Weight-Space Analysis

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1 paper in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

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Latest papers 28

Oct 1, 2026cs.LG

CrossGMN: Graph Metanetworks for Cross-Architecture Weight-Space Transformations

Weight-space networks operate directly on parameters of other neural networks, enabling tasks such as predicting model properties, editing trained models, and generating weights. Weight-space symmetries such as neuron permutations make equivariance a key design principle. However, existing equivariant weight-space architectures have primarily been studied for transformations that preserve the network architecture. In contrast, many practical transformations, including model compression and upscaling, map a trained source network into a target network with a different architecture. In this setting, the source and target permutation symmetries act on different parameter spaces, making equivariance less straightforward to formulate. Our key idea for addressing this mismatch is to reformulate cross-architecture operators with two inputs: a trained source network and an initialization of the target network. This lets us define equivariant cross-architecture operators that refine the initialization of the target network using information from the source network, while being invariant to source-network permutations and equivariant to target-network permutations. Based on this formulation, we introduce CrossGMN, a graph metanetwork that jointly processes both networks through symmetry-preserving cross-network message passing. We prove CrossGMN is universal for continuous cross-architecture operators on compact sets under a general-position assumption. We evaluate CrossGMN for model compression, predicting a smaller network's parameters to accelerate subsequent knowledge distillation. Across 2-D and 3-D INRs and image classification with MLPs, CNNs, and Vision Transformers, CrossGMN speeds up distillation by up to 8.89x, transfers across datasets without retraining (3.78x), and a single model can accelerate compression from heterogeneous source architectures into a common target architecture.

Adir Dayan, Yam Eitan, Haggai Maron

Technion – Israel Institute of Technology · NVIDIA Research

Model Compression Hypernetworks Weight-Space Analysis Equivariant GNNs

Sep 3, 2026cs.LG

Spectral characteristics of autoencoder parameters as a vector representation of data

This paper examines the relationship between the parameters of autoencoder models and the statistical properties of the data on which they are trained. Autoencoders are defined as models with an encoder-decoder architecture, trained to reconstruct input data through a compressed latent representation. It is proposed that the model parameters can be viewed as a dense vector representation of the corresponding sample. To test this hypothesis, a theoretical and experimental study is conducted in which a vector representation is formed based on the spectral characteristics of the autoencoder parameter matrices. Theoretical analysis shows that the singular values of the model parameter matrices are related to the eigenvalues of the covariance matrix of the training data, ensuring the transfer of information between the data space and the parameter space. Experimental results on the CIFAR-10 and FashionMNIST datasets confirm that the resulting vector representations allow for a high degree of accuracy in distinguishing between models trained on different data subsets, without resorting to complex vector generation algorithms or using the original samples. These results suggest that the parameters of trained autoencoders can be viewed as sample representations.

Maria Nikitina, Anton Bishuk, Oleg Bakhteev

Representation Learning Autoencoders Weight-Space Analysis

Aug 10, 2026cs.LG

When Do Task Vectors Interfere? Mapping the Validity Boundaries of Weight-Space Composition

Task arithmetic composes skills by adding weight displacements, and merged models are then judged on benchmark suites. We measure when that composition is functionally additive, and find that the answer depends as much on how the model is prompted as on which tasks are merged. Across two-dimensional composition surfaces -- five model settings from 0.5B to 8B, two families, LoRA and full fine-tuning -- pairwise non-additivity is real, seed-stable, and transfers in coarse order to unseen task pairs: all eight preregistered sign predictions held. But it is input-conditioned everywhere we measured: the same merged model that shows a six-point interaction contrast on code prompts shows none on math prompts, and wrapping the identical code prompts in the instruction template the adapters were trained on collapses the contrast twenty-fold, from +6.9 to +0.3 points -- while re-serializing them in an untrained chat template leaves it intact (+12.5), falsifying our own preregistered prediction. Execution benchmarks (pass@1) inherit the training-format wrapper's blindness. Weight-space composition therefore supports coarse, input- and format-conditioned functional statements -- not a universal merging-performance predictor, and not one that training-format evaluations can see.

Chencheng Zhu, Xiaoyang Li, Taotao Cai

UNSW Sydney · University of Southern Queensland

Prompt Sensitivity Weight-Space Analysis Task Arithmetic Model Merging

Aug 7, 2026cs.AI

Who Built This Model? Tracing LLM Lineage via Spectral Fingerprints in Weight Space

Open-weight large language models (LLMs) are increasingly developed through complex, multi-stage pipelines, leading to intricate lineage relationships that reflect model origin, ownership, and evolution. Understanding these relationships is important for model provenance, governance, and supply-chain integrity. In this work, we investigate the notion of LLM "biometrics" (analogous to human biometrics) to ask whether LLMs exhibit intrinsic fingerprints in weight space alone, without access to input data, that reveal their origin and lineage. We formulate this as a lineage discrimination problem, distinguishing among independent-origin, same-series, and shared-base models. To characterize these relationships, we propose a unified geometric fingerprinting framework that analyzes weight matrices from two complementary perspectives: (i) spectral energy, captured by singular value distributions to encode global magnitude patterns, and (ii) subspace alignment, quantified via subspace deviations to capture directional geometry. Our analysis uncovers a clear hierarchy of structural similarity in weight space: spectral energy reliably distinguishes independently trained models and different model families, while subspace alignment enables fine-grained discrimination among closely related models, including variations in dataset scale and post-training procedures. Extensive experiments on over 110 diverse open-weight LLM pairs demonstrate that weight-space geometry provides a robust and interpretable signal for model lineage, enabling coarse-grained regime separation and fine-grained discrimination within shared-base models.

