LLM Training

Sign-based optimization algorithms, such as SignSGD, have garnered significant attention for their remarkable performance in distributed learning and training large foundation models. Despite their empirical superiority, SignSGD is known to diverge on non-smooth objectives, which are ubiquitous in modern machine learning due to ReLUs, max-pools, and mixture-of-experts. To overcome this fundamental limitation, we propose StoSignSGD, an algorithm that injects structural stochasticity into the sign operator while maintaining an unbiased update step. In the regime of (online) convex optimization, our theoretical analysis shows that StoSignSGD rigorously resolves the non-convergence issues of SignSGD, achieving a sharp convergence rate matching the lower bound. For the more challenging non-convex non-smooth optimization, we introduce generalized stationary measures that encompass prior definitions, proving that StoSignSGD improves upon the best-known complexity bounds by dimensional factors. Empirically, StoSignSGD exhibits robust stability and superior efficiency across diverse large language model (LLM) training regimes. Notably, in low-precision FP8 pretraining -- a setting where AdamW fails catastrophically -- StoSignSGD remains highly stable and yields a remarkable 1.44$\times$ to 2.14$\times$ speedup relative to established baselines. Furthermore, when fine-tuning 7B LLMs on mathematical reasoning tasks, StoSignSGD delivers substantial performance gains over both AdamW and SignSGD. Finally, to dissect the mechanisms driving its success, we develop a sign conversion framework capable of transforming any general optimizer into its unbiased, sign-based counterpart. Utilizing this framework, we deconstruct the core components of StoSignSGD and present a comprehensive ablation study to empirically validate our algorithmic design choices.

Large Language Models (LLMs) exhibit strong mathematical reasoning when trained on high-quality Chain-of-Thought (CoT) that articulates intermediate steps, yet costly CoT curation hinders further progress. While existing remedies such as distillation from stronger LLMs and self-synthesis based on test-time search alleviate this issue, they often suffer from diminishing returns or high computing overhead.In this work, we propose CoTEvol, a genetic evolutionary framework that casts CoT generation as a population-based search over reasoning trajectories.Candidate trajectories are iteratively evolved through reflective global crossover at the trajectory level and local mutation guided by uncertainty at the step level, enabling holistic recombination and fine-grained refinement. Lightweight, task-aware fitness functions are designed to guide the evolutionary process toward accurate and diverse reasoning. Empirically, CoTEvol improves correct-CoT synthesis success by over 30% and enhances structural diversity, with markedly improved efficiency. LLMs trained on these evolutionary CoT data achieve an average gain of 6.6% across eight math benchmarks, outperforming previous distillation and self-synthesis approaches. These results underscore the promise of evolutionary CoT synthesis as a scalable and effective method for mathematical reasoning tasks.

Supervised fine-tuning (SFT) is a common first stage of LLM post-training, teaching the model to follow instructions and shaping its behavior as a helpful assistant. At the same time, SFT may harm the fundamental capabilities of an LLM, particularly after long pretraining: a phenomenon known as catastrophic overtraining (Springer et al., 2025). To understand overtraining, we first investigate catastrophic forgetting in finetuning through the lens of implicit regularization of the learning rate. For models trained to the same SFT loss, we identify how the learning rate mediates optimization: finetuning with large and small steps converges to qualitatively different models. Next, we link forgetting to overtraining: learning rate decay increases the sharpness of the pretrained model, which in turn exacerbates catastrophic forgetting during SFT, leading to overtraining. Our findings paint a picture of the overtraining mechanism in LLMs and broadly contribute to the understanding of the interplay between optimization dynamics during pretraining and finetuning.

