continual midtraining, and continual instruction tuning, OP-Mix consistently finds near-optimal mixtures while using a fraction of the compute of the baselines. In pretraining, OP-Mix improves upon training without mixing by 6.3% in average perplexity. For continual learning, OP-Mix matches the performance of both retraining and on-policy distillation while using 66% and 95% less overall compute, respectively. OP-Mix suggests a different view of language model training: not a sequence of distinct phases, but a single continuous process of learning from data.

Longitudinal clinical notes contain rich evidence of how patients evolve over time, but converting this signal into training supervision for clinical prediction remains challenging. We extend Foresight Learning to clinical prediction by converting time-ordered MIMIC-III notes into examples consisting of past patient context, a natural-language question about a possible future event, and a label resolved from later documentation. This process yields 6,900 prediction examples from 702 admissions across medications, procedures, organ support, microbiology, and mortality. A small LoRA adapter trained on these examples improves over the prompted base model, reducing expected calibration error from 0.1269 to 0.0398 and Brier score from 0.199 to 0.145, while slightly outperforming GPT-5 point estimates on held-out questions. The approach enables reusable clinical prediction supervision from longitudinal notes without hand-engineered structured features or endpoint-specific classifiers.

Large language models (LLMs) are pretrained by minimizing the cross-entropy loss for next-token prediction. In this paper, we study whether this optimization strategy can induce geometric structure in the learned model weights and context embeddings. We approach this problem by analyzing a constrained layer-peeled optimization program, which serves as a mathematically tractable surrogate for LLMs by treating the output projection matrix and last-layer context embeddings as optimization variables. Our analysis of this nonconvex optimization program demonstrates that symmetries in the target next-token distributions are transferred to the global minimizers of the layer-peeled model in a precise group-theoretic sense. Specifically, we prove that when the target tokens exhibit a cyclic-shift symmetry (such as the seven days of the week or the twelve months of the year), the optimal logit matrix is exactly circulant, and the Gram matrices of both the output projections and the context embeddings form circulant geometries as well. Next, for exchangeable target distributions invariant under the symmetric group and, more generally, under two-transitive group actions, we show that the global optimal output projection matrix forms a simplex equiangular tight frame, while the optimal logit matrix and context embeddings inherit the permutation symmetries present in the input data. A key technical step is to reduce the constrained nonconvex factorized problem to an explicit logit-level convex characterization for cyclic symmetry and to a symmetry-based lower bound for permutation symmetry, together with a sharp characterization of the optimal factorization. Finally, we empirically demonstrate that open-source LLMs naturally exhibit symmetries consistent with our theoretical predictions, despite being trained without any explicit regularization promoting such geometric structure.

As language models scale, the amount of data they require grows -- yet many target data sources, such as low-resource languages or specialized domains, are inherently limited in size. A common strategy is to mix this scarce but valuable target data with abundant generic data, which presents a fundamental trade-off: too little target data in the mixture underexposes the model to the target domain, while too much target data repeats the same examples excessively, yielding diminishing returns and eventual overfitting. We study this trade-off across more than 2,000 language-model training runs spanning multiple model and target dataset sizes, as well as several data types, including multilingual, domain-specific, and quality-filtered mixtures. Across all settings, we find that repetition is a central driver of target-domain performance, and that mixture training tolerates much higher repetition than single-source training: scarce target corpora can be reused 15-20 times, with the optimal number of repetitions depending on the target data size, compute budget, and model scale. Next, we introduce a repetition-aware mixture scaling law that accounts for the decreasing value of repeated target tokens and the regularizing role of generic data. Optimizing the scaling law provides a principled way to compute effective mixture configurations, yielding practical mixture recommendations for pretraining under data constraints.