Yiwei Chen, Bingqi Shang, Sijia Liu

Michigan State University

Language Model Fingerprinting Open-Weight Language Models Weight-Space Analysis

Aug 7, 2026cs.AI

Finding Usable Weight Mechanisms with Tiled SVD

The dominant approach to mechanistic interpretability trains proxy dictionaries such as sparse autoencoders and labels features from max-activating text. The best such atlases identify con- cepts, but that identity lives in the learned dictionary rather than in the network weights them- selves. We propose extracting mechanism mounts directly from linear sites by column-tiled SVD: each mount is a triple (v,u,σ) read as trigger, write, and strength. Identity is the weight rule. We evaluate mounts with a pre-registered suite judged on full-write energy lift rather than tile-local lift. On Gemma-2-2B with WikiText-2 (16,384-token subsample), all seven linear maps are scored: residual writes (mlp.down, attn.o) receive full A/B/C with steer after post-sublayer RMSNorm and pass 52/52 site-layers; other maps receive A/B only (mlp.gate/attn.q/attn.k/effective mlp.up/attn.v 26/26 each). Aggregate: 182/182 GO. We release library code, the corpus builder, the experiment entrypoint, and unit tests.

Ash Manvi, Samreena Tajreen

Aquin Labs

LLM Interpretability Mechanistic Interpretability Weight-Space Analysis

Aug 4, 2026cs.AI

Cross-Layer Interaction under Weight-Space Ablation: A Closed-Form Attention Jacobian Bound and a Test on a Real Pretrained Model

A companion paper studies when activation patching and weight-space ablation agree, inside an idealized model where a conditional computation is carried additively through a residual stream. For the one composition in that model where two carriers are architecturally dependent, an attention head and its own layer's normalization-MLP composition, it derives an exact first-order interaction formula, zero when only the MLP is ablated and second-order bounded when the head is also ablated. That result is confined to a single residual block and checked only on small transformers on a synthetic task. This paper extends the result past both limits. First, the interaction from ablating carriers spanning several layers decomposes exactly into same-block terms, one per touched layer, plus a cross-layer remainder on which the decomposition makes no claim of smallness. Second, we isolate that remainder exactly, for two layers, as a double integral of a mixed second derivative, and name the missing ingredient needed to bound it: a Jacobian bound for the attention sub-block. We derive this bound in closed form and verify it, without a single violation, against Qwen2.5-1.5B-Instruct's real weights, though we do not yet chain it across layers. We also give, in closed form, the curvature constant the companion paper's bound leaves unexhibited. Third, on that same model, we search for and find an emergent circuit for indirect object identification, never designed into it, using the original activation-patching method for this task, and test collapse, dissociation, and interaction on it. The result is mixed: a shared carrier emerges across all five tested instances, collapse and dissociation hold on most but not all, and a nonzero interaction is measurable on three of five, at layer pairs outside the same-block case the companion theorem covers.

Abdallah Khemais

ISITCOM, University of Sousse

Transformer Interpretability Weight-Space Analysis Activation Patching

Aug 4, 2026cs.LG

A Theory of Conditional Collapse under Low-Rank Weight-Space Ablations: I. The Single-Block Theory and Synthetic Validation

Activation patching and weight-space ablation both claim a component is causally responsible for a behavior, yet they act on different objects: one forward pass versus the parameters behind every forward pass. We ask when they agree. We study an idealized model where a conditional computation is carried additively through a residual stream,

F(x)=F_0(x)+\sum_iα_i(x)v_i

, read out by a linear functional, and prove three exact results. First, deleting a subset of carriers collapses a matched input pair onto the same unconditional output \emph{if and only if} the removal is symmetric on the pair and leaves no outside contrast; the error is deterministic, and we give its exact form even when the two conditions hold only approximately. Second, patching a carrier moves the readout by its donor-receiver \emph{contrast}, while ablating it moves the readout by its \emph{absolute level}; neither bounds the other, and we construct pairs where every single-carrier patch flips the decision while no single-carrier ablation does. Third, for an attention head composed with its own layer's normalization and MLP, we derive an exact first-order interaction formula with a provably second-order remainder, vanishing identically when only the MLP is ablated but not, in general, when a head is. Small transformers trained on a synthetic conditional task illustrate all three predictions: across thirty-nine ablation configurations the measured interaction is strongly rank-correlated with the idealized model's predictive accuracy (Spearman

-0.83

), and a second task and architecture reproduces the same pattern, including a further polarity reversal. The single-block interaction result extends past one residual block, and the synthetic validation is tested against a real pretrained model, in a companion paper that takes this theory further along both axes.

Abdallah Khemais

ISITCOM, University of Sousse

Transformer Interpretability Weight-Space Analysis Causal Interventions in Language Models Activation Patching

Jul 28, 2026cs.AI

Are the High-weight Neurons the Important Ones in Image Classification Neural Networks?

