COEC (Calibrated Orthogonal-Equivalence Compensation), a training-free compensation framework that applies alternating left and right orthogonal rotations to the retained weight, improves perplexity on every model and zero-shot accuracy in most settings over existing compensation methods.
Abstract
Structured pruning reduces the size and inference cost of large language models (LLMs) by removing weight columns, but the resulting output error can degrade accuracy. Existing training-free compensation methods use an additive bias or a single orthogonal rotation on the output side of the retained weight. These corrections leave its input singular frame unchanged and therefore limit how the retained weight can adapt after column removal. We propose COEC (Calibrated Orthogonal-Equivalence Compensation), a training-free compensation framework that applies alternating left and right orthogonal rotations to the retained weight. The right rotation is optimized on a reduced Stiefel manifold, while singular values are rescaled using generalized cross-validation to select the regularization strength for each layer. COEC further tempers the calibration Gram matrix to reduce the dominance of high-energy activation directions and introduces an alignment penalty that preserves the geometric relation between adjacent attention projections.All components use second-order statistics from a small calibration set and require neither backpropagation through the LLM nor retraining of the model parameters. COEC is independent of the column pruning criterion and can be applied to multiple structured pruning methods. Experiments on the Llama-3, Llama-3.1, and Qwen2.5 model families across multiple structured sparsity levels show that COEC improves perplexity on every model and zero-shot accuracy in most settings over existing compensation methods, with larger gains at higher sparsity. These results show that post-pruning compensation can recover part of the performance lost to column removal.
Transformer-based language models achieve strong performance but incur substantial inference cost due to repeated high-dimensional matrix multiplications. We propose Reduced Matrix Multiplication (RMM), a training-free, input-adaptive inference method that reduces Transformer matrix products by selecting informative slices along their contraction dimensions, without modifying model weights. Under a simple retention-ratio control, RMM provides a smooth and predictable accuracy-efficiency trade-off. Across language models ranging from 1B to 70B parameters, we find that reduction tolerance depends on the model family, task, component, and retention ratio, although it often improves with model scale. Under moderate reduction, RMM remains robust across the evaluated discriminative, autoregressive generation, and long-context settings. We further show that the same principle extends to multimodal vision-language inference. Mechanistic ablations reveal a structural asymmetry within Transformers: attention-side computations are substantially more reducible than MLP components. Finally, wall-clock benchmarks with custom kernels on an NVIDIA A100 show that these computational savings can translate into practical runtime gains, especially at longer sequence lengths. Together, these results position RMM as a scalable direction for input-adaptive inference-time optimization.
Structured pruning compresses large language models (LLMs) by removing whole computational units, such as attention heads and feed-forward (FFN) channel groups. Most training-free methods, however, rank these units independently, implicitly treating the loss from pruning a set as the sum of its individual losses. This view fails for Transformers, whose sublayers are coupled through a shared residual stream. Two individually weak units can thus be jointly indispensable, yet independent scoring is blind to such dependence and removes them together. We introduce CoCurve (Cross-Module Co-Pruning Curvature), a calibration-only, fine-tuning-free method that prunes attention and FFN units jointly. A second-order Taylor expansion of the token-level KL between the frozen model and its masked copy yields a single Fisher matrix whose diagonal is classical node saliency and whose off-diagonal entries are co-pruning curvature edges: the extra damage of removing two units together. Under a single-ablation additivity approximation this matrix reduces to a Gram product of single-unit ablation features, so the full M x M interaction is recovered from M forward passes, with no pairwise sweeps or gradients. Pruning then reduces to one budgeted quadratic program, solved in a single shot under a shared attention--FFN budget, with no labels, fine-tuning, or recovery.
Z. Gong, Zihao Zeng, Zijie Wang et al.· 0 citations
Pruning reduces the inference cost of large language models, but existing criteria primarily preserve large activations or reconstruct layer outputs. We argue that this overlooks a key computation performed by particularly sparsity-sensitive neurons in the MLP up and gate projections: separating similar inputs into dissimilar outputs. This suggests that effective pruning should preserve not only activations, but also the differences between outputs more broadly. We introduce a family of difference-informed pruning methods built upon this principle. Wisp is a first-order, update-free method that scores weights using input-difference norms, and Wisp+ refines this score neuronwise using the input pairs each neuron separates most strongly. Finally, Whisper is a second-order method that uses a lightly regularized difference Hessian as its reconstruction objective. Across Llama 2 and 3.1 models from 7B to 405B parameters, our second-order variant consistently improves over strong reconstruction-based baselines, while our update-free variants improve over activation-aware baselines, especially in constrained settings. The improvements over Wanda and SparseGPT extend to structured sparsity, downstream evaluations, and other model families. Augmenting stronger techniques such as RIA and ALPS with our difference-informed criteria yields further improvements, shifting the overall accuracy-runtime frontier outward at negligible additional cost. These results suggest that preserving output differences is a broadly useful and composable signal for post-training LLM sparsification.
