Transformer Pruning

Muon has emerged as a strong optimizer for neural network training and admits an interpretation as steepest descent under a spectral-norm geometry. Yet we find that Muon-trained Transformers can degrade sharply when their MLP hidden channels are pruned after training. To reconcile Muon's optimization performance with structured compressibility, we introduce Budget Muon (BMuon), which modifies Muon's spectral geometry so that hidden channels across blocks compete for a shared allocation budget. The resulting oracle is exactly normalized steepest descent under a family of norms that interpolate between Muon's geometry and structured sparse geometries. Our principal sparsity control is an interpretable global channel-allocation budget, rather than a setting-dependent sparsity-penalty coefficient. For linear factorization models, we show that Muon admits minimum-cost exact representations with redundant hidden width, whereas under the BMuon oracle geometry and a sufficiently scarce budget, every minimum-cost representation is width-minimal. For practical training, we derive a minorization-maximization surrogate for the exact allocation problem. On ImageNet-1K with ViT-S/16, BMuon improves over Muon under gradual structured MLP pruning, and its learned allocations provide a more effective pruning criterion than weight magnitude. On a 1B-parameter LLaMA-style model trained on FineWeb, BMuon improves over Muon under post-training MLP channel pruning.

Scaling up transformers has produced models with broad capabilities, deployed across heterogeneous hardware and fluctuating workloads. Yet, model families offer only a few fixed sizes (e.g., S, B, L), forcing users to commit to a model based on hardware and latency constraints. This rigidity is often suboptimal under varying query loads. We introduce a retraining-free method that elastifies pre-trained transformers into a single model that adapts on-the-fly across a continuum of computational budgets. Our key contribution is a differentiable relaxation of the functional unit-ranking problem: unlike prior work, which optimizes a single importance weight per MLP block or attention head, we rank every individual MLP neuron and attention head jointly, on a common scale, by minimizing the model's loss under soft pruning across many sparsity targets, all at once. Across 27 vision and text transformer encoders ranging from 22M to 8B parameters, our method yields smooth degradation up to 60% sparsity and outperforms one-shot baselines under deep pruning. For example, pruning DINOv3 ViT-H+/16 to 50% sparsity removes 427M parameters while reducing ImageNet-1k linear-probing accuracy by only 0.8%, without the need for weight correction or retraining. At 60% sparsity, a pruned AugReg ViT-B/16 model achieves up to $1.80\times$ higher throughput and $1.26\times$ lower single-query latency on an A100 GPU. Elastic models are produced in minutes, with construction time scaling sub-linearly with parameter count.

Post-training pruning enables efficient deployment, but conventional methods do not explicitly preserve internal-gradient alignment between sparse and dense models. We study novel connections between downstream performance of compressed models and the ability to retain gradient information via influence-function preservation. Central to this connection is a curvature-aware objective that accounts for both layer activations and backpropagated gradients. Despite its promise, this objective remains underexplored in pruning due to a lack of efficient solvers. We introduce $\texttt{CACTUS}$, a novel ADMM-based optimizer supporting both pruning and sparse-plus-low-rank decompositions of pre-trained weights. Compared to LLM-Surgeon which targets the same objective, $\texttt{CACTUS}$ can achieve over an order-of-magnitude speedup. At $50\%$ pruning of Qwen3-4B, $\texttt{CACTUS}$ reduces the C4 perplexity gap to the dense model by $45\%$, improves compressed-to-dense per-sample gradient cosine similarity on WikiText-2 from $0.670$ to $0.755$, and runs over $28\times$ faster than LLM-Surgeon on substantially weaker hardware. By preserving influence functions, $\texttt{CACTUS}$ supports effective data selection. On Llama-3.2-3B, fine-tuning a fresh dense model on the $5\%$ of data selected by $\texttt{CACTUS}$ achieves $49.44\%$ accuracy on BIG-Bench Hard, compared with $47.22\%$ using ALPS and $49.54\%$ using dense-model selection. Finally, integrating $\texttt{CACTUS}$ with LoGRA, a recent gradient-projection strategy, on Qwen3-4B with MLP layers pruned to 2:4 sparsity and a rank-64 correction retains a $0.711$ cosine alignment with dense LoGRA-projected C4 gradients.