Emergent misalignment (EM), where fine-tuning on a narrow task (like insecure code) causes broad misalignment across unrelated domains, was first demonstrated by Betley et al. (2025). We conduct the most comprehensive EM study to date, reproducing the original GPT-4o finding and expanding to 12 open-source models across 4 families (Llama, Qwen, DeepSeek, GPT-OSS) ranging from 8B to 671B parameters, evaluating over one million model responses with multiple random seeds. We find that EM replicates in GPT-4o but is far from universal: only 2 of 12 open-source models (17%) exhibit consistent EM across seeds, with a significant correlation between model size and EM susceptibility. Through checkpoint-level analysis during fine-tuning, we demonstrate that EM emerges late in training, distinct from and subsequent to near convergence of the primary task, suggesting EM emerges from continued training past task convergence. This yields practical mitigations: early stopping eliminates EM while retaining an average of 93% of task performance, and careful learning rate selection further minimizes risk. Cross-domain validation on medical fine-tuning confirms these patterns generalize: the size-EM correlation strengthens (r = 0.90), and overgeneralization to untruthfulness remains avoidable via early stopping in 67% of cases, though semantically proximate training domains produce less separable misalignment. As LLMs become increasingly integrated into real-world systems, fine-tuning and reinforcement learning remain the primary methods for adapting model behavior. Our findings demonstrate that with proper training practices, EM can be avoided, reframing it from an unforeseen fine-tuning risk to an avoidable training artifact.

Modern large language model (LLM) training is inherently dynamic: resource fluctuations, RLHF phase shifts, and cluster elasticity continually reshape the optimal parallelism layout, posing a significant challenge to existing training frameworks built around a static execution model. We present DynaTrain, a distributed training system for sub-second, online reconfiguration across arbitrary multi-dimensional parallelism. At its core, we propose a Virtual Parameter Space (VPS) abstraction that unifies all distributed training states under one logical coordinate space, turning any parallelism configuration into a deterministic mapping and collapsing complex transition into manageable geometric intersections. On top of VPS, a state routing-and-transition layer executes rank-local transfers under a memory-aware, deadlock-free schedule, and an Elastic Device Manager overlaps new-world construction with ongoing training to mask topology-change cost. On dense and MoE models up to 235B parameters, DynaTrain reconfigures a 70B dense model in under 2s and a 235B MoE model in 4.36s, outperforming state-of-the-art checkpoint-based and elastic systems by up to three orders of magnitude while preserving correctness.

We present Hebatron, a Hebrew-specialized open-weight large language model built on the NVIDIA Nemotron-3 sparse Mixture-of-Experts architecture. Training employs a three-phase easy-to-hard curriculum with continuous anti-forgetting anchoring, followed by supervised fine-tuning on 2 million bilingual Hebrew--English samples. The curriculum ordering alone yields a 3-point aggregate benchmark gain over the reversed configuration. Hebatron achieves a Hebrew reasoning average of 73.8%, outperforming DictaLM-3.0-24B-Thinking (68.9%) and remaining competitive with Gemma-3-27B-IT on GSM8K-HE and Israeli Trivia, while activating only 3B parameters per forward pass across a 30B-parameter model, delivering approximately 9 times higher inference throughput at native context lengths up to 65,536 tokens. To our knowledge, this is the first language-specific adaptation of the Nemotron-3 architecture for any target language, and the first open-weight Hebrew-specialized MoE model with native long-context support. Model weights are released openly to support further research in Hebrew and Semitic-language NLP.

Data is fundamental to large language models (LLMs). However, understanding of what makes certain data useful for different stages of an LLM workflow, including training, tuning, alignment, in-context learning, etc., and why, remains an open question. Current approaches rely heavily on extensive experimentation with large public datasets to obtain empirical heuristics for data filtering and dataset construction. These approaches are compute intensive and lack a principled way of understanding the essence of how specific data characteristics drive LLM behavior. In this position paper, we advocate for the need of developing systematic methodologies for generating synthetic sequences from appropriately defined random processes, with the goal that these sequences can reveal useful characteristics when they are used in one or multiple stages of the LLM workflow. We refer to such sequences as data probes. By observing LLM behavior on data probes, researchers can systematically conduct studies on how data characteristics influence model performance, generalization, and robustness. The probing sequences exhibit statistical properties that can be viewed using theoretical concepts, such as typical sets, which are generalized to describe the behaviors of LLMs. This data-probe approach provides a pathway for uncovering foundational insights into the role of data in LLM training and inference, beyond empirical heuristics.