As neural network models for image classification advance, neurons play critical roles in pruning, backdoor defense, and interpretability. Yet existing work lacks clarity on the weight-importance relationship. We address this with a neuron importance assessment method using three experiments: quantifying overlap between high-weight and accuracy-impacting neurons, analyzing high-weight neuron perturbation effects, and testing post-retraining accuracy after high-weight neuron ablation. Experiments on CIFAR-10 and Mini-ImageNet reveal key patterns. Overlap analysis shows top 10% high-weight neurons overlap with important ones by only about 25% at maximum, dropping further in subsequent intervals. Perturbation tests find top 10% high-weight neurons cause 45-80% accuracy degradation under certain operations compared to 3-7% for random perturbations, but a third of them show minimal impact. Ablation-retraining results show removing top 10% high-weight neurons leaves accuracy 10-20% below baseline with no recovery, while ablating top 0.1% allows near-full recovery. Notably, some low-weight intervals show 10-17% degradation when perturbed, comparable to mid-range high-weight neurons. These results confirm not all high-weight neurons are important: their importance is nonlinear. Low-weight neurons also contribute significantly. This challenges weight-importance equivalence, offering refined neuron role insights. It supports applications like encryption prioritizing critical high-weight neurons and pruning removing non-critical ones, advancing neural network analysis.

Qitao Chen, Dongfu Yin, F. Richard Yu

WeBank Institute of FinTech, ShenZhen University, YueHai, ShenZhen, 518060, GuangDong, China. · Artificial Intelligence and Digital Economy Guangdong Provincial Laboratory, YuTang, ShenZhen, 518132, GuangDong, China.

Neural Network Interpretability Weight-Space Analysis Image Classification

Jul 17, 2026cs.LG

Neural spectroscopy of AlphaFold2 reveals encoded protein conformational landscapes

AlphaFold2's 93 million parameters, shaped by the evolutionary record of protein structure encoded in the Protein Data Bank and in sequence alignments, are conventionally treated only as machinery for converting sequence to structure. We propose they are also a scientific object that can be analyzed directly: a learned encoding of protein conformational organization that can be probed and characterized. By smoothing the Evoformer's weight tensors with a Gaussian convolution and scaling the result, we show that the trained model produces physically structured conformational landscapes. Under perturbation, ubiquitin's native contacts break in the order established by decades of folding experiments. For KaiB, five independently trained models agree that the alternative fold is not recovered under perturbation. For alpha-synuclein, five models produce five different but coherent landscapes, mapping where the training signal has determined the representation and where it has not. Matched-power noise controls confirm that random corruption of equal magnitude produces debris, not conformations. The model learned to predict static structures; the conformational organization visible under perturbation was not an explicit training target, suggesting it emerged as a byproduct of that objective. AlphaFold2's weights appear to encode structural constraints, shaped by evolutionary and structural training data, that extend beyond what unperturbed inference reveals. We call the approach of reading them neural spectroscopy, and Scaled Gaussian Convolution one such protocol.

Kaustav Mehta

Independent researcher, India

Protein Structure Prediction Neural Network Interpretability Weight-Space Analysis Protein Representation Learning

Jul 8, 2026hep-lat

Weight-Space Physics: Interpretable Hypernetworks for Lattice Quantum Field Theories

Lattice field theory is the workhorse of non-perturbative physics, used to simulate phenomena from the strong nuclear force to critical phenomena in materials. Its Boltzmann distributions are parametrized analytically by coupling constants, but these bare parameters are weak predictors of observables -- extracting physics typically requires extensive simulation. While normalizing flows have emerged as effective samplers at fixed couplings, it remains difficult to interpret what these networks have learned. This raises a natural question: can the physics be read off directly from the flow network parameters themselves, and can those parameters be generated for unseen theories? We propose lattice field theory as a testbed for neural network interpretability: because the target physics is qualitatively well-understood and smoothly varying, it provides ideal synthetic data with known ground truth. To this end, we introduce JEPAWG, a Joint-Embedding Predictive Architecture-based Weight Generator that maps couplings directly to flow weights via a learned latent space. On a scalar theory at lattices of size

6^2

to

11^2

, the JEPAWG latent space recovers the correct intrinsic dimension of the underlying manifold, locates the phase transition, and encodes a finite-size shift aligned with the 2D Ising exponent

ν\approx 1

, allowing us to uncover physical structure by studying the network weights alone. This suggests the fascinating idea of treating the network weights as a new type of physical observable. As a generator, JEPAWG also interpolates and extrapolates to unseen couplings effectively and remains robust to weight-space discontinuities introduced by multi-seed training data, outperforming PCA, AE, and VAE baselines.