Transformer architectures have achieved strong results in natural language processing and computer vision, but their deployment is limited by high computational, memory and storage costs, motivating research into model compression techniques, such as pruning, while preserving performance. Prior work has shown substantial redundancy in large language models (LLMs), and redundancy in vision transformers has also been investigated, but it remains less systematically analyzed than in LLMs. In this work, we extend similarity-based redundancy analysis to vision models by measuring cosine similarity between layer inputs and outputs to identify transformations with minimal impact. We study redundancy patterns across several transformer architectures and find that deep vision transformers such as DINOv2 and SwinV2, like language models, exhibit significant redundancy. We then evaluate how this redundancy can be exploited to improve efficiency, analyzing the trade-off between inference speed and performance degradation under different pruning strategies. Our results show that moderate pruning can yield substantial acceleration with limited impact on accuracy, and that 20% of the DINOv2 blocks can be removed without any retraining, for a 1.24x throughput gain and a 20% lower energy per image at a relative accuracy loss below 1% on ImageNet-1K. We further propose a model selection pipeline that automatically identifies the best pruned configuration for a given dataset, reducing FLOPs by 13% to 27% on average across architectures with an average accuracy change between -0.3 and +1.0 points.

In-context-learning Tabular Foundation Models (TFMs) are uniquely suited to scenarios with limited resources or privacy constraints, as they solve new tasks without additional training. However, their architecture consists of multiple transformer blocks, resulting in high computational and memory footprints. Meanwhile, traditional alternatives like Gradient-Boosted Decision Trees (GBDTs) remain highly competitive and run efficiently on CPUs, suggesting that tabular tasks may not inherently require deep architectures. This contrast raises a fundamental question: can TFMs be simplified by removing architectural redundancies without sacrificing performance? To answer this, we introduce a closed-form, label-free affine translator that replaces a contiguous window of up to 96% of the blocks, leaving the rest unchanged. Evaluating eight frontier TFMs on 171 classification datasets, we reveal that tabular transformers are vastly overparameterized: replacing half of a model's blocks costs at most $0.002$ median AUROC across all architectures, with the half-depth TabFM still outperforming every other full-depth TFMs and tuned GBDTs. Furthermore, different model families are overparameterized in different ways: TabPFN-3 relies on its encoders, maintaining performance regardless of which single block is retained. Other single-axis models spread computation thinly, needing only their first block, while dual-axis models concentrate it in one critical block. Ultimately, removing depth saves up to 1.5B parameters, speeds up GPU inference by up to $6\times$ at a median cost of $0.03$ AUROC, while a single-block TabPFN-3 serves cached queries $2.4\times$ faster using $6\times$ less memory at negligible cost.

Mid-prefill pruning can reduce the sequence processed by deeper transformer layers, but attention concentration alone does not certify that discarded context is dispensable. We formulate EntroPrefill as a Renyi-guided proposal mechanism coupled to explicit constraints on discarded attention mass. Sink-isolated, regularized head pooling respects grouped-query attention while exposing a quantitative trade-off between specialization and worst-head coverage. We derive a mixture-to-head deletion envelope, a computable upper bound on feasible token removal, and a finite-sample observer guarantee that remains valid when the pruning layer is selected adaptively. We then establish a conditional transformer perturbation bound with explicit sufficient Lipschitz constants and a first-token decision-margin corollary. A counterexample shows why shallow observations alone cannot imply an unconditional future-output guarantee. The systems analysis distinguishes query-head unions, physical page allocation, and KV-transfer payload, and gives an arithmetic break-even condition for pruning. This manuscript is theoretical in scope: it defines the procedure, its assumptions, and its formal limits, but does not report measured acceleration or task-accuracy preservation. Experiments are reserved for subsequent validation of the assumptions, approximation tightness, and end-to-end resource trade-offs.

The large KV-cache size of modern LLMs creates a barrier to efficient deployment. Recent work has explored replacing attention layers' RoPE positional embeddings with alternative decay-based mechanisms, which can then be used to prune KV-cache during inference. However, these decay functions have limited expressivity, and in practice devolve into sliding-window-like eviction patterns. In this work, we propose a unifying framework for complementary and novel decay mechanisms, capturing complex key statistics and interactions while preserving expressive RoPE embeddings and Softmax attention. The resulting Universal Attention is a highly expressive and end-to-end trainable architecture, whose composite decay mechanism acts as a natural, $\textit{adaptive}$ pruning criterion, removing tokens that contribute least to attention computation. Experimentally, Universal Attention achieves state-of-the-art $10\times$ compression on natural language and synthetic task data, while $\textit{improving}$ downstream performance compared to both state-of-the-art baselines and unpruned oracles. It further demonstrates superior long-context generalization with unprecedented $25\times$ compression at length 16k.

