Model Weights

Weight-space post-training quantization (PTQ) must choose finite formats, granularities, quantizer families, transformations, and bits before the completed quantized model reveals its output-distribution drift. Existing PTQ methods predict important pieces of this degradation, including reconstruction error, Hessian sensitivity, transformation effects, and downstream loss, but these pieces are usually scored after fixing the quantization geometry or inside separate configuration families. We formulate weight-space PTQ as pre-deployment configuration selection using priced layer-output error. Each admissible layer configuration is treated as an error generator with a deployment cost, which induces a layer-output error covariance $\boldsymbolΣ_l(α_l)$, and the full-precision model prices that covariance by downstream curvature, $\widehatρ_l(α_l)=\frac{1}{2}\operatorname{Tr}\left(\widehat{\mathbf{H}}_l\,\widehat{\boldsymbolΣ}_l(α_l)\right)$. The price follows from full-precision-to-quantized forward KL, whose first-order term cancels at the reference model. It turns reconstruction and diagonal scores into reduced proxies that drop price factors, while finite formats, codebooks, granularities, and equivalent transformations become comparable candidates through the covariances they induce and the costs they pay. A trace reduction then yields a calibration-time price table and a budgeted price-guided selector, making fixed-geometry bit allocation a special case rather than the organizing problem.

Transformer architectures exhibit cross-layer redundancies, yet post-training compression pipelines typically optimize layers in isolation or rely on heuristic grouping strategies that disregard layer-specific activation geometries. We introduce a principled, training-free framework that sequentially optimizes cross-layer weight pairings and shared-dictionary factorizations. Rather than forcing weights of adjacent layers to share a basis or heuristically merging activation statistics, our approach identifies structurally compatible projections and learns a shared representation that better preserves each layer's distinct calibration geometry. Coupled with structured sparsity, this yields highly efficient weight decompositions without sacrificing functional fidelity. Across diverse architectures, scales, and modalities, our method achieves state-of-the-art results, consistently outperforming independent structured weight decompositions and alternative pairwise weight factorizations, which operate under heuristic grouping strategies. By replacing heuristic engineering strategies with a convergent, optimization-driven pipeline, we establish a theoretically grounded foundation for scalable, transformer compression across different modalities.

Mixed-precision weight quantization is commonly formulated as a Multiple-Choice Knapsack Problem (MCKP), yet existing solvers rely on scalar sensitivity proxies that collapse each weight matrix's Hessian into a single number and treat every module independently. We prove that even the optimal scalar proxy incurs multiplicative distortion up to $\sqrt{κ(\mathbf{A})κ(\mathbf{B})}$ relative to the full activation-aware quadratic, where $κ(\mathbf{A})$ and $κ(\mathbf{B})$ denote the condition numbers of the input- and output-side Hessian factors. This bound varies from $10^1$ to $10^{13}$ for typical LLM modules, making inter-module sensitivity ranking unreliable. To address these limitations, we propose Cross-layer Activation-aware Sensitivity Allocation (CASA), a two-phase method. In Stage 1, the scalar proxy is replaced by an activation-aware metric derived from the Kronecker-factored Hessian, reducing the MCKP to a form whose continuous relaxation admits a closed-form solution. In Stage 2, a cross-layer-aware local search evaluates bit-width updates using the end-to-end model loss. Experiments on multiple LLMs across different bit budgets show that CASA achieves lower perplexity than the latest scalar-proxy baselines, especially at ultra-low bit-widths ($<3$ bits per weight). Moreover, the performance gain in zero-shot accuracy tracks the per-model average condition-number over modules, confirming the distortion bound as a practical indicator of scalar-proxy failure.