Tobias Göbel, Julian R. Ebelt, Zier Mensch +2

Institute of Physics, University of Amsterdam, Amsterdam, Netherlands · Department of Physics, National Taiwan University, Taipei, Taiwan · Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA +2

Phase Transitions Neural Network Interpretability Hypernetworks Weight-Space Analysis

Jul 3, 2026cs.LG

Observable- and Positional-Encoding-Dependent Symmetry Readout from Neural Network Weights

Post-hoc analysis of trained neural network weights often seeks to recover geometric structure directly from the parameters. We show that, for positional-encoding-equipped neural fields, the symmetry visible from weights is not the true symmetry group itself, but an observable symmetry set determined by the trained parameters, the positional encoding (PE), and readout observable. We formulate this dependence through an exact observability hierarchy,

G_{\mathrm{obs}}^{\mathrm{exact}} \subseteq G_{\mathrm{lift}}^{\mathrm{exact}}(φ) \cap G_{\mathrm{true}}

, where

G_{\mathrm{lift}}^{\mathrm{exact}}(φ)

is the set of input transformations that the PE can exactly lift to the feature space. The hierarchy implies that even when a target function has a geometric symmetry, that symmetry may be structurally invisible to weight-level observables if the PE does not represent the corresponding transformation. We test this prediction using MLPs trained on two-dimensional signed distance functions with multiple shape symmetry groups, positional encodings, and Gram-based observables. The results show a consistent PE-dependent pattern: DyadicAxisPE supports

D_4

-sensitive readout but structurally suppresses

D_3

rotations, TriAxisPE yields lower

D_3

/

D_6

readout scores under the tested Gram observables by replacing coordinate axes with three 120-degree-separated axes, and random Fourier features mainly exhibit a

π

-rotation response under these readouts. These findings show that PE design affects not only approximation behavior but also which structures are accessible to post-hoc weight-level readouts. This provides a basis for a principled observable-dependent symmetry readout.

Naoya Chiba, Satoshi Sugiyama, Yuki Uranishi

D3 Center, The Unversity of Osaka

Neural Representation Geometry Implicit Neural Representations Positional Encoding Weight-Space Analysis

Jul 2, 2026cs.LG

WARP: Weight-Space Analysis for Recovering Training Data Portfolios

Foundation models are routinely released to the public, yet the data recipes used to train them -- such as domain mixture weights that determine how different sources are sampled -- are rarely disclosed. This creates an access asymmetry: researchers study the resulting models but lack visibility into the training distribution that produces them. Prior works for inferring training data, such as membership inference, detect at the level of individual samples and thus cannot characterize the global composition of the training corpus. We introduce WARP, a framework that recovers a fine-tuned model's training mixtures directly from its released weights. WARP interpolates between the base and fine-tuned models using model merging, generating pseudo-checkpoints that approximate the missing training trajectory and expose a geometric footprint of the training data in the weight space. From these simulated footprints, WARP extracts geometric features and maps them to domain proportions using either a parameter-free softmax readout or an MLP projector trained on synthetic mixtures. In controlled experiments with BERT and GPT-2, WARP recovers domain mixtures with an average MAE as low as 0.046 and 0.104 respectively, outperforming membership inference and a variant with access to the true training trajectory.

Tzu-Heng Huang, Aditya Goyal, John Cooper +1

University of Wisconsin-Madison

Weight-Space Analysis Training Data Attribution

Jun 21, 2026cs.LG

Weight-Space Geometry of Offline Reasoning Training

Offline reinforcement-learning losses (RFT, RIFT, DFT, Offline GRPO, DPO) are widely used to distill reasoning from large teachers into smaller students, and are typically compared on downstream accuracy alone. We ask whether they are mechanistically distinct or converge to a similar weight update. Training six methods (SFT, RFT, DFT, RIFT, Offline GRPO, DPO) on identical math rollouts from a single base model (Qwen3-4B) with attention-only LoRA, we analyze the resulting deltas via cosine similarity, principal-angle subspace analysis, linear mode connectivity, and CKA. We observe: (i) SFT, RFT, and RIFT have nearly colinear weight deltas (cosine >= 0.97, top-1 principal angle ~7 deg median over 144 modules) and comparable GSM8K accuracy (87-88%, n=1319; pairwise McNemar p >= 0.15); (ii) DFT diverges further in direction than any reward-weighted method despite using the same data; (iii) Offline GRPO adds a substantial component orthogonal to the SFT direction (~67% globally, up to ~86% in late layers) while staying in the SFT loss basin; (iv) DPO sits in a near-orthogonal subspace, shows a mode-connectivity barrier, and collapses late-layer CKA to ~0.46. DPO also reaches the highest accuracy in our protocol on both GSM8K (93.5%, McNemar p < 10^-9 vs. each other method) and AIME26 (30.0% vs. 3.3-10.0%); its training uses a 10x smaller learning rate than the others (the standard convention), so the update-norm and accuracy gaps reflect loss-function and optimizer choices jointly, and a learning-rate-matched DPO comparison is left for future work.

Aleksandr Nikolich, Igor Kiselev, Vladimir Platonov +1

1Keenable AI · 2Accenture · 3Yandex

RL for Language Models Direct Preference Optimization Offline RL Weight-Space Analysis Language Model Distillation

Jun 11, 2026cs.LG

Different Layers, Different Manifolds: Module-Wise Weight-Space Geometry in Transformer Optimization

Weight-space geometry plays a central role in neural network optimization, yet manifold constraints are often applied uniformly across all weight matrices. In this work, we ask whether different transformer modules prefer different manifold geometries. We study Manifold Muon for GPT-2 pretraining and compare layer-wise assignments of Stiefel and DGram constraints across attention and MLP blocks. Our results show a clear asymmetry: constraining attention layers with Stiefel geometry while assigning DGram geometry to MLP layers gives the best performance among the tested configurations, whereas the inverted assignment and all-DGram configuration become unstable under the shared hyperparameter setting. We trace this failure to singular value growth in DGram-constrained attention weights, which can amplify attention logits and induce softmax saturation. These findings suggest that symmetry-aware and geometry-aware optimization for transformers should be module-specific rather than uniform.