Psychological support hotlines provide critical support for individuals experiencing mental health emergencies, yet current assessments largely rely on human operators whose judgments may vary with professional experience and are constrained by limited staffing resources. This paper proposes a large language model (LLM)-based framework for automated crisis level classification, a key indicator that supports many downstream tasks and improves the overall quality of hotline services. To better capture emotional signals in spoken conversations, we introduce a paralinguistic injection method that inserts identified non-verbal emotional cues into speech transcripts, enabling LLM-based reasoning to incorporate critical acoustic nuances. In addition, we propose a reasoning-enhanced training strategy that trains the model to generate diagnostic reasoning chains as an auxiliary task, which serves as a regulariser to improve classification performance. Combined with data augmentation, our final system achieves a macro F1-score of 0.802 and an accuracy of 0.805 on the three-class classification task under 5-fold cross-validation.

Modern Large Foundation Model (LFM) training has transformed the data pipeline from a static ingestion layer into a dynamic component that must co-evolve with the training process. Existing systems are ill-equipped: colocated dataloaders offer no failure isolation, while message queue-based disaggregated dataloaders operate on a record/offset abstraction that cannot express the batch-level semantics required by distributed training. We present BatchWeave, an object-store-native training data plane for distributed LFM training. BatchWeave uses versioned manifests and conditional object writes to coordinate batch publication, recovery, and lifecycle management. First, it introduces the Transactional Global Batch (TGB), which builds on versioned-manifest ACID storage semantics and extends them with training-specific consistency, including atomic all-rank batch visibility, a globally ordered step sequence, checkpoint-aligned lifecycle management, and end-to-end exactly-once recovery. Second, it realizes recovery and retention directly in the storage layer, by durably persisting producer state through the commit protocol and tying reclamation to distributed checkpoint state. Third, its Decentralized Adaptive Commit (DAC) algorithm sustains stable ingestion throughput as the manifest grows, without any inter-producer communication. Evaluations on large-scale multimodal pre-training and SFT workloads using 64 GPUs show that BatchWeave outperforms colocated dataloader throughput while providing full failure isolation, outperforms Apache Kafka in ingestion throughput, and achieves lower consumer read latency than Kafka.

Large-scale AI training is fundamentally a distributed systems problem, where hardware failures are routine operating conditions rather than rare exceptions, yet public operational evidence from production training clusters remains limited. This report presents an empirical analysis of a 63-node NVIDIA B200 production cluster (504 GPUs), using 55 days of Prometheus time-series data and 73 days of operational logs covering 224 multi-node training sessions. The environment is cross-organizational: five parties (SKT, Upstage, Lablup, NVIDIA Korea, VAST Data) share a unified monitoring pipeline. This enabled joint diagnosis of a 60-node-scale storage I/O bottleneck absent in 2-4-node tests, a production-scale phenomenon no single team could isolate alone. We perform three quantitative analyses yielding four findings. First, over 751 Prometheus metrics and 10 XID-identified GPU failures, no single metric is consistently dominant across failure types, motivating multi-signal detection. Second, 523 checkpoint events trace the save/load path from GPU VRAM to the NFS server: restart loading reaches 21.5% of maximum read bandwidth (700 GB/s) and save bursts 16.0% of maximum write bandwidth (250 GB/s), with NFS/RPC queueing and transport-layer backlog rising together. Third, across 224 sessions over 73 days, node exclusions concentrate so the top 3 of 63 nodes account for over 50%. Fourth, auto-retry chain analysis shows a 33.3% success rate over 12 chains (73 attempts), 2.7x the 12.5% manual rate, with a median retry interval of 11 minutes (IQR 10-11). All analyses are grounded in production infrastructure providing session-level workload management, GPU-centric scheduling, and unified observability.