Scaling laws hold that language models grow more capable with more parameters and more training data. Mixture-of-Experts (MoE) architectures are a remarkable demonstration of these laws, activating only a fraction of an enormous parameter bank for each token. But this success is built on static pretraining data --- the facts and corrections supplied by users during live interactions are a significant untapped source of potential improvement for a deployed model, but cannot be exploited by conventional architectures whose weights are frozen after training. Instead, this newfound knowledge must be placed in the context (by instruction or retrieval) and re-read on every request, only to be discarded afterwards. We seek instead to learn from live interactions by dynamically updating model weights. Inspired by MoEs, we propose the \textbf{Infinite-Parameter LLM}. A compact hypernetwork turns the online data into low-rank modulations of a shared base network, so feed-forward weights are generated from live data, not read from static memory. Whereas existing weight generators are held fixed after reading the context once, we form a Bayesian belief over the generator's latent state and update it online, such that the effective weights are re-derived as our belief evolves during the session. Although the model's memory footprint is constant, the feasible space of generated weights is thus effectively infinite. Representing live data in the weights rather than the prompt amortises compute, frees the context window, persists updates across turns, and can generalise better than in-context use. Our evaluation protocol applies this methodology to in-context learning and retrieval.

Deep neural networks that are independently trained to similar performance can be connected by low-loss parametric curves in weight space, a phenomenon known as Mode Connectivity (MC). This geometric property underpins practical techniques such as weight averaging, model ensembling, and model merging. We argue that low-loss connectivity is an incomplete geometric criterion: it controls loss only along a one-dimensional trajectory while leaving the surrounding weight-space neighborhood unconstrained, so the optimized curve may traverse sharp ridges that become fragile under distribution shift. We therefore reformulate mode connectivity as a neighborhood-robust path optimization problem, seeking a curve whose entire local neighborhood maintains low loss. We propose Sharp Mode Connectivity (SMC), which applies a first-order sharpness-aware approximation to the resulting minimax functional, enforcing flatness along the entire curve rather than only on it. We derive a practical optimization algorithm for connectivity paths under this sharpness-aware objective. Under severe blur corruptions from CIFAR-10-C, SMC achieves up to 6.09% absolute accuracy improvement over standard MC. Remarkably, SMC produces negative loss barriers, meaning that models obtained at interior points of the optimized path can outperform the average endpoint loss. These results, validated across ResNet-18, VGG16-BN, and ViT-Tiny on CIFAR-10 and ImageNet-100, establish path-wise flatness as a practical principle for robust weight-space interpolation.

Ternary Large Language Models (LLM) store every weight as one of three symbols $\{-1,0,+1\}$, so the cost of a ternary model is conventionally referenced to the information-theoretic $\log_2 3 \approx 1.585$ bits per weight. The prevailing deployment format packs five ternary weights into one byte (five-trit packing), and due to the power-of-two group sizes used in practice this rounds up to $1.625$ bits per weight. This effective storage bit-width treats the three symbols $\{-1,0,+1\}$ as equiprobable. We measure the actual symbol distribution of 29 ternary LLM models and find that zeros account for up to $51.5\%$ of all weights. Motivated by this finding, we introduce BITCOS, a simple distribution-adaptive layout comprised of a dense presence bitmap plus a compacted sign vector, and costs $2 - z$ bits per weight element given a zero density $z$ in the model's weights. BITCOS stores weights more compactly than the five-trit packing in 26 of the 29 tested models, and reaches $1.485$ bits per weight on the sparsest of them. BITCOS is amenable to efficient unpacking on modern processors and GPUs, and we present optimized unpacking sequences for AVX-512, AVX2 and Intel Xe2 GPUs. Measured against production state-of-the-art ternary matrix-vector multiplication kernels, at the zero densities real-world ternary models exhibit, the realized gain with our proposed layout is up to $1.28\times$. Finally, we illustrate end-to-end LLM inference results on 5 different platforms (client and server CPUs, integrated and discrete Xe2 GPUs) where decode throughput improves by up to $1.18\times$ on CPUs and $1.27\times$ on GPUs.