Supervised Fine-Tuning (SFT) is the standard approach for adapting large language models (LLMs) to downstream tasks. However, we observe a persistent failure mode: even after convergence, models often fail to correctly reproduce a subset of their own supervised training data. We refer to this behavior as the Incomplete Learning Phenomenon(ILP). This paper presents the first systematic study of ILP in LLM fine-tuning. We formalize ILP as post-training failure to internalize supervised instances and demonstrate its prevalence across multiple model families, domains, and datasets. Through controlled analyses, we identify five recurrent sources of incomplete learning: (1) missing prerequisite knowledge in the pre-trained model, (2) conflicts between SFT supervision and pre-training knowledge, (3) internal inconsistencies within SFT data, (4) left-side forgetting during sequential fine-tuning, and (5) insufficient optimization for rare or complex patterns. We introduce a diagnostic-first framework that maps unlearned samples to these causes using observable training and inference signals, and study several targeted mitigation strategies as causal interventions. Experiments on Qwen, LLaMA, and OLMo2 show that incomplete learning is widespread and heterogeneous, and that improvements in aggregate metrics can mask persistent unlearned subsets. The findings highlight the need for fine-grained diagnosis of what supervised fine-tuning fails to learn, and why.

Training large foundation models at low numerical precision is one of the most promising directions for reducing the compute and memory cost of modern AI. Recent 4-bit floating-point formats such as MXFP4 and NVFP4 can be applied to linear GEMM operations in LLMs, but their limited dynamic range introduces numerical instability that prior work addresses by stacking stabilization mechanisms, typically executed at higher precision and partially eroding the efficiency gains that motivate FP4. In this work, we argue that numerical format design is itself a first-class lever for stable FP4 training, and present the first systematic study of FP4 LLM pretraining on energy-efficient Huawei Ascend NPUs. We compare the recently proposed HiFloat4 (HiF4) format against both MXFP4 and NVFP4, holding one recipe fixed across all three formats across dense (OpenPangu-1B, Llama3-8B) and Mixture-of-Experts (Qwen3-MoE-30B) architectures and executing all linear and expert GEMMs in FP4. At matched storage --- NVFP4 and HiF4 both spend 4.5 bits per value --- the three formats differ far more in what they require before they will train at all than in final accuracy. HiF4 reaches a relative loss of 1.55% with no stabilization, below fully stabilized MXFP4 (1.79%) and below NVFP4 carrying the per-tensor scaling it cannot train without (2.00%); NVFP4 diverges under every combination of stochastic rounding and Hadamard transform we tried. Our results suggest that stable, accurate FP4 training does not require an ever-growing stack of stabilization techniques; it requires the right numerical format.

Since their introduction, Transformer architectures have dominated Natural Language Processing (NLP). However, recent research has highlighted an inherent anisotropy phenomenon in these models, presenting a significant challenge to their geometric interpretation. Previous theoretical studies on this phenomenon are rarely grounded in the underlying representation geometry. In this paper, we extend them by deriving geometric arguments for how frequency-biased sampling attenuates curvature visibility and why training preferentially amplify tangent directions. Empirically, we then use concept-based mechanistic interpretability during training, rather than only post hoc, to fit activation-derived low-rank tangent proxies and test them against ordinary backpropagated true gradients. Across encoder-style and decoder-style language models, we find that these activation-derived directions capture both unusually large gradient energy and a substantially larger share of gradient anisotropy than matched-rank normal controls, providing strong empirical support for a tangent-aligned account of anisotropy.

Large language models (LLMs) can struggle to memorize factual knowledge in their parameters, often leading to hallucinations and poor performance on knowledge-intensive tasks. In this paper, we formalize fact memorization from an information-theoretic perspective and study how training data distributions affect fact accuracy. We show that fact accuracy is suboptimal (below the capacity limit) whenever the amount of information contained in the training data facts exceeds model capacity. This is further exacerbated when the fact frequency distribution is skewed (e.g. a power law). We propose data selection schemes based on the training loss alone that aim to limit the number of facts in the training data and flatten their frequency distribution. On semi-synthetic datasets containing high-entropy facts, our selection method effectively boosts fact accuracy to the capacity limit. When pretraining language models from scratch on an annotated Wikipedia corpus, our selection method enables a GPT2-Small model (110m parameters) to memorize 1.3X more entity facts compared to standard training, matching the performance of a 10X larger model (1.3B parameters) pretrained on the full dataset.

