Progressive Multi-Ancestor Bit-Depth Distillation

Modern deep neural networks achieve strong performance, but their scale makes them costly and slow, especially on resource-constrained edge devices. Pruning and quantization address this, but rely on manual, expert choices and on algorithms that are hard to apply across architectures. Uniform settings also ignore how differently individual layers respond to compression, which costs accuracy. We introduce APQF, an agentic profiling-guided framework that combines structured pruning, mixed-precision quantization-aware training, and accuracy recovery in one automated pipeline. A profiling agent measures how cost is distributed across the model and how sensitive each part is to pruning, and this evidence drives per-layer pruning ratios, per-layer bit-widths, and the recovery strategy, all proposed by LLM planners and validated before execution. To our knowledge, APQF is the first framework to combine LLM-guided, profiling-grounded decisions with a fully training-aware pruning and quantization pipeline for both CNNs and vision transformers. We evaluate APQF on ResNet, VGG7, ViT, DeiT, and Swin using ImageNet-1k and CIFAR-10. On ImageNet it cuts compute to 5.6-7.7 percent of the original bit-operations, a 13-18x reduction, while keeping accuracy close to the baseline, and under a 200K-image budget it stays roughly 17 points higher in Top-1 than existing joint pruning and quantization methods. On CIFAR-10 it compresses further than that method on four of five architectures. On VGG7 it reaches 93.15 percent using only 0.41 percent of baseline bit-operations, the only method at that compression level to improve on its full-precision baseline. Ablations show that uniform compression loses the most accuracy at matched compute, and that withholding profiling data from the planner hurts every model. Six LLM planners, including free open-weight ones, all reach 97.4-97.9 percent on Swin-Tiny.

We study distillation for large language models under explicit compute constraints, with the goal of producing student models that are not only cheaper to train, but structurally efficient at inference time. While prior approaches to parameter-efficient distillation, such as LoRA, reduce adaptation cost, they leave the dense backbone unchanged and therefore fail to deliver meaningful inference savings. We propose Budgeted LoRA, a distillation framework that treats model compression as a structured compute allocation problem. Instead of using a fixed student architecture, we introduce a global compute budget that sets the final target fraction of dense computation retained. Under this constraint, the model redistributes capacity across dense and low-rank pathways via (i) module-level dense retention coefficients, (ii) adaptive low-rank allocation, and (iii) post-training compression that selectively removes, approximates, or preserves dense components. This formulation yields a family of students controlled by a single budget dial. Empirically, Budgeted LoRA matches standard LoRA perplexity at a moderate budget with a 1.74x compressed-module speedup; at an aggressive budget it achieves a 4.05x speedup with moderate perplexity degradation, and it preserves higher accuracy on function-style in-context learning probes. These results suggest that, under compute-constrained distillation, retaining behavior is less about matching perplexity or removing more parameters than it is about controlling how dense computation is transferred to low-rank pathways.

Quantization-aware distillation (QAD) restores much of the short-form question-answering performance lost to sub-3-bit quantization, yet leaves mathematical and code reasoning substantially impaired. Long generations often degenerate into repetitive loops, exhausting the decoding budget without completing a solution. We trace this gap to quantization-amplified exposure bias: QAD trains on fixed corpus prefixes, while quantization-induced deviations compound along the model's own autoregressive trajectories. To address this mismatch, we introduce an on-policy distillation (OPD) stage that places teacher supervision where the quantized model actually goes. Starting from a QAD checkpoint, the student generates through the quantized forward path used at deployment and receives feedback from a frozen full-precision teacher on its own prefixes, combining dense token-level guidance with task-verifier rewards. Across four models at 2.79 and 1.88 effective bits, OPD raises average BF16 performance retention from 35% to 70% on MATH-500 and from 66% to 91% on HumanEval while preserving short-form performance, with reasoning gains substantially exceeding those of continued teacher-forced QAD in matched-budget comparisons. By coupling QAD's stable low-bit initialization with OPD's on-policy reasoning recovery, our framework provides a comprehensive sub-3-bit solution that preserves broad capabilities while restoring long-form reasoning.