We revisit Kashin-decomposition-based weight quantization for large language models and propose an improved algorithm with stronger convergence properties and structured, efficient orthogonal transforms. The method retains the core factorization of each weight into two components -- one with bounded infinity norm and the other with bounded infinity norm after an orthogonal transformation -- but replaces the dense random orthogonal matrix with a sign-randomized Discrete Cosine Transform (DCT), reducing the per-iteration cost from $\mathcal{O}(N^2)$ to $\mathcal{O}(N \log N)$. The proposed greedy algorithm with alternating updates guarantees the four-peak distribution required for stable 2-bit clustering of each factor and admits closed-form initialization of cluster centers, removing the multi-restart k-means bottleneck of prior work. Composed with OPTQ-style sequential error compensation and QuIP-style incoherence preprocessing, the resulting JAX pipeline is competitive with OPTQ, QuIP, QuIP-RG and a fine-tuning- and vector-quantization-free variant of QuIP# at 4-bit per channel on OPT, Llama-2 and Pythia, with favorable wall-clock scaling. The bounded-$\ell_\infty$ factorization is also notably robust: on stress configurations where QuIP variants diverge to four-digit perplexity (Pythia-6.9B) or abort with NaNs in LDL back-substitution (Mistral-7B), Kashin-DCT remains numerically stable and stays close to FP16 baseline. At inference time, each weight decomposes into two 2-bit factor codes per channel that are structurally suited to native-2-bit hardware.

Deep neural networks exhibit regular macroscopic behavior despite highly nonlinear dynamics in vast parameter spaces. We develop a statistical-mechanical description of learning directly in function space, treating parameter configurations as microscopic realizations and functions with their dynamical operators as macroscopic variables. For mean-squared loss, the exact error dynamics are governed by the learning operator $M=JJ^\ast$. Combining the dynamical Boltzmann weight of the conditional stochastic dynamics with the parameter-space density of states, whose local curvature defines a statistical operator $B$, and integrating over local fluctuations yields $\Phi_{\mathrm{fluc}}(M;B)=\frac{\sigma_\xi^2}{2}\log\det(M^{-1}+B)+\mathrm{const}.$ At fixed spectrum, this term is rotationally stationary when $[M,B]=0$, is minimized by pairing large eigenvalues of $M$ with small eigenvalues of $B$, and generates a local restoring contribution against rotational mismatch. For ReLU-type function spaces under mild stable statistical conditions, $B=\sigma_\xi^2L^\ast\mathcal K L$, where $L$ measures coarse-grained second-order structure. Thus the low-$B$ sector corresponds, up to bounded anisotropy of $\mathcal K$, to low structural curvature, implying a preference for faster relaxation along smooth, data-adaptive directions. These results identify function space as a natural macroscopic level for studying stable collective organization in learning.

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.

Vision transformers (ViTs) have achieved remarkable generalization across visual domains, yet little is known about how they internally represent the structure of the world. To address this gap, we use Cross-Layer Transcoders (CLTs) to read concept circuits from ViTs: directed graphs whose nodes correspond to sparse, interpretable concepts and edges capture concept interactions across layers. Our method yields two complementary views of model behavior. The global concept circuit is input-invariant and can be recovered directly from learned cross-layer weights, exposing the reusable "world knowledge" encoded in the model. The instance concept circuit is input-dependent and identifies the concepts and pathways actually used for a specific prediction, enabling faithful example-level explanations. We demonstrate the utility of concept circuits in three ways: (1) Automatic spurious correlation discovery: leveraging the statistics of our global concept circuits to identify shortcut dependencies within the model. (2) Spurious correlation removal: intervening on the instance concept circuit to steer the model towards correct predictions. Empirical results show that our method outperforms existing counterparts by 11.0% on the Waterbird dataset. (3) Model comparison: contrasting the global concept circuits of different foundation models (e.g., CLIP vs. DINO) to reveal how supervision paradigms shape representational structure. Our code is available at https://github.com/deep-real/VisionCLT