Training large language models requires optimization algorithms that are not only statistically effective, but also computationally and memory efficient at extreme scale. Although Adam remains the dominant optimizer for large-scale language-model pretraining and fine-tuning, recent work has revisited nearly every component of the optimization stack: adaptive moment estimation, decoupled weight decay, memory footprint, curvature approximation, sign-based updates, large-batch stability, low-rank gradient structure, and matrix-wise orthogonalized updates. This survey reviews optimizer design for large language models through a systems-and-optimization lens. We organize the literature into classical first-order optimizers, adaptive optimizers, memory-efficient variants, second-order and curvature-aware methods, sign-based and discovered optimizers, low-rank and projection-based methods, and matrix-based optimizers such as Muon. We also discuss benchmarking methodology, including hyperparameter fairness, scale dependence, wall-clock efficiency, token efficiency, memory overhead, and downstream evaluation. We argue that optimizer research for LLMs is entering a new phase: moving from single-algorithm speedup claims toward rigorous, scale-aware comparisons that jointly evaluate convergence, stability, memory, and implementation complexity.

We introduce a predictive model that estimates the pre-training loss of large models from model size (N), batch size (B) and number of weight updates (K). This is the first loss prediction model that can handle changing batch size. The model outperforms Chinchilla's loss model, a model of the test loss using the batch size and number of tokens, in terms of projecting the loss at extrapolated compute budgets (up to 1000 folds). A natural use of the model is to find optimal N, B, K configurations under explicit and compound resource constraints like time, memory and compute. In our experiments, the model-selected configurations are close to ground-truth optimal. Our work advocates for loss prediction as a better alternative to heuristic-based laws, which are growing in complexity. The implementation is available on https://github.com/chuningxdy/Noisy-Quadratic-System.

Mixture-of-Experts (MoE) language models organize knowledge into explicitly routed expert modules, making expert-level representations traceable and analyzable. By analyzing expert activation patterns in MoE large language models (LLMs), we find that a subset of experts is consistently activated across diverse knowledge domains. These common experts encode cross-domain, generalizable knowledge that is closely related to model generalization, naturally raising the question of how such identifiable expert knowledge can be practically reused. Motivated by this observation, we propose XPERT, a framework that extracts, consolidates, and reuses expert knowledge from pre-trained MoE LLMs to support more effective training of language models across different model scales. XPERT identifies cross-domain experts via inference-only analysis, refines their representations through tensor decomposition, and adapts the extracted knowledge to reuse in downstream models. Experiments on language understanding and dialogue generation benchmarks show that models benefiting from reused expert knowledge achieve consistently stronger performance and faster convergence compared to strong baselines. These results highlight MoE LLMs as structured and reusable knowledge sources, and demonstrate the value of expert-level knowledge reuse for improving model training.

The effectiveness of Reinforcement Learning (RL) in Large Language Models (LLMs) depends on the nature and diversity of the data used before and during RL. In particular, reasoning problems can often be approached in multiple ways that rely on different forms of reasoning, and exposure to only a limited range of such approaches in the training data may limit the effectiveness of RL. Motivated by this, we investigate using diverse self-generated data during mid-training as an intermediate step before RL training. Specifically, we adopt a bootstrapped data-generation framework guided by George Polya's problem-solving approaches for generating multiple variants of correct answers for each question in the training data, and then perform fine-tuning. We first provide a theoretical perspective on how mid-training on such data improves RL and explain how policy-gradient updates can incentivize combining multiple approaches. We then empirically demonstrate that RL-trained models initialized with our mid-training data achieve consistent improvements across various mathematical reasoning benchmarks and other OOD tasks like code generation and narrative reasoning. Overall, our investigative study shows that a language model learning multiple problem-solving approaches, through self-generated data helps subsequent RL.

