LLM Training Dynamics

• LLM Training Dynamics is the study of evolving learning mechanisms in large language models, integrating gradient decompositions, data curation, and multi-stage pipelines.
• It examines techniques like gradient-space frameworks, feature drift tracking, and reduced-precision impact to enhance generalization and diagnostic metrics.
• Practical insights include optimized data mixtures, fairness bias mitigation via early stopping, and real-time parallel training diagnostics for robust performance.

LLM training dynamics comprise the time-evolving behaviors and mechanisms by which LLMs adjust their internal parameters, representations, and outputs in response to specific training objectives, data mixtures, architectural constraints, and optimization protocols. This field integrates gradient-space analyses, dataset composition effects, precision constraints, feature representational changes, and fairness trajectories to provide a detailed understanding of learning, generalization, and downstream performance. Recent studies offer both unifying mathematical frameworks for update-by-update influence, empirical measurements of representational and behavioral shifts, and principled diagnostic metrics for interpretability and production robustness.

1. Gradient-Space Frameworks for Fitting and Generalization

LLM training dynamics can be precisely tracked using step-wise decompositions of parameter and prediction changes following each gradient update. In instruction tuning (supervised fine-tuning, SFT) and preference tuning (e.g., Direct Preference Optimization, DPO), the change in the model probability $\pi_\theta(y|x)$ for candidate response $y$ to prompt $x$, under a single SGD step on an observed example $(x_u, y_u)$, is given by: $$\Delta \log \pi^t(y_o|x_o) = -\eta \cdot \underbrace{A^t(x_o)}_{\text{centering}} \cdot \underbrace{K^t((x_o,y_o),(x_u,y_u))}_{\text{emp. NTK}} \cdot \underbrace{G^t(x_u,y_u)}_{\text{supervised dir.}} + O(\eta^2)$$ where $A^t$ centers the change by current prediction, $K^t$ is the empirical neural tangent kernel (NTK) linking the current and updated prompt-response pairs, and $G^t$ encodes the loss-dependent gradient at $(x_u, y_u)$. Recursive composition across SGD steps aggregates these effects over training.

This decomposition unifies SFT—where $G_{\text{SFT}}^t$ pulls up gold responses and similar ones for other prompts—and DPO/other preference methods—where $G_{\text{DPO}}^t$ both lifts preferred responses and pushes down dispreferred responses, with gradient strength adapting to current margin. These analytic tools predict phenomena such as “hallucinations” (where similar training responses unduly raise the probability of unrelated facts) and “repeater” degeneracy in off-policy preference tuning (Ren et al., 2024).

2. Data Composition, Deduplication, and Multi-Stage Pipelines

Training loss trajectories, convergence rates, and downstream generalization are sensitive to the composition and curation of pretraining corpora. The SlimPajama-DC study demonstrates that:

• Global deduplication (across all sources) removes $\sim$48% of tokens, ensuring unique and diverse training examples and yielding more robust models compared to local deduplication.
• Optimal performance arises from balanced data mixtures (e.g., 50% web data, $\sim$25% curated/common crawl, %%%%12$K^t$13%%%%10% code, %%%%14$A^t$15%%%%8% books, %%%%16$\sim$17%%%%15% Wiki/small corpora), rather than code- or web-only mixes.
• Aggressive deduplication—and diversity—improves performance on evaluation benchmarks such as ARC, HellaSwag, MMLU, and TruthfulQA, even if training loss is not minimal (Shen et al., 2023).

Mid-training as a distinct phase, operating after general pretraining and before instruction or RLHF alignment, introduces specialized data and model adaptations while preserving base competencies. The phase proceeds with explicit mixture ratios, three-phase learning rate schedules, and, as needed, architectural enhancements (e.g., long-context RoPE modifications), maximizing efficient skill acquisition in target areas such as reasoning, coding, and mathematics (Tu et al., 27 Oct 2025).