Wanda (Sun et al., 2024) prunes large language models by scoring weights independently within each linear projection, although queries and keys interact through dot products. We introduce QK-Wanda, which scores query and key weights by their individual deletion costs under an unmasked pre-RoPE reconstruction objective. It augments Wanda scores with information from the opposite projection (keys for query weights, and queries for key weights), allowing both projections to share a pruning budget. Its closed-form scores require no gradients or weight updates; full pruning takes 1.3% longer than Wanda on A100 and 3.1% longer on H200 with the calibration used in our main experiments. We evaluate QK-only pruning across 15 models from TinyLlama, Llama 2, Llama 3, and Qwen2.5, spanning 0.5B-72B parameters. Relative to Wanda, QK-Wanda reduces QK reconstruction error by an average of 60% at 50% sparsity and 45% at 80%. Downstream gains depend on the model. At 80% sparsity on Llama 2 70B, WikiText-2 and C4 perplexity decrease by 20.3% and 13.5%, while mean zero-shot accuracy rises by 5.94 percentage points. Qwen2.5-72B also improves, but Llama-3.1-70B has substantially higher perplexity despite lower reconstruction error. These results show both the promise of coupled pruning criteria and the limits of local reconstruction as a predictor of model quality.

Video diffusion transformers (DiTs) increasingly adopt mixture-of-experts (MoE) architectures to reduce active computation, but their full expert storage remains costly. Existing one-shot pruning criteria mainly rely on static activation or routing statistics and cannot capture layer-level re-routing after expert deletion. We introduce DIET, a training-free expert pruning framework based on deletion responses. A single all-expert calibration pass records expert outputs and router states for matched conditional and unconditional tokens. Candidate deletions are then replayed from cached tensors, requiring no additional model forward passes. The resulting deletion-response signatures characterize each expert by the changes induced when it is removed. DIET selects retained experts by minimizing Overall Diversity Loss (ODL), which preserves directional coverage in signature space, and combines intra-layer local search with an inter-layer regression-guided budget search to allocate experts across layers. On LingBot-Video 30B-A3B, pruning 50% of experts (6,144 to 3,072) reduces the checkpoint from 57 GB to 30 GB and enables single-card deployment on a 48 GB GPU without fine-tuning. Under a fixed 284-case VBench protocol, the VBench Total increases from 0.7941 to 0.8115. Across tested retention budgets, DIET consistently outperforms competitive pruning baselines adapted from large language models.

Which layers of a feed-forward geometry model are needed to preserve both camera poses and dense 3D structure? We study layer redundancy in VGGT, $π^3$, and VGGT-$Ω$: 3,018 pruned configurations, scored on seven camera-pose and dense-geometry metrics across four indoor and outdoor datasets. Four findings follow: (i) Removable layers cluster in two redundancy regions: a dominant early region and a narrower late one, while deletions spanning the intervening layers are consistently more disruptive. This recurring pattern holds across models, datasets, and metrics, and contrasts with the middle-to-late redundancy commonly reported in the literature. (ii) Within these regions, we observe that the joint degradation from deleting two intervals is approximately the sum of their individual degradations, reducing the number of model evaluations for pruning search from $O(L^4)$ to $O(L^2)$, where $L$ is the aggregator depth. (iii) We find that CKA provides a cheaper representation-based proxy for interval degradation, offering a practical trade-off between pruning quality and calibration cost. (iv) Closed-form linear calibration recovers accuracy after pruning without end-to-end retraining. A least-squares analysis shows that using a shared map for special and patch tokens generally incurs excess reconstruction loss, motivating token-aware recovery. Recovery maps fitted on just 100 calibration scenes generalize to held-out scenes and unseen datasets. The resulting models reduce aggregator parameters by up to 44% while maintaining accuracy comparable to their intact counterparts. Code and experimental results will be available at our project page: https://xian-bei.github.io/vggt-family-layer-redundancy/