Kirato Yoshihara

School of Engineering Science, The University of Osaka, Osaka, Japan.

Stiefel Manifold Optimization Neural Network Optimization Weight-Space Analysis Constrained Optimization Neural Network Training Dynamics

Jun 11, 2026cs.LG

Weibull Weight-Scale Parameter Evolution under AdamW Training Dynamics

Building on a two-parameter Weibull framework for diagnosing transformer weight distributions, we study why the Weibull weight-scale parameter

λ

grows, overshoots, and then relaxes during AdamW training. We derive a leading-order three-force decomposition of the squared weight norm from the AdamW update: an alignment force measuring the correlation between weights and the adaptive update direction, an injection force from adaptive step magnitude, and a decay force from decoupled weight decay. On self-trained Pythia-70M models with ground-truth optimizer moments, alignment dominates the rise phase, contributing 88-94% of the absolute force budget across four random seeds and remaining robust to super-weight removal. Near saturation, alignment and decay approach balance, explaining the transition from weight-scale growth to relaxation. These force dynamics directly govern the squared-norm component underlying

λ(t)

; the remaining RMS-to-Weibull reconstruction offset is measurable and decomposes into bridge and integration components, totaling approximately 5-6% in densely sampled regions. To extend the analysis to real models where optimizer moments are unavailable, we introduce a spline displacement method that recovers the alignment force from sparse checkpoints with approximately 92-94% accuracy, about twice the naive two-point baseline. We further observe that the peak value of

λ(t)

varies with training-data coherence in our experiments, suggesting a data-dependent component of weight-scale growth that we leave to a controlled follow-up study. Code and data are available at https://github.com/tiexinding/NPM-Weibull-public.

Tiexin Ding

Independent Researcher.

Weight-Space Analysis Adaptive Gradient Methods Neural Network Training Dynamics

May 30, 2026cs.LG

Exploiting weight-space symmetries for approximating curvature

Many machine learning techniques rely on approximating a loss function's curvature, but this is notoriously hard to do at the scale of modern deep networks. Surprisingly, no previous work has exploited the curvature constraints that arise from well known weight-space symmetries in loss landscapes. By analytically averaging over group actions that leave the loss invariant, we construct structured Hessian approximations from single gradients that can be tractably estimated, stored, and inverted. The choice of user-specified symmetry group directly governs the trade-off between approximation accuracy and computational cost. Moreover, our framework provides a unifying theoretical lens for viewing existing methods; in particular, a specific choice of symmetry group recovers Shampoo/Muon-like curvature estimates. We validate our method on a range of network architectures, and deploy it to second-order optimization benchmarks, including a small language model. Our curvature estimation framework might find applications in other machine learning problems such as uncertainty estimation, continual learning, compression/pruning, training data attribution, and more.

Artem Artemev, Rui Xia, Benjamin M. Boyd +4

MediaTek, Cambridge, UK · University of Cambridge, Cambridge, UK · Vector Institute, Toronto, Canada

Neural Network Optimization Second-Order Optimization Weight-Space Analysis Loss Landscape Geometry

May 28, 2026cs.LG

Access Sets Matter: Budgeting Expert Reads for Scalable Weight-Space Model Merging

Weight-space model merging is usually formulated as an algebraic operation on checkpoints, yet at LLM scale the limiting resource is often the set of expert weights that must be read. We introduce MergePipe, a budget-aware execution layer that casts LLM merging as an \emph{expert access-set} problem: given a merge operator and a checkpoint family in a shared weight coordinate system, choose which expert delta blocks to access under an explicit I/O budget. MergePipe indexes parameter blocks, builds deterministic access plans, and executes the induced budgeted merge with replayable manifests. The plan is budget-sound by construction and recovers the full-read merge at full budget; for fixed-coefficient additive operators, the omitted-update error is bounded by the norm of omitted deltas. Across Qwen and Llama merging workloads, MergePipe reduces expert-read I/O by up to an order of magnitude and achieves up to

11\times

speedups. Representative budget sweeps show

O(10^{-3})

parameter deviation from full-read merges and no monotonic degradation on downstream benchmarks.

Yuanyi Wang, Yanggan Gu, Su Lu +5

The Hong Kong Polytechnic University, PolyU · Hong Kong Polytechnic University Daya Bay Technology and Innovation Research Institute.

Weight-Space Analysis Language Model Merging Model Merging

May 26, 2026cs.LG

Extra-Merge: Tracing the Rank-1 Subspace of Model Merging in Language Model Pre-Training

Model merging has emerged as a lightweight paradigm for enhancing Large Language Models (LLMs), yet its underlying mechanisms remain poorly understood. In this work, we analyze late-stage pre-training trajectories and uncover a \textbf{Rank-1 Subspace} phenomenon: while raw optimization steps oscillate violently, consecutive \emph{merged} checkpoints collapse onto a stable, approximately one-dimensional linear manifold. We theoretically ground this observation in a \emph{river-valley} landscape analysis: averaging acts as a geometric low-pass filter that dampens high-curvature noise to reveal the optimal descent direction. Capitalizing on this insight, we propose \textbf{Extra-Merge}, a training-free strategy that extrapolates along this subspace to minimize loss without additional gradient updates. Extensive experiments across GPT-2 and LLaMA families (124M to 2B) demonstrate that Extra-Merge consistently outperforms standard merging baselines. Notably, it yields consistent zero-shot accuracy gains on Pythia-12B downstream tasks and generalizes effectively to the Muon optimizer \citep{jordan2024muon}.