3. Dynamics of Reasoning, Memorization, and Generalization

The partition between reasoning and memorization during LLM fine-tuning is sharply characterized by “pre-memorization train accuracy” (PreMemAcc): the fraction of train examples successfully solved (by correctness of final answer) before the model enters straight memorization, as diagnosed by collapse of perplexity on gold solution traces. Across models, datasets, and hyperparameters, PreMemAcc pre-training values predict held-out test accuracy with $R^2>0.9$, outperforming traditional proxies (gradient noise, weight distance) (Kang et al., 2024).

Low PreMemAcc instances are fragile and vulnerable to prompt perturbations, while high PreMemAcc examples indicate robust, generalized reasoning. Dynamic data curation—by prioritizing new collection around low-PreMemAcc examples—yields 1.5%%%%19$x$20%%%% sample efficiency gains for achieving target test performance.

4. Feature Formation and Representational Drift

During autoregressive training, feature evolution can be decomposed into three phases:

1. Initialization/Warmup: Token-level (“lexical”) features solidify early; concept-level feature representations remain scattered.
2. Emergent Phase: Concept-level features form and cluster, with progress calibrated by increases in inter-activation similarity (progress measure $M_i(t)$).
3. Convergent Phase: Both token and concept features stabilize; direction vectors for decoded features (e.g., columns of an SAE decoder) continue to drift smoothly towards final orientations even after semantic regions form.

The SAE-Track methodology provides continual monitoring of these phenomena, tracking cosine similarities between evolving feature vectors and diagnosing shifts, groupings, or stabilization in mechanistically interpretable representations (Xu et al., 2024).

5. Precision Constraints and Loss Landscape Instabilities

Reduced-precision arithmetic (BF16, FP8) promises improved computational throughput but impacts training stability and robustness. Empirical and simulated reductions in exponent or mantissa width in floating-point multiplications lead to:

• High sensitivity to seed, learning rate, and even minor changes in early training.
• Loss landscape "sharpness" (measured by the $\phi_\epsilon$ metric) increases rapidly as precision decreases, preceding visible loss divergence.
• Failure rates grow with lower mantissa and exponent bits; e.g., E8M3 divergences occur in as few as 16 K steps, while higher-precision BF16 is more robust but still not immune to instability (Lee et al., 2024).

Practical recommendations include hybrid or dynamic-precision schemes, hardware-specific stabilization mechanisms, and careful loss-sharpness monitoring for early instability detection.

6. Fairness, Bias Emergence, and Early-Stopping Criteria

Fairness metrics such as Average Rank (AR) and Jensen-Shannon Divergence by Parts (JSD-P) provide granular, per-token insight into class-wise bias emergence during training. Empirical studies on gender-prediction tasks show that:

• Bias toward dominant classes (e.g., “male”) can suddenly emerge $~80$ K steps into pretraining, independent of global performance metrics (LAMBADA accuracy, perplexity).
• Early-stopping at inflection points identified by fairness metrics can reduce bias by over 90% at the cost of minimal (<2%) standard performance loss.
• Model scale accentuates bias, with larger models (e.g., 6.9B vs. 160M) amplifying gendered assumptions in ambiguous contexts (Patel et al., 2 Jun 2025).

A general decision rule for intervention is $\min_t$ fairness gap subject to a minimal performance threshold.

7. Performance Diagnostics and Parallel Training Steps

Operational monitoring of LLM training workflows, especially in multi-tenant production settings, can be achieved by reconstructing training step timelines from network flow records. The LLMPrism system identifies job and GPU groupings, parallelism strategies (data-parallel or pipeline-parallel), and step boundaries by analyzing communication periodicities and packet size signatures. Diagnosis based on per-step and per-group durations efficiently localizes bottlenecks (e.g., switch congestion, straggling GPUs) with $<$0.3% error against ground truths, facilitating continual health monitoring and mitigation in large-scale distributed training (Jiang et al., 1 May 2025).

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This synthesis reflects the current understanding of LLM training dynamics across gradient update mechanisms, data composition, feature evolution, reduced-precision stability, fairness metrics, and operational monitoring, as established in recent empirical and theoretical work.