Linghao Kong, Inimai Subramanian, Micah Adler et al.· 0 citations
Recent training-free post-training quantization methods restore model accuracy through closed-form residual compensation. To constrain additional model storage overhead, several existing methods gate layer selection by goodness-of-fit, retaining only those layers whose compensation yields a positive residual fit score and discarding the rest. In this paper, we show that, under the low-bit W4A4 setting, this gating mechanism fails to distinguish poorly predictable quantization error from numerical solver failure. Rank-deficient input activations yield severely ill-conditioned or numerically singular Gram matrices, causing the closed-form solver to become unstable and produce spuriously negative fit scores. Consequently, existing goodness-of-fit gates misclassify affected layers as uncompensable and discard them. Many of these discarded layers can nevertheless provide substantial error recovery when their compensation is computed using a numerically stable solver. To address this problem, we propose a parameter-free truncated pseudoinverse solver which removes collapsed directions prior to inversion. On ViT-B with the W4A4 setting, our training-free method achieves 81.42\% top-1 accuracy, outperforming prior post-training methods and fine-tuning-based baselines. Combined with joint low-rank and quantization compression, the proposed method reaches a deployable operating point of 80.26\% accuracy at 54.7 MB, providing a well-balanced trade-off between model size and accuracy.
A Last-Layer Ensemble (LLE), $K$ linear units on one shared frozen feature map, is an efficient single-pass approach to the disagreement-based epistemic uncertainty for out-of-distribution (OOD) detection. Its weakness is that members share the backbone gradient and can converge toward the same function, collapsing the inter-member diversity the signal depends on. Whether last-layer diversity can be restored, and what mitigates the collapse, is an open question. The weight-orthonormality defining Orthonormal Certificates (OC), the weight-orthonormal special case of the LLE, is only an indirect correction; it decorrelates the weights of the members, not their predictions. Here, we instead target the collapse directly in function space, with a Covariance Last-Layer Ensemble (cov-LLE) that places a direct covariance penalty on member activations. Cov-LLE restores the function-space diversity that weight-orthonormality cannot, and at matched $K$ recovers much of the diversity and calibration of a deep ensemble at $1\times$ backbone cost (in-distribution prediction variance $0.05\!\to\!9.3$ vs. $22.1$ ($\times10^{-3}$), and ECE $0.135\!\to\!0.090$ vs. $0.035$, for a $K\times$-cost deep ensemble), at no cost to accuracy. Viewing OC as a last-layer ensemble also organizes detectors into a two-axis taxonomy (by how their units are trained and how their outputs are scored) and exposes the OC score as a magnitude, motivating a scale-invariant, label-free direction score that repairs its near-OOD failure, adding $+0.16$ to $+0.18$ ROC AUC on every backbone.
H. M. Gillis, Isaac Xu, Gabriel Spadon et al.· 0 citations
SHIFT-LLM, a training-free post-pruning correction framework that inserts a Linear Residual Adapter at each pruning site, consistently recovers accuracy lost to depth pruning across most configurations, achieving gains up to +15.7 points on Llama-3.1-8B-Instruct.
Ali Bahri, Hang Li, Hongliang Li et al.· 0 citations
What if pathology foundation models could do more with less? GigaPath-Flash and GigaTIME-Flash cut computational demands while maintaining strong performance, opening the door to larger studies and broader exploration. The post GigaPath-Flash and GigaTIME-Flash: Toward population-scale discovery with efficient pathology foundation models appeared first on Microsoft Research.
MIT News · Artificial Intelligence· news.mit.eduAug 31, 2026
With millions of users across the world, Julia has been used to conduct cutting-edge research and to design new drugs, jet engines, heat pumps, and more.