The Potts model extends the Ising model to multinomial data. We introduce a Rater Ising-Potts model that uses agreement indicators between pairs of ratings and category labels, with weights derived from LLM embeddings. The model does not presuppose ordered category thresholds or equidistant scoring; instead, it focuses on pairwise agreement among ratings and assigns category-specific positive weights, making it suited for multi-category scoring reliability. We evaluate the model on three constructed-response datasets spanning a corpus of K=14,466 short answers on a three-level rubric and two AERA essay prompts of roughly 1,200-1,400 responses on four-point rubrics. We compare three strategies for sharpening the similarity signal: top-K pruning, min-max normalization with a power transformation, and ColBERT late-interaction similarities. Top-K pruning, which replaces the dense similarity graph with a sparse local network of strongest semantic neighbors, consistently yields the highest accuracy and Cohen's kappa, and the selected neighborhoods are always a small fraction of the corpus. Power tuning consistently ranks second, while ColBERT is competitive on longer essay prompts and adds little on short answers. Across all settings, most misclassifications occur between adjacent score levels, confirming that the model preserves the ordinal structure of scoring rubrics without imposing rigid assumptions. These findings suggest that LLM-derived similarities, combined with a parsimonious Potts formulation and a sparse local graph, offer a robust and interpretable framework for reliability auditing in educational assessment. We discuss extensions to multiple raters and hierarchical rating designs.

Machine-learning weather models (MLWMs) now match or outperform operational numerical weather prediction (NWP) at global medium-range forecasting, at far lower inference cost. Many deployed MLWMs are deterministic, producing a single forecast with no estimate of its own uncertainty, whereas a growing family of trained-probabilistic models generate calibrated ensembles directly, at the price of a dedicated training run. We ask instead how much uncertainty can be extracted from a deterministic checkpoint that already exists, without retraining it. Where physical ensembles represent model uncertainty by stochastically perturbing parametrisation tendencies, we perturb the network's raw weight tensors at inference time, a scheme we call stochastically perturbed weights (SPW). We also ask whether it works, where and on which scales to inject the noise, and where it fails. A three-phase ablation across four deterministic backbones, Aurora, GraphCast, SFNO, and AIFS, selects one production baseline per model, benchmarked against the trained-probabilistic AIFS-ENS, FourCastNet 3 and Atlas as well as the operational ECMWF ensemble (IFS-ENS) over 112 initialisation times. At a 240 h (10-day) lead time the SPW ensembles reach continuous ranked probability skill scores (CRPSS) between 0.04 and 0.13 below the best trained-probabilistic baseline, at zero marginal training cost. No injection site works across models: the productive tensor group is architecture-specific, so SPW is at present a tuning procedure rather than a plug-and-play recipe. Its main failure mode is a coherent whole-field offset that overdisperses the domain mean, and restricting the noise to coarse scales or perturbing the initial conditions each repair part of it.

Equivariant networks are commonly trained with Adam, yet recent work reports that matrix-structured optimizers such as Muon can perform better on these architectures without explaining why. We identify one source of this difference inside equivariant linear layers. Each irrep block learns a channel-mixing matrix $W_l$ shared across its $2l+1$ components, giving the expanded map $W_l \otimes I_{2l+1}$. For a single application of the layer, the gradient of $W_l$ sums $2l+1$ outer product contributions and has rank at most $2l+1$. Adam rescales stored weights individually without using the irrep boundaries, so one learning rate can produce different spectral step sizes across blocks within a layer. We address this mismatch by normalizing each block update separately, without introducing a new hyperparameter. This changes only the scale of the update, leaving Adam's moment estimates and its direction within each block unchanged. We evaluate the mechanism in a controlled $\mathrm{SO}(3)$-equivariant model with a matched dense control and in an e3nn interatomic potential model trained on rMD17 and MD22. The toy setup isolates a mismatch that grows with width while the dense control shows no corresponding growth. In the interatomic potential model, block normalization and tuning Adam's momentum coefficients independently improve performance, but neither alone matches Muon. Combined, they make Adam competitive with Muon on all datasets, indicating that blockwise step control and momentum accumulation account for much of Muon's advantage.