Large Language Models (LLMs) have demonstrated remarkable capabilities in natural language understanding and generation. However, their immense number of parameters and complex transformer-based architectures result in significant resource demands and computational complexity during training, making it challenging to optimize them efficiently on large datasets. To reduce training costs while preserving performance, researchers have investigated coreset selection techniques, which aim to identify small, representative subsets of the entire training dataset to accelerate LLM training. However, existing coreset selection methods fail to adapt to the dynamic nature of LLM training and often struggle with scalability for models of this size. To address these limitations, we propose a graph-guided adaptive and dynamic coreset selection framework for LLMs, namely GRACE. GRACE dynamically constructs and updates coresets by combining representation diversity with gradient-based importance metrics, ensuring both informativeness and efficiency. To mitigate the computational cost of frequent updates, GRACE leverages a $k$-NN graph-based propagation mechanism and selectively updates scores and embeddings, adapting to evolving training dynamics. Extensive experiments on three benchmarks demonstrate that GRACE significantly improves training efficiency and downstream performance across diverse LLMs and tasks.

Data mixing strategy is essential for large language model (LLM) training. Empirical evidence shows that inappropriate strategies can significantly reduce generalization. Although recent methods have improved empirical performance, several fundamental questions remain open: what constitutes a domain, whether human and model perceptions of domains are aligned, and how domain weighting influences generalization. We address these questions by establishing formal connections between gradient dynamics and domain distributions, offering a theoretical framework that clarifies the role of domains in training dynamics. Building on this analysis, we introduce DoGraph, a reweighting framework that formulates data scheduling as a graph-constrained optimization problem. Extensive experiments on GPT-2 models of varying scales demonstrate that DoGraph consistently achieves competitive performance.

Quantization is an effective way to reduce the memory cost of large-scale model training. However, most existing methods adopt fixed-precision policies, which ignore the fact that optimizer-state distributions vary significantly across layers and training steps. Such uniform designs often introduce noticeable accuracy degradation. To move beyond fixed quantization, we propose STQuant, a distributed training framework that reduces the memory footprint of optimizer states via dynamic precision allocation across layers, state variables, and training steps, while maintaining model quality. Naively applying dynamic quantization during training is challenging for two reasons. First, optimizer states are numerically sensitive, and quantization noise can destabilize quality. Second, jointly considering multiple states and layers induces a large combinatorial search space. STQuant addresses these challenges with two key techniques: 1) a provably near-optimal factor selection strategy that accurately identifies the most influential factors for precision adaptation. 2) a dynamic transition decision algorithm that reduces the search cost from exponential to linear complexity. Experiments on GPT-2 and ViT show that STQuant reduces optimizer-state memory by 84.4%, achieving an average bit-width of as low as 5.1 bits, compared with existing solutions. Moreover, STQuant incurs only O(N/K) computational overhead and requires O(1) extra space.

In modern LLMs, linguistic features function not as stylistic artifacts but as probes of probability mass, allocated under training alignment objectives. Language models trained with contemporary pipelines exhibit severe reshaping of linguistic features, leading to extreme language re-distribution. While previous stylometric analyses explored linguistic differences between AI-generated and human texts, we focus on the reshaping plaguing the LLM training pipeline itself. We analyze 17 models (410M-100B+ parameters) across 24 linguistically-motivated probes, documenting that instruction-tuned systems systematically collapse language entropy along discourse and structural dimensions (mean amplification: 1,949-16,853%, peaks: 5,181-209,675%), while selectively suppressing complex punctuation to 3.2-23.2% of baseline frequencies. These effects do not worsen under RLHF, as divergence patterns are statistically indistinguishable (p > 0.25) across matched base and instruction-tuned model pairs. Weak intervention (lambda=1.0) exacerbates collapse by 240%, while strong control (lambda=5.0) achieves 40.5% improvement and outperforms frontier models by 96.7-98.2% despite 200-1000x scale disadvantage. Additionally, lambda=5.0 delivers 15% higher distinct-4, 27% higher vocabulary diversity, and 78% lower repetition than moderate regularization, establishing that alignment requires sufficient control strength, not merely distributional smoothing. Our findings underscore how modern LLMs reallocate stylistic probability mass, despite RLHF and scale. More broadly, our work reveals a structural limitation of current alignment pipelines: preference optimization reshapes language distributions invisible to standard quality metrics yet detectable through distributional probes, with implications for AI detection, training data contamination, and long-term linguistic evolution.

