Inference energy per token drives the cost and carbon footprint of deployed transformers. It is dominated by dense matrix products that incur fused multiply-accumulate (FMA) operations and memory traffic. To reduce these computations while retaining dense tensors for high GPU throughput, we develop a methodology from first principles to adapt structural complexity during training to maximize inference utility per unit compute. Channel penalties drive entire tensor slices to zero to enable physical removal while preserving density and the network function. The natural approach, penalizing the norm of operator components acting through each channel, is provably destabilized by gauge freedom. We resolve this pathology with GaugeLasso: additive symmetric group-lasso penalties that recover a monotone function of product-norms when the network converges to gauge balance. Our equilibrium analysis enables per-channel calibration to correctly suppress slices that under-perform in inference utility per unit compute. Under adaptive pressure, the network reorganizes into depth-dependent structural profiles that can be far smaller than the architecture required to learn the task. On polynomial long division over F31, compute compresses from 148 to 255 times with perfect accuracy. On character-level language modeling, compressed models outperform the hand-designed baseline at equal FMA. On masked autoencoding, a compression trial exposes which axes were over-provisioned and which saturated, guiding a better second design. Compaction also accelerates training monotonically as the model progresses. Post-hoc pruning with the same utility ranking cannot reach these structures, showing that sustained pressure is central to discovery of efficient models. Retraining a discovered architecture recovers baseline quality on our statistical tasks, but fails on our exact algorithmic task.
Transformer architectures exhibit cross-layer redundancies, yet post-training compression pipelines typically optimize layers in isolation or rely on heuristic grouping strategies that disregard layer-specific activation geometries. We introduce a principled, training-free framework that sequentially optimizes cross-layer weight pairings and shared-dictionary factorizations. Rather than forcing weights of adjacent layers to share a basis or heuristically merging activation statistics, our approach identifies structurally compatible projections and learns a shared representation that better preserves each layer's distinct calibration geometry. Coupled with structured sparsity, this yields highly efficient weight decompositions without sacrificing functional fidelity. Across diverse architectures, scales, and modalities, our method achieves state-of-the-art results, consistently outperforming independent structured weight decompositions and alternative pairwise weight factorizations, which operate under heuristic grouping strategies. By replacing heuristic engineering strategies with a convergent, optimization-driven pipeline, we establish a theoretically grounded foundation for scalable, transformer compression across different modalities.
Unstructured pruning produces sparse weight tensors, but the standard implementation keeps tensor shapes unchanged so the deployed model is no smaller than before pruning. We present an exact structural rewrite, which we call minimization, that converts a masked network into a smaller dense network with the same forward function up to floating-point rounding. The Squeeze-Release cycle iterates pruning and minimization with an intermediate release step that re-enables the exact-zero positions inside the compacted tensors as small calibrated noise, turning otherwise wasted capacity back into trainable parameters. Successive cycles use that capacity to find structural redundancy a single pass cannot reach. We additionally introduce CompensatedLayerNorm, a function-preserving replacement for LayerNorm that extends minimization to channel reduction across LayerNorm-equipped residual streams. Squeeze-Release compresses the deployable network to 39x smaller than the unpruned model on a fully-connected model network and 14.8x smaller on modern CNN (ConvNeXt-Tiny), at comparable accuracy. In addition we prove that the rewrite can be extended to transformer architectures.
Large language models (LLMs) are dominated by dense linear transformations, whose storage, memory and computational overheads hinder efficient adaptation and deployment while masking the functional impacts of structural simplification. Here we present Tensor Mixture (MixT), a general tensor-structured compression scheme that replaces targeted dense linear layers with natively executable mixtures of tensor operators. Operating directly on generic linear projections instead of model-specific components, MixT is potentially applicable across Transformer-based LLMs and other dense neural mappings. We evaluate MixT on Qwen3-8B and LLaMA2-7B under a unified recovery protocol, identifying a broad compressible regime in which MMLU accuracy is largely preserved before an abrupt transition at model-specific boundaries. This transition coincides with coordinated shifts in output entropy, prediction entropy and inter-layer geometry. At the LLaMA2-7B transition boundary, MixT reduces full-model parameters by 47.5%, inference FLOPs by 37.1%, training FLOPs by 52.1% and peak inference memory by 60.4%, demonstrating its practical potential for lower-cost LLM compression.