Wenjie Zhou, Bohan Wang, Hongtao Zhang +3

State Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences, China · University of Chinese Academy of Sciences, China · Alibaba Group, China +2

Language Model Pretraining Neural Network Optimization Weight-Space Analysis Language Model Merging

May 22, 2026cs.LG

What Linear Probes Miss: Multi-View Probing for Weight-Space Learning

The explosive growth of open-source model repositories has created a Model Jungle, where checkpoints are frequently shared without adequate documentation or metadata. While weight-space learning offers a pathway to identify and analyze these models directly from their parameters, processing full-scale weights is computationally prohibitive. Probing-based methods have emerged as a lightweight alternative, extracting permutation-equivariant representations via learnable probe vectors. However, existing probing methods are limited by a single-view design: they capture first-order structures but fail to encode the rich, higher-order correlation patterns inherent in row-column interactions. To bridge this gap, we introduce MVProbe, a multi-perspective probing framework that synthesizes first-order signals with interaction-aware (Gram-based) views. Our approach is theoretically grounded; we analyze the scaling laws of different probing orders to derive a principled standardization and fusion strategy that ensures balanced contributions from all branches. On the Model Jungle benchmark, MVProbe consistently outperforms the state-of-the-art ProbeX across diverse architectures, including discriminative backbones (ResNet, SupViT, MAE, DINO) and large-scale generative LoRA adapters (Stable Diffusion LoRA).

Eunwoo Heo, Kyeongkook Seo, Jaejun Yoo

Graduate School of Artificial Intelligence, Ulsan National Institute of Science and Technology, Ulsan, Republic of Korea.

Multi-View Learning Weight-Space Analysis

May 17, 2026cs.LG

A Two-Parameter Weibull Framework for Diagnosing Transformer Weight Distributions

We apply the Weibull distribution -- a two-parameter family from extreme-value theory -- as a diagnostic framework for element-wise weight magnitude distributions in transformers. At initialization, i.i.d. Gaussian weights give |w| ~ HalfNormal, yielding k ~ 1.20 via middle-80% probability-plot fit (the protocol used throughout this work). This anchor makes k a principled, architecture-independent measuring stick for training dynamics; fitting each weight matrix independently at every layer at every checkpoint enables per-component, per-layer, and per-step diagnostics that aggregate statistics cannot resolve. Applying this framework to 12 model entries spanning 7 architectural families (Pythia, OLMo-1/2, LLaMA-3, Mistral, Qwen2.5/3) reveals three findings. First, FFN modules and the attention output projection W_o -- the Transmission Class -- fall in a narrow k band: median terminal k in [1.186, 1.204] across 12 entries (cross-family CV = 0.51%), shared across SwiGLU/GeLU activations, Pre-LN/QK-Norm placements, and 70M-14B sizes. Second, the attention input projections W_q, W_k -- the Selection Class -- depart from the Weibull family, with severity shaped by storage: separately-stored Q/K (OLMo-1, OLMo-2) yields k in [0.76, 0.99] (deep); GQA models yield k in [1.10, 1.16] (mild); Pythia's merged W_qkv occupies a transitional zone tracking training budget T/tau monotonically. Third, lambda grows substantially during training and scales with sqrt(eta/lambda_wd) within the Pythia family (Pearson r = 0.94, three Transmission kinds), directionally consistent with Fan et al. (2025). The two parameters carry independent information: k labels the functional class, lambda labels training progress. We release npm-weibull-py v0.4 (Python library) and DATABASE_v9_1 at https://github.com/tiexinding/NPM-Weibull-public .

Tiexin Ding

Independent Researcher

Transformer Weight-Space Analysis Neural Network Training Dynamics

May 15, 2026cs.LG

Where Pretraining writes and Alignment reads: the asymmetry of Transformer weight space

Cross-entropy pretraining and preference alignment update the same transformer weights, but leave geometrically distinct traces. We characterise this asymmetry with a relative-subspace-fraction probe that tracks how weight deltas align with residual-stream activation subspaces and with the prediction subspace defined by the unembedding. Alignment deltas concentrate in the read pathway (

W_Q

,

W_K

), along principal directions of attention-input activations, while remaining near-isotropic in the write pathway (

W_O

,

W_2

) relative to the prediction subspace. We explain this pattern through anisotropic gradient accumulation: updates to a matrix

W

are sums of outer products

δ_t a_t^\top

, and inherit directional structure from whichever side has concentrated covariance. For read-pathway matrices, this side is the input activation

a_t

, whose covariance is spiked in trained transformers and therefore produces objective-agnostic concentration. For write-pathway matrices, the relevant side is the upstream gradient

δ_t

, whose anisotropy depends on the loss. Cross-entropy supplies the canonical sharp per-sample signal, inducing write-pathway prediction geometry during pretraining; alignment objectives typically add little further write-side concentration. We support this explanation with a within-checkpoint trajectory, a graded contrastive-objective control, and a closed-form rank-1 intervention with matched direction controls, providing causal evidence for the proposed weight-space geometry.