We present MegaTrain, a memory-centric system that efficiently trains 100B+ parameter large language models at full precision on a single GPU. Unlike traditional GPU-centric systems, MegaTrain stores parameters and optimizer states in host memory (CPU memory) and treats GPUs as transient compute engines. For each layer, we stream parameters in and compute gradients out, minimizing persistent device state. To battle the CPU-GPU bandwidth bottleneck, we adopt two key optimizations. 1) We introduce a pipelined double-buffered execution engine that overlaps parameter prefetching, computation, and gradient offloading across multiple CUDA streams, enabling continuous GPU execution. 2) We replace persistent autograd graphs with stateless layer templates, binding weights dynamically as they stream in, eliminating persistent graph metadata while providing flexibility in scheduling. On a single H200 GPU with 1.5TB host memory, MegaTrain reliably trains models up to 120B parameters. It also achieves 1.84$\times$ the training throughput of DeepSpeed ZeRO-3 with CPU offloading when training 14B models. MegaTrain also enables 7B model training with 512k token context on a single GH200.

This paper presents an open source methodology for allowing users to query structured non textual datasets through natural language Unlike Retrieval Augmented Generation RAG which struggles with numerical and highly structured information our approach trains an LLM to generate executable queries To support this capability we introduce a principled pipeline for synthetic training data generation producing diverse question answer pairs that capture both user intent and the semantics of the underlying dataset We fine tune a compact model DeepSeek R1 Distill 8B using QLoRA with 4 bit quantization making the system suitable for deployment on commodity hardware We evaluate our approach on a dataset describing accessibility to essential services across Durangaldea Spain The fine tuned model achieves high accuracy across monolingual multilingual and unseen location scenarios demonstrating both robust generalization and reliable query generation Our results highlight that small domain specific models can achieve high precision for this task without relying on large proprietary LLMs making this methodology suitable for resource constrained environments and adaptable to broader multi dataset systems We evaluate our approach on a dataset describing accessibility to essential services across Durangaldea Spain The fine tuned model achieves high accuracy across monolingual multilingual and unseen location scenarios demonstrating both robust generalization and reliable query generation Our results highlight that small domain specific models can achieve high precision for this task without relying on large proprietary LLMs making this methodology suitable for resource constrained environments and adaptable to broader multi dataset systems.

While textual frequency has been validated as relevant to human cognition in reading speed, its relatedness to Large Language Models (LLMs) is seldom studied. We propose a novel research direction in terms of textual data frequency, which is an understudied topic, to the best of our knowledge. Our framework is composed of three units. First, this paper proposes Textual Frequency Law (TFL), which indicates that frequent textual data should be preferred for LLMs for both prompting and fine-tuning. Since many LLMs are closed-source in their training data, we propose using online resources to estimate the sentence-level frequency. We then utilize an input paraphraser to paraphrase the input into a more frequent textual expression. Next, we propose Textual Frequency Distillation (TFD) by querying LLMs to conduct story completion by further extending the sentences in the datasets, and the resulting corpora are used to adjust the initial estimation. Finally, we propose Curriculum Textual Frequency Training (CTFT) that fine-tunes LLMs in an increasing order of sentence-level frequency. Experiments are conducted on our curated dataset Textual Frequency Paired Dataset (TFPD) on math reasoning, machine translation, commonsense reasoning and agentic tool calling. Results show the effectiveness of our framework.

Modern LLMs scale at test-time, e.g. via repeated sampling, where inference cost grows with model size and the number of samples. This creates a trade-off that pretraining scaling laws, such as Chinchilla, do not address. We present Train-to-Test ($T^2$) scaling laws that jointly optimize model size, training tokens, and number of inference samples under fixed end-to-end budgets. $T^2$ modernizes pretraining scaling laws with pass@$k$ modeling used for test-time scaling, then jointly optimizes pretraining and test-time decisions. Forecasts from $T^2$ are robust over distinct modeling approaches: measuring joint scaling effect on the task loss and modeling impact on task accuracy. Across eight downstream tasks, we find that when accounting for inference cost, optimal pretraining decisions shift radically into the overtraining regime, well-outside of the range of standard pretraining scaling suites. We validate our results by pretraining heavily overtrained models in the optimal region that $T^2$ scaling forecasts, confirming their substantially stronger performance compared to pretraining scaling alone. Finally, as frontier LLMs are post-trained, we show that our findings survive the post-training stage, making $T^2$ scaling meaningful in modern deployments.