Residual stream pruning methods reduce inference cost by shrinking the model's hidden dimension, but existing approaches typically choose these dimensions by minimizing activation reconstruction error. This criterion implicitly treats all perturbation directions as equally important, ignoring the sensitivity of downstream layers. We introduce a sensitivity-aware approach to residual-stream pruning that directly accounts for this direction-dependent sensitivity. Using a second-order approximation to the output KL divergence, we characterize the effect of a residual-stream perturbation through both its activation covariance and the local sensitivity of the model output. The resulting subspace selection objective couples these two quantities, but is difficult to optimize directly. We derive a tractable spectral upper bound that reduces subspace selection to an eigendecomposition of a sensitivity-weighted covariance matrix, retaining the efficiency and structural simplicity of rotation-based pruning methods. Across several instruction-tuned language model families, our method consistently reduces calibration KL divergence relative to activation-only pruning and improves perplexity and downstream task performance over a range of compression levels. Our results show that preserving activation energy alone is insufficient for residual-stream pruning, and that explicitly accounting for how perturbations propagate to the model output provides a more effective criterion for selecting dimensions to remove.

Pruning large pre-trained transformer-based ASR models such as OpenAI's Whisper has seen great adoption, as pruning the decoder led to significant end-to-end transcription speedups. For instance, the {\tt whisper-large-v3-turbo} variant reduced the decoder from 32 to 4 layers, while Distill-Whisper similarly reduced the decoder to only 2 layers. Although some attention has been put towards reducing the size of the encoder, no approach has seen wide adoption. This could be due to the need for custom inference implementations to take advantage of the compressed model. We present an approach that ranks encoder layers by the leave-one-layer-out change in Word Error Rate (WER). The six layers that cause the least change are removed, corresponding to $18.5\%$ of the encoder stack. The pruned model requires no custom inference code as it is simply a more shallow encoder with fewer layers. We further distill using unlabeled monolingual speech data to recover performance degradation caused by the zero-shot layer pruning. Mean WER across four languages increases to $20.1\%$ after distillation, compared to $21.9\%$ zero-shot, going from a baseline of $18.2\%$. We release all of our code (https://github.com/rasgaard/whisper-encoder-layer-prune) and the pruned model (https://huggingface.co/rasgaard/whisper-large-v3-turbo-encoder-pruned).

Depth pruning reduces large language model (LLM) inference cost by removing complete Transformer blocks. Activation-based methods collect hidden states through forward passes on calibration data, while existing forward-free methods score each Transformer block separately without measuring similarity between blocks. We propose Weight-Redundancy Pruning (WRP), a forward-free depth-pruning method that estimates inter-layer redundancy from checkpoint weights to select blocks without calibration data or model forward passes. WRP compares attention output and MLP down-projection weights across layers and combines their pairwise similarities with relative projection-scale information. The resulting all-pairs similarity matrix guides layer grouping and block selection. Across multiple pruning settings, model families, and downstream tasks, WRP consistently outperforms existing forward-free magnitude pruning and approaches the performance of activation-based methods.

Pathology foundation models improve transferable representation learning for histopathology, but recent gains often rely on encoders with hundreds of millions of parameters and high inference cost. We propose TAP-Path, a task-adaptive compression framework that directly restructures a pretrained Virchow2 encoder rather than distilling it into a separate student. TAP-Path combines validation-driven transformer-block selection, physical removal of redundant blocks, input-adaptive patch-token pruning, multi-depth feature recovery, and a lightweight gated task head. The final model retains 24 of 32 transformer blocks and 70% of patch tokens after pruning, reducing encoder parameters by 24.96% (631.24M to 473.70M) and analytical encoder compute by 35.20% (340.13G to 220.40G FLOPs). Across three task-head optimization seeds, TAP-Path achieved $87.98 \pm 0.067$ test accuracy, $81.26 \pm 0.49$ balanced accuracy, and $82.38 \pm 0.48$ macro-F1 on a 32-class histopathology benchmark, compared with 86.89% for full Virchow2 and 87.67% for UNI2-h. TAP-Path achieved a Brier score of $0.1800 \pm 0.0005$ and failure-detection AUROC of $0.9047 \pm 0.0060$. A validation-only rare-aware objective improved rare-class balanced accuracy in a secondary operating analysis. Frozen external evaluation on 433 CPTAC samples yielded $91.22 \pm 0.83$ accuracy and $91.10 \pm 0.81$ balanced accuracy. These results show that task-adaptive structural and token sparsification can improve the accuracy-efficiency trade-off of large pathology foundation models while preserving reliability under internal and external evaluation.