Valeria Ruscio, Eli-Shaoul Khedouri, Keiran Thompson

Intuition Machines

Language Model Pretraining Transformer Interpretability Weight-Space Analysis Preference Alignment

May 14, 2026cs.LG

When Are Two Networks the Same? Tensor Similarity for Mechanistic Interpretability

Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to out-of-distribution mechanisms, or basis-dependent parameters, meaning they disregard weight-space symmetries. To address these issues for the class of tensor-based models, we introduce a weight-based metric, tensor similarity, that is invariant to such symmetries. This metric captures global functional equivalence and accounts for cross-layer mechanisms using an efficient recursive algorithm. Empirically, tensor similarity tracks functional training dynamics, such as grokking and backdoor insertion, with higher fidelity than existing metrics. This reduces measuring similarity and verifying faithfulness into a solved algebraic problem rather than one of empirical approximation.

ML Nissen Gonzalez, Melwina Albuquerque, Laurence Wroe +3

MARS & University Heidelberg · MARS · MARS & Stanford University +2

Mechanistic Interpretability Weight-Space Analysis

May 8, 2026cs.CV

Is Class Signal Clustered or Routed in Task-Induced Implicit Neural Representation Weight Spaces?

Implicit neural representations (INRs) encode images as neural-network weights, making image classification a problem of weight-space classifiability. A natural geometric hypothesis is that classifier feedback should make image-specific weights cluster by class in the shared-anchor coordinate. We test this hypothesis in the SIREN-based Meta Weight Transformer (MWT) regime, where end-to-end training meta-learns a shared initialization and inner-loop update schedule for fitting image-specific SIRENs. We find that this prediction fails. Exposed weight-space geometry and supervised clustering pressure do not reliably track trained-reader accuracy; clustering can even make local neighborhoods more class-consistent while making the trained reader worse. Crucially, the reader constructs rather than inherits class-aligned geometry: token-flow diagnostics show that class-aligned neighborhoods become strongly predictive of trained-reader accuracy only after late reader interactions, not in the input coordinate. We further identify the native SIREN bias column in the augmented weight token as a low-dimensional, sample-dependent causal readout route for the trained reader; targeted controls rule out generic scalar-column and marginal-distribution artifacts. The diagnosis motivates interventions that strengthen reader routing, add an explicit bias route, or use denser inner-loop fitting; under the lane-specific training conventions used here, route-directed variants often outperform the shared-anchor baseline but interact non-additively. Task-induced INR weights are classifiable not because they form raw geometric clusters, but because their class signal is routed through the reader.

Xinyi Guo, Mingyi He, Haobin Ding +7

South China Normal University · Beijing University of Chemical Technology · Tsinghua University +1

Neural Representation Geometry Implicit Neural Representations Neural Network Interpretability Weight-Space Analysis Image Classification

May 2, 2026cs.LG

Model Merging: Foundations and Algorithms

Modern deep learning usually treats models as separate artifacts: trained independently, specialized for particular purposes, and replaced when improved versions appear. This thesis studies model merging as an alternative paradigm: combining independently trained neural networks directly in weight space, with little or no optimization and without requiring access to the original training data. The thesis considers two main regimes. In the single-task setting, where models share an objective but differ in initialization, we introduce C

^2

M

^3

, a cycle-consistent merging algorithm based on Frank-Wolfe optimization. C

^2

M

^3

aligns multiple networks into a shared, reference-free parameter space, making weight averaging meaningful without privileging any individual model. In the multi-task setting, where models are fine-tuned for different downstream tasks from a common pretrained initialization, we first develop a theoretical account of task vectors as approximate gradients. This explains both the effectiveness and the limitations of task arithmetic. Building on this view, we show that task vectors inherit the low-rank structure of gradients and introduce Task Singular Vectors (TSV), a decomposition that enables compression and interference reduction through TSV-Merge. We then present MASS, an input-adaptive routing method that uses TSV geometry to select task-relevant subspaces at inference time. Finally, we introduce MERGE

^3

, an evolutionary merging framework that uses Item Response Theory to reduce evaluation costs by up to 50

\times

while preserving solution quality. Together, these contributions provide theoretical and algorithmic foundations for model merging, supporting a paradigm in which learned capabilities can be composed, reused, and extended across models.

Donato Crisostomi

SAPIENZA UNIVERSITY OF ROME · GLADIA research lab · Department of Computer Science +1

Multi-Task Learning Task Vector Merging Weight-Space Analysis Task Arithmetic Model Merging

Apr 28, 2026cs.LG

The Role of Symmetry in Optimizing Overparameterized Networks

Overparameterization is central to the success of deep learning, yet the mechanisms by which it improves optimization remain incompletely understood. We analyze weight-space symmetries in neural networks and show that overparameterization introduces additional symmetries that benefit optimization in two distinct ways. First, we prove that these symmetries act as a form of diagonal preconditioning on the Hessian, enabling the existence of better-conditioned minima within each equivalence class of functionally identical solutions. Second, we show that overparameterization increases the probability mass of global minima near typical initializations, making these favourable solutions more reachable. These results offer a potential link between loss landscape geometry and simplicity bias. Empirically, we observe wider networks have lower top eigenvalues, smaller condition numbers and faster convergence, matching our analysis. Our analysis provides a unified framework for understanding overparameterization and width growth as a geometric transformation of the loss landscape.