Large language models often achieve strong benchmark gains without corresponding improvements in broader capability. We hypothesize that this discrepancy arises from differences in training regimes induced by data distribution. To investigate this, we design controlled data interventions that isolate distributional effects under fixed training settings. We find that benchmark-aligned data improves narrow evaluation metrics while limiting broader representational development, whereas coverage-expanding data leads to more distributed parameter adaptation and better generalization. We further introduce parameter-space diagnostics based on spectral and rank analyses, which reveal distinct structural signatures of these regimes. Similar patterns are observed across diverse open-source model families, including multimodal models as a key case study, suggesting that these effects extend beyond controlled settings. A case study on prompt repetition shows that not all data artifacts induce regime shifts. These results indicate that benchmark performance alone is insufficient to characterize model capability, and highlight the importance of data distribution in shaping learning dynamics.

Pretraining Large Language Models (LLMs) from scratch requires massive amount of compute. Aurora super computer is an ExaScale machine with 127,488 Intel PVC (Ponte Vechio) GPU tiles. In this work, we showcase LLM pretraining on Aurora at the scale of 1000s of GPU tiles. Towards this effort, we developed Optimus, an inhouse training library with support for standard large model training techniques. Using Optimus, we first pretrained Mula-1B, a 1 Billion dense model and Mula-7B-A1B, a 7 Billion Mixture of Experts (MoE) model from scratch on 3072 GPU tiles for the full 4 trillion tokens of the OLMoE-mix-0924 dataset. We then demonstrated model scaling by pretraining three large MoE models Mula-20B-A2B, Mula-100B-A7B, and Mula-220B-A10B till 100 Billion tokens on the same dataset. On our largest model Mula-220B-A10B, we pushed the compute scaling from 384 to 12288 GPU tiles and observed scaling efficiency of around 90% at 12288 GPU tiles. We significantly improved the runtime performance of MoE models using custom GPU kernels for expert computation, and a novel EP-Aware sharded optimizer resulting in training speedups up to 1.71x. As part of the Optimus library, we also developed a robust set of reliability and fault tolerant features to improve training stability and continuity at scale.

The memory wall remains the primary bottleneck for training large language models on consumer hardware. We introduce Spectral Compact Training (SCT), a method that replaces dense weight matrices with permanent truncated SVD factors W = U diag(s) V^T, where the full dense matrix is never materialized during training or inference. Gradients flow through the compact spectral factors via standard backpropagation, and U, V are retracted to the Stiefel manifold via QR decomposition after each optimizer step. SCT achieves up to 199x memory reduction per MLP layer at rank 32, enabling full training steps of 70B-parameter architectures on a Steam Deck handheld (7.2 GB peak memory vs. 1,245 GB for dense FP32 training with Adam). Rank-sweep experiments on SmolLM2-1.7B (ranks 32-256, 2000 steps, NVIDIA A100) show that all tested ranks converge to the same loss floor (~4.2-4.5), identifying the learning rate schedule -- not MLP rank -- as the primary bottleneck. Rank 128 emerges as the efficiency sweet spot at 11.7x MLP compression with the lowest perplexity. GPU memory drops 46% at rank 32 while training throughput doubles.

As Large Language Models (LLMs) scale in size and complexity, the consequences of failures during training become increasingly severe. A major challenge arises from Silent Data Corruption (SDC): hardware-induced faults that bypass system-level detection mechanisms. SDC may behave like benign numerical noise, but can also cause harmful gradient corruption that leads to loss spikes, divergence, or stalled progress. This work provides a controlled study of how intermittent SDC affects LLM pretraining. Using targeted fault injection at the level of GPU matrix-multiply instructions, we characterize the sensitivity of different bit positions, kernel functions, and execution stages. Our analysis shows that locally originating faults can produce impactful corruption, including NaN propagation, short-lived spikes in loss, gradient norm, and attention logits, as well as persistent parameter divergence. Building on the observed corruption signatures, we propose a lightweight detection method that identifies potentially harmful parameter updates. Experiments on LLaMA models with 60M, 350M, and 1.3B parameters demonstrate that recomputing the most recent training step upon detection can effectively mitigate the impact of these events.