Removing complete transformer layers preserves a standard serving architecture, but existing depth-compression methods can lose substantial quality, and the loss varies unpredictably across models. We introduce XMerge, a post-training method with two components. Cross-axis selection identifies a block with low relative-magnitude and angular hidden-state change, and local boundary reconstruction re-fits the adjacent surviving block to match the original two-block output. XMerge uses no task labels or end-to-end fine-tuning, and it introduces neither architectural changes nor additional inference-time parameters. Across seven Llama and Qwen backbones (0.5B-8B), five published baselines, and three layer-reduction levels, its advantage over baselines is largest at the most aggressive removal: at k=4 it ranks first on six of seven backbones on CORE (a 22-task aggregate) and, separately, on six of seven on MMLU (five of seven on both at once), while avoiding the large perplexity increases of several competing operators. In a task-level bootstrap, the 95% confidence intervals for the three largest CORE margins exclude zero; the remaining margins are consistent with ties. Across the 14 (model, regime) cells it is also the only evaluated operator that never collapses, ranking top-2 in both zero-shot and in-context regimes; on a first calibration probe (one backbone) it is the best-calibrated operator. Ablations show that local reconstruction provides most of the gain, while cross-axis fusion helps when the two selection axes disagree. The additional construction cost is recovered through per-token decode savings after roughly tens of thousands of requests.

Depth pruning removes entire Transformer blocks to reduce the inference cost of large language models, but disrupts the hidden-state distributions expected by downstream layers, leading to significant accuracy loss. We introduce SHIFT-LLM, a training-free post-pruning correction framework that inserts a Linear Residual Adapter (LRA) at each pruning site. Each LRA preserves the identity pathway of the original residual block and adds a lightweight affine residual correction. This correction is calibrated via closed-form least-squares regression on a small held-out set, without gradient computation, to approximate the missing residual update produced by the pruned block. Together with the preserved identity pathway, the resulting LRA output approximates the hidden state produced by the original block, thereby mitigating the distributional mismatch introduced by layer removal while avoiding the expensive attention and feed-forward computations of the removed blocks. The resulting LRAs support low-rank factorization and exact merging across consecutive pruned layers for additional compression, and combine naturally with parameter-efficient fine-tuning for further recovery beyond fine-tuning the pruned model alone. Experiments on five model families, six layer-selection criteria, and seven zero-shot benchmarks show that SHIFT-LLM consistently recovers accuracy lost to depth pruning across most configurations, achieving gains up to +15.7 points on Llama-3.1-8B-Instruct while requiring only a few hundred calibration samples and no gradient computation.

With the rapid development of large-scale pre-trained language models based on Transformer architectures, their high computational and memory costs have become a major obstacle to deployment, especially in resource-constrained environments. Traditional pruning methods typically depend on full gradient-based importance estimation, and they necessitate prior finetuning of the model to achieve satisfactory performance. This process often results in intolerable resource consumption. This paper proposes REP-LIE, a new approach to enable resource-efficient pruning during the process of finetuning. REP-LIE leverages the gradients of LoRA low-rank matrices to estimate the importance of weights without requiring full gradient computation. To address the inherent randomness in importance estimation, a stability score is introduced, serving as the basis for iterative pruning of unimportant model parameters. The pruned model is further finetuned through lightweight updates, eliminating the need for full-parameter optimization in the process of finetuning. Extensive experiments on both medium-scale encoder models and large-scale generative models (LLaMA-7B and Mistral-7B) demonstrate that REP-LIE still achieves competitive performance compared to existing approaches.