Trust-Hub reuses host circuits: several files differ mainly in the inserted Trojan. When gates from sibling variants enter both training and test folds, a detector can benefit from host logic it has already seen. We measure that effect instead of proposing another classifier. The corpus contains 49,124 gates from 16 netlists grouped into five host families. We left the parser, 36 gate features, class weighting, model settings, threshold, and family-level aggregation unchanged and altered one choice: the test boundary. The three settings draw test gates from the pooled corpus, withhold a complete netlist, or withhold every variant of one host. The choice matters. Random forest records F1/AP of 0.914/0.978 with pooled gates, 0.636/0.851 with one netlist held out, and 0.460/0.577 with a host family held out. XGBoost falls from 0.946/0.976 to 0.464/0.544 across the same comparison. Logistic regression loses AP, although its fixed-threshold F1 is not monotonic. Each family shows the same pooled-to-family direction. Feature removal, repeated model and simulator seeds, score normalization, parser-related exclusions, and a smaller sample change the size of the gap without reversing it. Aggregation also matters: a gate-weighted average is dominated by the larger ISCAS files, so the headline values give each host family one vote. Bootstrap and jackknife summaries keep the gap positive, but their folds reuse training families. We treat the five family rows as descriptive evidence rather than independent trials. Five host families are too few for a population claim, and the experiment says nothing about transfer to a new cell library or an industrial design. It supports a narrower conclusion: sibling benchmark variants can inflate apparent transfer. Benchmarks with several variants of one host circuit should report family-aware holdouts and all five family results beside pooled scores.

Weight-only post-training quantization (PTQ) can alleviate the computational burden of serving large language models (LLMs) at scale. However, existing PTQ methods often fail to generalize across models and suffer severe accuracy loss below 2 bits. Many leverage unstructured sparsity to mitigate this loss, but at the cost of regularity and GPU-friendly execution. We present QTEA, a sub-2-bit PTQ framework that quantizes weights into ternary values and uses salient weights as residual error compensators. To maintain hardware efficiency, residuals are assigned to selected columns with semi-structured $1:4$ sparsity within the salient columns. We further add column-wise rescale refinement to GPTQ-style column-by-column quantization, alternately updating per-column scales and ternary assignments to reduce reconstruction error. We also identify order-dependent error propagation in GPTQ and introduce error decay to attenuate late-stage error accumulation. On Qwen3-14B, QTEA compresses all weights to an effective 1.7 bits per weight while improving average accuracy over the strongest ternary PTQ baseline by 16.7%. It also achieves 1.40$\times$ and 2.61$\times$ lower perplexity on WikiText and C4 respectively. This trend holds on Llama3-8B, where QTEA obtains a 6.6% accuracy gain and 1.34$\times$ / 1.95$\times$ lower perplexity on the same datasets. Finally, we develop a lookup-table based kernel that achieves 7.2$\times$ faster per-token generation over an FP16 baseline. Code is available at https://github.com/Intelligent-Microsystems-Lab/QTEA.

Agent performance depends jointly on the model parameters and the executable harness code that manages context and control flow. Optimizing either component in isolation can leave the system bottlenecked by its frozen counterpart: weight updates can change which harness is effective, while harness updates can change which model capabilities are exposed. Existing joint-adaptation methods optimize weights and textual prompts but leave the broader harness fixed. We propose Weight-Harness Alternating LEarning (WHALE), a simple recipe that alternates two phases: updating the model under the current harness, then searching for a better harness under the updated model. We instantiate these two phases with online rejection-sampling fine-tuning and Meta-Harness, respectively. When to switch is a key design choice: to separate real improvements from noise without over-optimizing against a changing counterpart, WHALE uses either fixed phase durations or an adaptive patience rule over training signals. Using Qwen3.5-2B/4B agents across three domains (search question answering, mathematical reasoning, and chess puzzles), WHALE outperforms weight-only, harness-only, and Fast-Slow Training by 4.15-24.38 percentage points in best mean@8 accuracy. Either component can be the bottleneck: harness search matches peak weight-only accuracy with far fewer rollouts in SearchQA, but improves math accuracy only after a weight update. Small interleaved updates also outperform stagewise weight-then-harness optimization in accuracy and rollout cost. The code is available at https://github.com/krafton-ai/WHALE.

