Chronicals: A High-Performance Framework for LLM Fine-Tuning with 3.51x Speedup over Unsloth

Large language model fine-tuning is bottlenecked by memory: a 7B parameter model requires 84GB--14GB for weights, 14GB for gradients, and 56GB for FP32 optimizer states--exceeding even A100-40GB capacity. We present Chronicals, an open-source training framework achieving 3.51x speedup over Unsloth through four synergistic optimizations: (1) fused Triton kernels eliminating 75% of memory traffic via RMSNorm (7x), SwiGLU (5x), and QK-RoPE (2.3x) fusion; (2) Cut Cross-Entropy reducing logit memory from 5GB to 135MB through online softmax computation; (3) LoRA+ with theoretically-derived 16x differential learning rates between adapter matrices; and (4) Best-Fit Decreasing sequence packing recovering 60-75% of compute wasted on padding. On Qwen2.5-0.5B with A100-40GB, Chronicals achieves 41,184 tokens/second for full fine-tuning versus Unsloth's 11,736 tokens/second (3.51x). For LoRA at rank 32, we reach 11,699 tokens/second versus Unsloth MAX's 2,857 tokens/second (4.10x). Critically, we discovered that Unsloth's reported 46,000 tokens/second benchmark exhibited zero gradient norms--the model was not training. We provide complete mathematical foundations: online softmax correctness proofs, FlashAttention IO complexity bounds O(N^2 d^2 M^{-1}), LoRA+ learning rate derivations from gradient magnitude analysis, and bin-packing approximation guarantees. All implementations, benchmarks, and proofs are available at https://github.com/Ajwebdevs/Chronicals with pip installation via https://pypi.org/project/chronicals/.

Disproving the Feasibility of Learned Confidence Calibration Under Binary Supervision: An Information-Theoretic Impossibility

We prove a fundamental impossibility theorem: neural networks cannot simultaneously learn well-calibrated confidence estimates with meaningful diversity when trained using binary correct/incorrect supervision. Through rigorous mathematical analysis and comprehensive empirical evaluation spanning negative reward training, symmetric loss functions, and post-hoc calibration methods, we demonstrate this is an information-theoretic constraint, not a methodological failure. Our experiments reveal universal failure patterns: negative rewards produce extreme underconfidence (ECE greater than 0.8) while destroying confidence diversity (std less than 0.05), symmetric losses fail to escape binary signal averaging, and post-hoc methods achieve calibration (ECE less than 0.02) only by compressing the confidence distribution. We formalize this as an underspecified mapping problem where binary signals cannot distinguish between different confidence levels for correct predictions: a 60 percent confident correct answer receives identical supervision to a 90 percent confident one. Crucially, our real-world validation shows 100 percent failure rate for all training methods across MNIST, Fashion-MNIST, and CIFAR-10, while post-hoc calibration's 33 percent success rate paradoxically confirms our theorem by achieving calibration through transformation rather than learning. This impossibility directly explains neural network hallucinations and establishes why post-hoc calibration is mathematically necessary, not merely convenient. We propose novel supervision paradigms using ensemble disagreement and adaptive multi-agent learning that could overcome these fundamental limitations without requiring human confidence annotations.