Structured pruning of attention heads provides a hardware-friendly way to compress Transformer language models. However, existing methods for measuring head-level importance require calibration data, gradient computation, or Hessian estimation. These requirements add extra overhead and make the methods depend on the data. Our work presents Magnitude Profile (MP) scoring, a training-free criterion for head importance that identifies dispensable heads through statistical outlier detection on weight row norms. Heads whose projection weights fall within the population bulk are pruned, while heads exhibiting outlier norms, which carry disproportionate representational capacity, are preserved. Our work further gives MP-G, a variant that handles Grouped Query Attention (GQA) by distributing shared key-value group scores across associated query heads. Across five models evaluated on WikiText-2 perplexity at 12.5%-50% head sparsity, MP-G achieves the best perplexity on OPT-6.7B at all sparsity levels (18.46 at 12.5%, 27.87 at 25%, 152.0 at 50%). MP-G also gives the best results on RoBERTa-large at 12.5% and 25% sparsity, with perplexity values of 7.27 and 10.28, outperforming calibration-dependent baselines including Wanda-Head, SparseGPT-Head, and Gradient-Head. It requires zero forward passes, calibration samples, or gradient computation. At 50% sparsity, head pruning yields up to 16% parameter reduction with 50% attention FLOP savings. Our results show that weight-only statistical scoring can match or outperform data-dependent methods for structured head pruning, providing a practical, zero-cost criterion for Transformer compression.

Existing adaptive inference methods for Large Language Models rely on observational heuristics, such as hidden-state similarity or activation magnitudes, to drop redundant modules. However, these correlation-based metrics often fail to capture subtle, non-linear structural computations vital for semantic accuracy. We introduce CausalGate, an intervention-guided framework for compute-efficient transformer inference. During a calibration phase, CausalGate isolates individual Attention and MLP sub-layers, zeros out their respective outputs, and measures the exact semantic damage via the Kullback-Leibler divergence of the final logit distribution. To eliminate runtime routing overhead, this structural importance hierarchy is distilled into a global set of static, lightweight scalar gates using an Exponential Moving Average smoothing objective paired with a differentiable pairwise ranking loss. Evaluated on TinyLlama-1.1B, Qwen2.5-3B, and Llama-3.1-8B across language modeling and commonsense reasoning benchmarks, CausalGate consistently outperforms prominent dynamic routing and layer-skipping baselines, translating theoretical compute savings into concrete hardware latency reductions with zero operational overhead.

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.

One-shot pruning methods like Wanda and SparseGPT apply the same sparsity ratio to every layer of a transformer, ignoring known variation in layer importance. We propose PALS (Percentile-Aware Layerwise Sparsity), which adjusts per-layer sparsity based on the 99th percentile of activation magnitudes, bounded to $\pm 5\%$ around the target ratio. On LLaMA-2-7B at 50% sparsity, PALS achieves 10.96 WikiText-2 perplexity versus 12.92 for uniform Wanda (mean over 9 runs, $p < 0.001$). The benefit is architecture-dependent: LLaMA-3-8B shows marginal gains and Mistral-7B shows none. We also find that gradient-based allocation -- the seemingly more principled approach -- produces results worse than random, suggesting that gradient magnitude does not predict the impact of discrete weight removal. PALS adds negligible cost to the pruning pipeline and requires no fine-tuning.

Deep Transformers are composed of uniformly stacked residual blocks, yet their deepest layers often add little value. We present two efficiency methods that exploit this asymmetry. CascadeFormer tapers width with depth to match the uneven information flow across layers, achieving comparable perplexity to a uniform baseline at the same training budget while reducing latency by 8.6% and increasing throughput by 9.4%. CascadeFlow Pruning removes layers using accumulated training gradients, with no post hoc analysis. It outperforms standard heuristics on perplexity and rank-stability and stays competitive on downstream accuracy. To motivate these methods, we propose Gradient Fan-in Asymmetry (GFA) as a structural account of why deeper layers contribute less. In Pre-LayerNorm residual stacks, the gradient at a layer is the sum of an identity path and all downstream functional paths, producing a gradient fan-in that decays linearly with depth (and quadratically under deep supervision), yielding richer gradients for early layers and sparser ones for later layers. We provide correlational and interventional evidence for GFA on models trained from scratch up to 1.2B parameters. Across Transformers and ResNets, accumulated training gradients follow the theoretical fan-in and are associated with post hoc layer importance. Two interventions point to structure rather than magnitude as the bottleneck: equalizing per-layer gradient norms does not restore late-layer value, while increasing downstream path counts via parameter-shared repetition restores and elevates it. Whether gradient magnitude proxies fan-in beyond high-rank regimes, and how these dynamics behave at the 100B+ scale, remain open questions.