Using a statistical mechanics framework, we investigate the parameter space of transformer models trained on protein sequence data. We sample the loss landscape at varying temperatures using Langevin dynamics to characterize the low-loss manifold, and to understand the mechanisms underlying transformers' superior performance in protein structure prediction. We find that, at variance with networks not based on the attention mechanism, the lack of a first--order--like transition in the loss of the transformer produces a range of intermediate temperatures with good learning properties; this is true both for synthetic and natural protein sequences. We also show that the parameters of most layers are highly conserved at these temperatures if the dimension of the embedding is optimal, and we provide an operative way to find this dimension. Additionally, we show that the attention matrix is more predictive of the contact maps of the protein at higher temperatures and for higher dimensions of the embedding than those optimal for learning. Finally, we showed that the models sampled at intermediate temperatures can predict the free-energy variation upon mutation, better than models obtained through standard optimization techniques.

The foundational pretraining phase determines a model's capability ceiling, as post-training struggles to overcome capability foundations established during pretraining, yet it remains critically under-explored. This stems from a structural paradox: organizations with computational resources operate under commercial pressures that inhibit transparent disclosure, while academic institutions possess research freedom but lack pretraining-scale computational resources. daVinci-LLM occupies this unexplored intersection, combining industrial-scale resources with full research freedom to advance the science of pretraining. We adopt a fully-open paradigm that treats openness as scientific methodology, releasing complete data processing pipelines, full training processes, and systematic exploration results. Recognizing that the field lacks systematic methodology for data processing, we employ the Data Darwinism framework, a principled L0-L9 taxonomy from filtering to synthesis. We train a 3B-parameter model from random initialization across 8T tokens using a two-stage adaptive curriculum that progressively shifts from foundational capabilities to reasoning-intensive enhancement. Through 200+ controlled ablations, we establish that: processing depth systematically enhances capabilities, establishing it as a critical dimension alongside volume scaling; different domains exhibit distinct saturation dynamics, necessitating adaptive strategies from proportion adjustments to format shifts; compositional balance enables targeted intensification while preventing performance collapse; how evaluation protocol choices shape our understanding of pretraining progress. By releasing the complete exploration process, we enable the community to build upon our findings and systematic methodologies to form accumulative scientific knowledge in pretraining.

Large language models produce em dashes at varying rates, and the observation that some models "overuse" them has become one of the most widely discussed markers of AI-generated text. Yet no mechanistic account of this pattern exists, and the parallel observation that LLMs default to markdown-formatted output has never been connected to it. We propose that the em dash is markdown leaking into prose -- the smallest surviving unit of the structural orientation that LLMs acquire from markdown-saturated training corpora. We present a five-step genealogy connecting training data composition, structural internalization, the dual-register status of the em dash, and post-training amplification. We test this with a two-condition suppression experiment across twelve models from five providers (Anthropic, OpenAI, Meta, Google, DeepSeek): when models are instructed to avoid markdown formatting, overt features (headers, bullets, bold) are eliminated or nearly eliminated, but em dashes persist -- except in Meta's Llama models, which produce none at all. Em dash frequency and suppression resistance vary from 0.0 per 1,000 words (Llama) to 9.1 (GPT-4.1 under suppression), functioning as a signature of the specific fine-tuning procedure applied. A three-condition suppression gradient shows that even explicit em dash prohibition fails to eliminate the artifact in some models, and a base-vs-instruct comparison confirms that the latent tendency exists pre-RLHF. These findings connect two previously isolated online discourses and reframe em dash frequency as a diagnostic of fine-tuning methodology rather than a stylistic defect.