Training foundation models is computationally intensive and often slow to converge. We introduce PIQL,Privileged Information for Quick and Quality Learning, the first framework to systematically integrate privileged information (PI) to simultaneously accelerate learning and improve generalization in tabular foundation models (TFMs). We construct two complementary forms of PI: (i) aggregate dataset-level statistics that reduce the burden on in-context learning, and (ii) encodings of the underlying data-generating program, providing knowledge beyond observable data. We further design an architecture that effectively transfers the train-time-only PI by learning to reconstruct it from observed context at inference. We provide a theoretical analysis characterizing conditions under which PI reduces the population-level approximation gap and accelerates convergence in finite-data regimes. Empirical evidence shows that PIQL enables TFMs to achieve faster convergence, lower final loss, and better generalization, in effect, reducing data and compute requirements. Our work establishes PI-guided pretraining as a principled and practical paradigm for improving the efficiency and performance of foundation models.

Features in language models have life history: they emerge, persist, and die during training, yet the importance of that history remains largely unexplored. We find evidence of a persistent representational backbone, which we identify in Pythia-160M and -410M as the carrier scaffold: ${\sim}50$ sparse features with stable life histories, around which the model's representational structure organises. It has four properties. \emph{(i)}\emph{It assembles early:} features emerge, die, and reorganise ${\sim}40\!\times$ faster in the first $1\%$ of training than afterwards, and the scaffold is already largely fixed by then. \emph{(ii)}\emph{It is load-bearing:} joint cross-layer ablation identifies the carriers as far more load-bearing than any count-matched non-scaffold population, a gap invisible to per-firing single-feature methods. \emph{(iii)}\emph{Function precedes direction:} which features will become carriers is already predictable from training-onset firing patterns alone, correctly distinguishing future carriers from non-carriers in $4$ of $5$ cases, before the geometry has settled. \emph{(iv)}\emph{It seeds subsequent development:} by the end of training, scaffold carriers have recruited $64\%$ of all active features into the scaffold hierarchy. Life history is consistent with a two-phase account of training: selection appears to largely determine the scaffold in the first $1\%$; the remaining $99\%$ appears to calibrate geometry around a substrate already set.

Training large language models at 4-bit precision is critical for efficiency. We show that nGPT, an architecture that constrains weights and hidden representations to the unit hypersphere, is inherently more robust to low-precision arithmetic. This removes the need for interventions-such as applying random Hadamard transforms and performing per-tensor scaling calculations-to preserve model quality, and it enables stable end-to-end NVFP4 training. We validate this approach on both a 1.2B dense model and hybrid (Mamba-Transformer) MoE models of up to 3B/30B parameters. We trace this robustness to the dot product: while quantization noise remains largely uncorrelated in both standard and normalized architectures, the signal behaves differently. In nGPT, the hypersphere constraint enhances weak positive correlations among the element-wise products, leading to a constructive accumulation of the signal across the hidden dimension while the noise continues to average out. This yields a higher effective signal-to-noise ratio and a flatter loss landscape, with the effect strengthening as the hidden dimension grows, suggesting increasing advantages at scale. A reference implementation is available at https://github.com/anonymous452026/ngpt-nvfp4

Training loss and throughput can hide distinct internal representation in language-model training. To examine these hidden mechanics, we use spectral measurements as practical and operational diagnostics. Using a controlled family of decoder-only models adapted from the modded NanoGPT codebase, we introduce an empirical protocol based on activation covariance and per-sample gradient SVD spectra. This dual-view reveals three empirical findings and one mechanistic explanation. First, batch size acts as a latent determinant of representation geometry: runs that reach equal loss settle into systematically distinct activation spectra. Second, the activation covariance tail measured early in training reliably forecasts downstream token efficiency. Third, movement of the activation spectrum head (leading modes), together with gradient spectra, characterizes underlying learning-dynamics changes, separating learning-side architectural improvements from primarily execution-side gains. These predictive and diagnostic signals persist across the 12-, 36-, and 48-layer model tiers. Finally, a mechanistic model proves the main observations and explains how activation covariance spectra correlate with task-aligned feature learning.