Feed-forward networks (FFNs) dominate the parameter count and computation of modern language models, yet existing pruning methods often struggle to convert sparsity into hardware-friendly inference efficiency gains. We introduce PrunePath, a budget-adaptive structured sparsification framework for FFN layers. Built on MoEfication, PrunePath replaces independent expert-wise thresholding with a softmax-normalized routing distribution and activates important experts under a cumulative-mass threshold. This formulation imposes a token-level probability budget, enabling adaptive expert counts and a direct inference-time sparsity knob from a single checkpoint. Across NLU, NLG, and instruction-tuning evaluations, PrunePath achieves a favorable sparsity--performance trade-off compared with existing static pruning and MoEfication-based methods. We further implement Triton kernels for KV-cache decoding to translate the resulting structured sparsity into practical memory savings and measurable decoding-speed improvements. These results demonstrate the superior performance of PrunePath for building highly sparse, deployment-friendly large language models.

Large Language Models (LLMs) have experienced significant growth and development in recent years. However, performing inference on LLMs remains costly, especially for long-context inference or in resource-constrained devices. This motivates the development of new post-training pruning (PTP) methods. These methods reduce LLMs' requirements by removing a substantial part of the model's parameters. The discarded weights are selected depending on their impact on the models performance. Current PTP methods prune the models by removing the less informative hidden nodes from the FFN layers, and the least important attention layers. We propose Putri, a PTP method that introduces three changes to the State-of-the-art. First, we update the un-pruned weights of the FFN to compensate for the introduced pruning error. Second, the FFN layers are pruned sequentially, taking into account the updates done to the previous layers. Third, instead of removing full attention layers, we remove individual attention-heads. We extend this method such that it can also address Grouped-Query Attention. In summary, Putri is a structure pruning method which remains simple while showing SOTA performance. Pruning experiments on multiple models with a wide variety of sparsity ranges and on different datasets, validate the generality of Putri. Notably, we demonstrate that, unlike previous methods, Putri can prune LLMs on extreme sparsity ratios. The code is available at: https://github.com/Coello-dev/Putri.

When researchers ask whether two transformer layers are "equivalent" for compression, they often conflate distinct tests. Replacement asks whether one layer's map can substitute for another's in place; interchange asks whether two layers approximately commute when their positions are swapped. Both are output-grounded swap-KL probes, but they need not agree: on pretrained transformers the protocol gap can change which layers look safe to prune by several-fold under the same evaluator, especially when replacement distances are high. We measure both protocols across checkpoints and architectures. On a Pythia training trajectory (410M and 1.4B), the replacement-interchange gap grows from initialization to convergence. Under one matched WikiText-2 contract at 8B scale, Qwen3-8B enters a divergent regime: interchange-guided removal is several-fold safer than replacement-guided at the same layer budgets, while Llama-3.1-8B ties the two protocols for pruning cost even though interchange KL is lower, showing metric gaps need not map one-to-one to removal. Before layer removal or merging, score both swap-KLs on the target checkpoint; the diagnostic requires only unlabeled forward passes.

Layer pruning removes entire Transformer decoder blocks from large language models, but introduces a mismatch between the hidden state received by the next surviving layer and the distribution it was trained to process, leading to significant performance degradation. We propose Ghosted Layers, a training-free recovery module that addresses this issue by solving a boundary activation alignment problem. Our method derives a closed-form optimal linear operator from a small calibration set to reconstruct the activation discrepancy introduced by the pruned layers. We show that this solution corresponds to the unconstrained optimum of the alignment objective, whereas existing methods are restricted to constrained solutions over limited operator subspaces. Experiments across multiple LLM backbones and pruning strategies demonstrate that our method consistently improves accuracy and perplexity over prior training-free baselines, while preserving the efficiency gains of layer pruning. Official code repository: https://github.com/daniel-eai/ghosted_layers_official_repository/.