Despite rapid progress in open large language models (LLMs), European Portuguese (pt-PT) remains underrepresented in both training data and native evaluation, with machine-translated benchmarks likely missing the variant's linguistic and cultural nuances. We introduce AMALIA, a fully open LLM that prioritizes pt-PT by using more high-quality pt-PT data during both the mid- and post-training stages. To evaluate pt-PT more faithfully, we release a suite of pt-PT benchmarks that includes translated standard tasks and four new datasets targeting pt-PT generation, linguistic competence, and pt-PT/pt-BR bias. Experiments show that AMALIA matches strong baselines on translated benchmarks while substantially improving performance on pt-PT-specific evaluations, supporting the case for targeted training and native benchmarking for European Portuguese.

Data-centric training has emerged as a promising direction for improving large language models (LLMs) by optimizing not only model parameters but also the selection, composition, and weighting of training data during optimization. However, existing approaches to data selection, data mixture optimization, and data reweighting are often developed in isolated codebases with inconsistent interfaces, hindering reproducibility, fair comparison, and practical integration. In this paper, we present DataFlex, a unified data-centric dynamic training framework built upon LLaMA-Factory. DataFlex supports three major paradigms of dynamic data optimization: sample selection, domain mixture adjustment, and sample reweighting, while remaining fully compatible with the original training workflow. It provides extensible trainer abstractions and modular components, enabling a drop-in replacement for standard LLM training, and unifies key model-dependent operations such as embedding extraction, inference, and gradient computation, with support for large-scale settings including DeepSpeed ZeRO-3. We conduct comprehensive experiments across multiple data-centric methods. Dynamic data selection consistently outperforms static full-data training on MMLU across both Mistral-7B and Llama-3.2-3B. For data mixture, DoReMi and ODM improve both MMLU accuracy and corpus-level perplexity over default proportions when pretraining Qwen2.5-1.5B on SlimPajama at 6B and 30B token scales. DataFlex also achieves consistent runtime improvements over original implementations. These results demonstrate that DataFlex provides an effective, efficient, and reproducible infrastructure for data-centric dynamic training of LLMs.

The development of large-scale foundation models, particularly Large Language Models (LLMs), is constrained by significant computational and memory bottlenecks. These challenges elevate throughput optimization from a mere engineering task to a critical strategic lever, directly influencing training time, operational cost, and the feasible scale of next-generation models. This paper synthesizes evidence from recent academic and industry innovations to analyze key advancements in training efficiency. We examine architectural solutions to dataloader bottlenecks, such as the OVERLORD framework, which has demonstrated a 4.5% improvement in end-to-end training throughput. We investigate memory optimization techniques designed to overcome the GPU memory wall, including CPU offloading strategies like DeepSpeed's ZeRO-Offload, which enable the training of models far exceeding single-accelerator capacity. Furthermore, we explore the growing importance of compiler-centric optimizations, exemplified by Triton-distributed, which enables the joint optimization of computation, memory, and communication for substantial performance gains. The analysis is contextualized by advanced profiling tools and hardware characterization studies that identify and mitigate previously overlooked overheads like Dynamic Voltage and Frequency Scaling (DVFS). Findings indicate that a holistic, system-level approach, integrating innovations across data pipelines, memory management, network fabrics, and compiler technologies, is essential for accelerating AI development, managing costs, and pushing the boundaries of model scale.

We present MAGNET (Model Autonomously Growing Network), a decentralized system for autonomous generation, training, and serving of domain-expert language models across commodity hardware. MAGNET integrates four components: (1) autoresearch, an autonomous ML research pipeline that automates dataset generation, hyperparameter exploration, evaluation, and error-driven iteration; (2) BitNet b1.58 ternary training, enabling CPU-native inference via bitnet.cpp without GPU hardware; (3) DiLoCo-based distributed merging for communication-efficient aggregation of domain specialists; and (4) on-chain contribution tracking on the HOOTi EVM chain. We validate autoresearch through three case studies: video safety classification (balanced accuracy 0.9287 to 0.9851), cryptocurrency directional prediction (41% to 54.9% hit rate), and BitNet hyperparameter optimization (10-phase sweep, -16.7% validation loss).