Large Language Models (LLMs) excel at generating contextually appropriate responses but remain poorly calibrated for multi-party conversations, where deciding when to speak is as critical as what to say. In such settings, naively responding at every turn leads to excessive interruptions and degraded conversational coherence. We introduce When2Speak, a grounded synthetic dataset and four-stage generation pipeline for learning intervention timing in group interactions. The dataset comprises over 215,000 examples derived from 16,000 conversations involving 2-6 speakers, spanning diverse conversational styles, tones, and participant dynamics, and explicitly modeling SPEAK vs. SILENT decisions at each turn. Our pipeline combines real-world grounding, structured augmentation, controlled transcript synthesis, and fine-tuning-ready supervision, and is fully open-sourced to support reproducibility and adaptation to domain-specific conversational norms. Across multiple model families, supervised fine-tuning (SFT) on When2Speak significantly outperforms zero-shot baselines (e.g., the average Macro F1 increase across 4B+ parameter models was 60%, with the largest increase being 120%). However, SFT-trained models remain systematically over-conservative, missing nearly half of warranted interventions as seen through the Missed Intervention Rate (MIR), which was on average 0.50 and is noticed even at larger model sizes. To address this limitation, we apply reinforcement learning with asymmetric reward shaping, which reduces MIR to 0.186-0.218 and increases recall from 0.479 to 0.78-0.81. Our findings establish that temporal participation is a distinct and trainable dimension of conversational intelligence, and that grounded synthetic data provides an effective and scalable pathway for enabling LLMs to participate more naturally and appropriately in multi-party interactions.

Large language models (LLMs) are rapidly being adopted across various domains. However, their adoption in banking industry faces resistance due to demands for high accuracy, regulatory compliance, and the need for verifiable and grounded responses. We present a unified, data-efficient framework for training grounded domain-specific LLMs that optimizes answer quality, citation grounding, and calibrated refusal under real-world deployment constraints. First, we describe a data generation pipeline that combines LLM-as-a-Judge filtering, citation annotation, and curriculum learning with only 143M tokens. The resulting 12B model achieves high answer quality outperforming GPT-4.1 on citation grounding, with a modest citation tradeoff versus the untuned base. Second, we propose a calibrated refusal mechanism: training on 22% unanswerable examples yield a 12% "I don't know" rate, substantially improving over the base model's unsafe 4.3% rate while avoiding GPT-4.1's over-refusal (20.2%). Third, we present an end-to-end methodology spanning from data curation to quantized serving. The system is deployed at 40+ financial institutions, achieving a 7.1 percentage point improvement in query resolution (p < 0.001). Additionally, the model delivers 3-5x faster responses at 20-50x lower cost compared to GPT-4.1.

We introduce a simple yet powerful framework for training large language models. In contrast to the standard autoregressive next-token prediction based on an exact prefix, we propose a perturbation-based procedure that first transforms the prefix into a semantic neighbor and then conditions on this perturbed variant for next-token prediction. This yields a hierarchical model with a pre-post-additive noise structure. Within this framework, we develop a rigorous theory of extrapolability, namely, the capacity of a model class to make reliable predictions for token sequences that lie outside the empirical support of the training corpus. We evaluate the finite-sample performance of the proposed procedure using both synthetic and real-world language data. Results show that the proposed method consistently improves out-of-support prediction while maintaining competitive in-support performance, demonstrating that perturbation offers a practical route to language modeling.