Weight pruning is a common technique for compressing large neural networks. We focus on the challenging post-training one-shot setting, where a pre-trained model is compressed without any retraining. Existing one-shot pruning methods typically optimize a single objective, such as a layer-wise reconstruction loss or a second-order Taylor approximation of the training loss. We highlight that neither objective alone is consistently the most effective across architectures and sparsity levels. Motivated by this insight, we propose MOONSHOT, a general and flexible framework that extends any single-objective pruning method into a multi-objective formulation by jointly optimizing both the layer-wise reconstruction error and second-order Taylor approximation of the training loss. MOONSHOT acts as a wrapper around existing pruning algorithms. To enable this integration while maintaining scalability to billion-parameter models, we propose modeling decisions and introduce an efficient procedure for computing the inverse Hessian, preserving the efficiency of state-of-the-art one-shot pruners. When combined with state-of-the-art pruning methods on Llama-3.2 and Llama-2 models, MOONSHOT reduces C4 perplexity by up to 32.6% at 2:4 sparsity and improves zero-shot mean accuracy across seven classification benchmarks by up to 4.9 points. On Vision Transformers, it improves accuracy on ImageNet-1k by over 5 points at 70% sparsity, and on ResNet-50, it yields a 4-point gain at 90% sparsity.

Compressing transformer weights makes large language models cheaper to deploy. But each layer's compression introduces an error. These errors accumulate as the signal passes through later layers, and how they accumulate is not well understood. We measure this directly: at each layer, we take the ratio of output to input error, calling it rho. A value below one means the layer absorbs the error; above one means it grows. Computing rho on six transformers (117M to 8B parameters) yields three findings. (i) Errors at layer t scale downstream by the product of later rho values, predicting representation drift (Spearman r = -0.44, p < 10^-4). This explains why compressing early layers hurts more than late ones, and why depth-decreasing sparsity schedules outperform uniform ones. Across architecture families, however, model width and redundancy matter more than rho alone. (ii) Within a layer, naive pruning shows a ~600x spread in component sensitivity. Activation-aware pruning (Wanda) shrinks this to 3-7x; the ranking reverses across architectures, so fixed importance scores do not transfer. (iii) For depth pruning, ranking layers by how far rho is from one takes two forward passes. It beats ShortGPT's Block Influence with 1.6x lower perplexity at eight layers removed, and physical deletion delivers 1.22x wall-clock speed-up. A blend of the two criteria does best (perplexity 14.2, 60.0% downstream accuracy on LLaMA-2-7B). Twelve Lean 4 norm inequalities provide machine-checked per-matrix error bounds. The contraction profile thus gives a training-free instrument for two decisions: where to compress within layers, and which to remove.

Pruning is widely recognized as an effective method for reducing the parameters of large language models (LLMs), potentially leading to more efficient deployment and inference. One classic and prominent path of LLM one-shot pruning is to leverage second-order gradients (i.e., Hessian), represented by the pioneering work SparseGPT. However, the predefined left-to-right pruning order in SparseGPT leads to suboptimal performance when the weights exhibit columnar patterns. This paper studies the effect of pruning order under the SparseGPT framework. The analyses lead us to propose ROSE, a reordered SparseGPT method that prioritizes weights with larger potential pruning errors to be pruned earlier. ROSE first performs pre-pruning to identify candidate weights for removal, and estimates both column and block pruning loss. Subsequently, two-level reordering is performed: columns within each block are reordered in descending order of column loss, while blocks are reordered based on block loss. We introduce the relative range of block loss as a metric to identify columnar layers, enabling adaptive reordering across the entire model. Substantial empirical results on prevalent LLMs (LLaMA2-7B/13B/70B, LLaMA3-8B, Mistral-7B) demonstrate that ROSE surpasses the original SparseGPT and other counterpart pruning methods. Our code is available at https://github.com/mingluo-su/ROSE.

Time Series Foundation Models (TSFMs) leverage extensive pretraining to accurately predict unseen time series during inference, without the need for task-specific fine-tuning. Through large-scale evaluations on standard benchmarks, we find that leading transformer-based TSFMs exhibit redundant components in their intermediate layers. We introduce a set of tools for mechanistic interpretability of TSFMs, including ablations of specific components and direct logit attribution on the residual stream. Our findings are consistent across several leading TSFMs with diverse architectures, and across a diverse set of real-world and synthetic time-series datasets. We discover that all models in our study are robust to ablations of entire layers. Furthermore, we develop a theoretical framework framing transformers as kernel regressors, motivating a purely intrinsic strategy for ablating heads based on the stable rank of the per-head projection matrices. Using this approach, we uncover the specific heads responsible for degenerate phenomena widely observed in TSFMs, such as parroting of motifs from the context and seasonality bias. Our study sheds light on the universal properties of this emerging class of architectures for continuous-time sequence modeling.