Large language models are increasingly used to generate financial alpha signals, but many have memorized the historical data in their training corpora, producing apparent accuracy that collapses out of sample. Membership inference attacks (MIA) have been proposed as a diagnostic. What has not been established is whether MIA scores are informative about memorization in this setting, or whether signal-level filtering built on them helps once realistic costs are applied.We introduce MemGuard-Alpha, comprising a composite contamination score combining five MIA methods with a temporal proximity feature, and Cross-Model Memorization Disagreement, which exploits variation in training cutoffs across models. We then audit both. Across seven LLMs (124M-7B), 50 S&P 100 constituents, 42,800 prompts and 299,600 prompt-model MIA scores spanning 2019-2024, three findings emerge.First, where in-sample status is defined by a training cutoff, a temporal proximity feature recovers that label perfectly (ROC-AUC 1.000) because it is a monotone transform of the defining variable; any composite score containing such a feature reports separation that is arithmetic rather than detection. Second, the discriminative power of the MIA scores is largely attributable to scale differences between models: asked at a fixed date which models had that date in training, raw scores appear highly informative (AUC up to 0.99), but under three independent within-model normalizations discrimination falls to 0.487-0.537. Third, with transaction costs applied symmetrically, no filtering variant improves risk-adjusted performance over the unfiltered ensemble, none attains significant Fama-French five-factor alpha, and excluding the single weakest model outperforms every contamination-based filter.We report these as negative results with the failure modes that produced them, and release all artifacts needed to reproduce them.

Defining a constructive process to build general capabilities for language models in an automatic manner is considered an open problem in artificial intelligence. Towards this, we consider the problem of building a curriculum of tasks that grows a model via relevant skill discovery. We provide a concrete framework for this task, using a family of tasks called Cross-Entropy Games, which we postulate is universal in a suitable sense. We show that if it is possible to grow the curriculum for relevant skill discovery by iterating a greedy optimization algorithm, then, under natural assumptions, there is essentially only one meta-objective possible (up to a few hyper-parameters). We call the resulting process cognitive training. We postulate that, given sufficiently capable language models as players and meta-samplers, cognitive training provides a principled way to relevant skill discovery; and hence to the extent general capabilities are achievable via greedy curriculum learning, cognitive training would be a solution.

We present a controlled empirical comparison between autoregressive (AR) and masked diffusion (MDLM) language models. Both models are trained on identical data (50M tokens from TinyStories), identical compute budget (20,000 steps, batch size 32, sequence length 512), and identical hardware (NVIDIA H100 80GB), isolating the generation paradigm as the sole variable. We report three findings. First, both paradigms achieve comparable training throughput (~50K tokens/second), with MDLM requiring only 4.7% more wall-clock time. Second, AR converges faster and begins overfitting by step 14,000, while MDLM converges more slowly and is still improving at step 20,000, suggesting different compute-optimal training regimes. Third, quantitative diversity analysis over 1,000 generated samples reveals a structural diversity-fluency trade-off: AR produces fluent but repetitive outputs (99.8% begin with the same word), while MDLM generates more diverse narratives (93.4% unique 5-word openings, higher Distinct-n, lower Self-BLEU), at the cost of occasional grammatical inconsistencies. All code, trained checkpoints, and data pipelines are released for reproducibility.

Large language model (LLM) training is often bottlenecked by memory constraints and stochastic gradient noise in extremely high-dimensional parameter spaces. Motivated by empirical evidence that many LLM gradient matrices are effectively low-rank during training, we present an unbiased, memory-efficient, low-rank matrix estimator with the lowest variance that is applicable across common stochastic gradient estimation paradigms. The core idea is to project a high-dimensional stochastic gradient estimator onto a random low-dimensional subspace and lift it back, reducing memory while keeping the estimator unbiased and controlling mean-squared error via an optimally designed projection distribution, including Haar--Stiefel projections. The projection distribution is derived by solving a constrained functional optimization problem, yielding an optimal random projector that guides algorithm design. Empirically, the resulting low-rank gradient estimators deliver both practical memory savings and improved training behavior. In RoBERTa-large fine-tuning, our method attains the lowest peak GPU memory among compared methods (e.g., 3.83GB versus 16.7GB for full BP) while remaining competitive in accuracy; in autoregressive LLM pretraining (LLaMA-20M/60M/100M), our method outperforms the traditional methods, supporting the benefit of the proposed optimal projection strategy.