Shannon Scaling Law: A Noisy-Channel Framework for LLM Capacity and Non-Monotonic Training Phenomena
Researchers propose the Shannon Scaling Law, a theoretical framework that models LLM training as information transmission over a noisy channel using the Shannon-Hartley theorem. By mapping model parameters to channel bandwidth and training tokens to signal power, the framework introduces a fundamental SNR-based capacity limit that explains non-monotonic phenomena like catastrophic overtraining and quantization-induced degradation that classical power-law scaling laws cannot capture. Validated on Pythia and OLMo2 under Gaussian noise, quantization, and fine-tuning perturbations, the law achieves strong R² scores and successfully extrapolates from 6.9B to 12B parameter models trained on up to 307B tokens. The framework outperforms both classical and perturbation-aware scaling laws, predicting U-shaped performance degradation when SNR is insufficient.
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Parametric Memory Law for LoRA Finetuning: Quantifying LLM Memory Capacity
This paper introduces the Parametric Memory Law, a power-law relationship linking loss reduction to effective parameters and sequence length during LoRA-based LLM finetuning. The authors identify a phase transition at the token level where prediction probability p > 0.5 constitutes a sufficient condition for verbatim recall under greedy decoding. Building on these findings, they propose MemFT, a threshold-guided optimization strategy that dynamically reallocates training budget toward sub-threshold tokens, improving memory fidelity and efficiency.
Scaling Laws for Neural Language Models
OpenAI published foundational research establishing empirical scaling laws for neural language models, showing that model performance scales predictably with compute, data, and parameters. The work demonstrated power-law relationships between these factors and loss, providing a principled framework for allocating training resources. This paper became a cornerstone of modern large language model development strategy.
Optimizing your LLM in production
A Hugging Face blog post covering practical techniques for optimizing large language models in production environments. The post likely addresses inference efficiency methods such as quantization, batching, caching, and hardware utilization strategies. It serves as a practitioner-oriented guide for deploying LLMs at scale.
Predictable Confabulations: Factual Recall by LLMs Scales with Model Size and Topic Frequency
This paper establishes a quantitative scaling law linking LLM factual recall to both model parameter count and topic frequency in training data, evaluated across 38 models on 8,900+ scholarly references. Recall quality follows a sigmoid function in the log-linear combination of these two variables, explaining 60% of variance across 16 dense models from four families and 74-94% within individual families. The authors propose a superposition-inspired mechanism where recall is gated by a signal-to-noise ratio: concept frequency provides signal and model capacity sets the noise floor. This provides a predictive framework for understanding and anticipating LLM confabulation patterns.
Predictor-gated bank-wise sparsity recipe for dense-to-sparse LLM upcycling from Qwen2.5-8B
A new arXiv preprint introduces a continual training recipe to convert dense LLMs into channel-sparse models without post-hoc pruning. Starting from a Qwen2.5-8B checkpoint, the method uses a low-rank predictor to gate FFN channel routing, achieving 4x sparsity in FFN intermediate activations via a bank-wise top-k rule at 32K context. The routing module is trained on the main language modeling path, making the resulting sparsity hardware-oriented rather than approximate. The authors also identify and patch a layer-local long-context failure mode on the RULER-CWE benchmark.
Scaling Laws for Reward Model Overoptimization
OpenAI published research investigating how reward model overoptimization scales with policy and reward model size in RLHF pipelines. The work characterizes the relationship between KL divergence from the initial policy and gold-standard reward, finding predictable degradation patterns as optimization pressure increases. This provides empirical grounding for understanding Goodhart's Law dynamics in language model fine-tuning and has implications for designing safer, more robust RLHF training regimes.
Hyperfitting Explained: Terminal Geometric Expansion in Final Transformer Layers Drives Diversity Gains
This paper investigates the 'hyperfitting' phenomenon—where fine-tuning LLMs to near-zero loss on small datasets improves open-ended generation and reduces repetition—and demonstrates it is mechanistically distinct from temperature scaling. Entropy-matched control experiments falsify both the temperature-equivalence and static vocabulary reweighting hypotheses, instead localizing the effect to a 'Terminal Expansion' in the final transformer block where feature-space dimensionality expands by ~80.8 dimensions, enabling promotion of deep-tail tokens via context-dependent rank reordering. The authors introduce Late-Stage LoRA, a targeted fine-tuning strategy updating only the final 5 layers, achieving robust generation with minimal parameter updates.
Making LLMs even more accessible with bitsandbytes, 4-bit quantization and QLoRA
Hugging Face published a blog post detailing the integration of 4-bit quantization via bitsandbytes into the Transformers library, enabling large language models to run on consumer-grade hardware. The post covers NF4 (NormalFloat4) data type and double quantization techniques from the QLoRA paper, which together reduce memory footprint significantly while preserving model quality. It demonstrates how users can load models like LLaMA in 4-bit precision and fine-tune them using QLoRA with minimal code changes.