Kusha Sareen, Mohammad Pedramfar, Sékou-Oumar Kaba +2

McGill University · Mila - Quebec Artificial Intelligence Institute

Neural Network Optimization Weight-Space Analysis Loss Landscape Geometry

Apr 28, 2026cs.LG

Gradient-Direction Sensitivity Reveals Linear-Centroid Coupling Hidden by Optimizer Trajectories

We show that replacing the rolling SVD of AdamW updates with a rolling SVD of loss gradients changes the diagnostic by 1-2 orders of magnitude. Performing SVD on the loss gradient instead of the AdamW update increases the measured perturbative coupling between SED directions and Linear Centroid Hypothesis (LCH) features from

\bar{R}_k \approx 3

--

9\times

to

100

--

330\times

across four single-task modular arithmetic operations, eliminating the apparent operation dependence in the original measurement. On a multitask transformer with a shared encoder, update-based SED gives

\bar{R}_k \leq 1

-- an apparent failure of the diagnostic -- while per-operation gradient-based SED recovers

\bar{R}_k = 20

--

45\times

across all four operations. Gradient aggregation across competing tasks is the main obstruction; performing SVD on per-task gradients resolves it. A causal intervention shows that constraining attention updates to any rank-3 subspace (whether SED-derived or random) accelerates grokking by approximately

2.3\times

across random seeds and operations, while removing the rank-3 component has negligible effect under proper gradient-projection methodology. The SED-LCH coupling is therefore a strong diagnostic of where feature formation concentrates in parameter space, but it is not a unique causal pathway: the natural full-rank AdamW attention update is highly rank-redundant under our hyperparameters.

Yongzhong Xu

Weight-Space Analysis Grokking Gradient Descent Dynamics

Apr 18, 2026cs.AI

Understanding and Enforcing Weight Disentanglement in Task Arithmetic

Task arithmetic provides an efficient, training-free way to edit pre-trained models, yet lacks a fundamental theoretical explanation for its success. The existing concept of ``weight disentanglement" describes the ideal outcome of non-interfering task composition but does not reveal its underlying cause. Crucially, what intrinsic properties of the pre-trained model (

θ_0

) or the task vectors (

τ_t

) enable this disentanglement remains underexplored. In this paper, we introduce Task-Feature Specialization (TFS), a model's ability to allocate distinct internal features to different tasks, as the fundamental principle. We first prove that TFS is a sufficient condition for weight disentanglement. More importantly, we find that TFS also gives rise to an observable geometric consequence: weight vector orthogonality. This positions TFS as the common cause for both the desired functional outcome (disentanglement) and a measurable geometric property (orthogonality). This relationship provides the key insight for our method: since the abstract TFS property is intractable to enforce directly, we can instead promote weight disentanglement by shaping its concrete geometric consequence, orthogonality. Therefore, we propose OrthoReg, a simple and effective regularization method that actively enforces an internal orthogonal structure on weight updates (

ΔW

) that constitute

τ_t

during fine-tuning. And we theoretically prove that OrthoReg promotes disentanglement. Extensive experiments demonstrate that OrthoReg consistently and significantly enhances the performance of various task arithmetic methods. Code is available at https://github.com/RL-MIND/OrthoReg.

Shangge Liu, Yuehan Yin, Lei Wang +5

State Key Laboratory for Novel Software Technology, Nanjing University, China · University of Wollongong, Australia · Nanyang Technological University, Singapore

Task Vectors Weight-Space Analysis Task Arithmetic

Apr 17, 2026cs.LG

FLARE: A Data-Efficient Surrogate for Predicting Displacement Fields in Directed Energy Deposition

Directed energy deposition (DED) produces complex thermo-mechanical responses that can lead to distortion and reduced dimensional accuracy of a manufactured part. Thermo-mechanical finite element simulations are widely used to estimate these effects, but their computational cost and the complexity of accurately capturing DED physics limit their use in design iteration and process optimization. This paper introduces FLARE (Field Prediction via Linear Affine Reconstruction in wEight-space), a data-efficient surrogate modeling framework for predicting post-cooling displacement fields in DED from geometric and process parameters. We develop a predefined-geometry DED simulation workflow using an open-source finite element framework and generate a dataset of simulations with varying geometry, laser power, and deposition velocity. Each simulation provides full-field displacement, stress, strain, and temperature data throughout the manufacturing process. FLARE encodes each simulation as an implicit neural field and regularizes the corresponding neural-network weights so that they follow the affine structure of the input parameter space. This enables prediction of unseen parameter combinations by reconstructing network weights through affine mixing of training examples. On this DED benchmark, the method shows improved accuracy compared to baseline methods in both in-distribution and extrapolation settings. Although the present study focuses on DED displacement prediction, the proposed affine weight-space reconstruction framework offers a promising approach for data-efficient surrogate modeling of physical fields.

Kittipong Thiamchaiboonthawee, Ghadi Nehme, Ram Mohan Telikicherla +5

Massachusetts Institute of Technology, Cambridge, MA, USA · GE Vernova Advanced Research Center, Niskayuna, NY, USA

Neural Surrogate Modeling Implicit Neural Representations PDE Surrogate Modeling Weight-Space Analysis