We present Arkios, a 1.04B-parameter dense transformer pretrained from scratch on 150B tokens of bilingual English-Nepali text, using a custom single-file C/CUDA training stack and a Devanagari-aware byte-level BPE tokenizer built for this project. On ARC-Easy and ARC-Challenge, Arkios exceeds three comparably sized open models (Pythia-1.4B, TinyLlama-1.1B, OLMo-1B) despite an order of magnitude fewer training tokens, likely aided by a match between our educational-web-text pretraining data and ARC's grade-school-science format rather than a general capability advantage. We report full evaluation results under standard protocols, including a correction to an earlier partial-sample estimate, and findings specific to evaluating small models in a low-resource language: the standard multiple-choice-letter prompt format used by common evaluation harnesses places this model at chance on Nepali reading comprehension, and simultaneously at chance on English in the same format, which would lead a naive benchmark run to conclude the model has no Nepali ability when in fact it does. Concretely, both languages score at chance in the letter-choice format (0.240 Nepali, 0.236 English, against a chance baseline of 0.250), while scoring the answer text directly reveals genuine, English-favoring comprehension (0.306 Nepali, 0.387 English). We describe a manifest-conditioned tool-use contract introduced during instruction tuning, where tool calls are permitted only when a tool manifest is declared in context and suppressed otherwise, and report where that contract holds and where it does not. We release both the base and instruction-tuned model weights under Apache-2.0. The training code and a small privately-sourced portion of the Nepali pretraining corpus are not released; everything needed to reproduce the reported numbers from the released weights is included here.

Recent years have witnessed remarkable achievements of Large Language Models (LLMs) in multiple domains, while the excessive resource requirements of LLMs hinder the deployment on resource-constrained devices. Although model quantization stands out as an effective approach, conventional quantization approaches typically incur severe performance degradation due to uniform bit-width or simple heuristic sensitivity evaluation. In this paper, we propose a novel Fisher information-based Adaptive Mixed Precision Weight Quantization approach, i.e., FAMPWQ, which performs layer-adaptive weight quantization for effective LLM inference on commodity GPUs. First, we propose a system model with a novel Fisher information metric to measure the layer-wise sensitivity to quantization. Second, we propose a reinforcement learning-based bit-width allocator in FAMPWQ, which generates an adaptive bit-width allocation strategy based on the Fisher information sensitivity metric. Extensive experiments on 7 models and 5 benchmarks demonstrate that FAMPWQ significantly outperforms 7 baseline approaches in terms of PPL (up to 3.39 smaller), accuracy (up to 6.87% higher), and LLM-as-a-judge comparison (up to 76% win rate).

Low-bit weight quantization saves storage but leaves errors that degrade LLM quality. We introduce activation-weighted seeded residual coding (AWSRC), a compact repair codec for an existing quantization backbone. Given a reconstructed weight $W_0$, AWSRC encodes the residual $W-W_0$ using deterministic seed-generated bases. The sidecar stores seed selectors, low-bit coefficients, and scales rather than an explicit codebook. Two variants combine activation weighting with per-module byte quotas ($\mathrm{AWSRC\text{-}U}$), or blended activation/Fisher weighting with globally ranked progressive prefixes ($\mathrm{AWSRC\text{-}P}_{F}$) that support multiple byte budgets without refitting. On Qwen2.5-3B-Instruct, adding $0.162$ scope-bits/weight to an RTN-INT4 baseline closes $88.2\%$, $78.9\%$, and $71.3\%$ of the PPL, KL, and 11-task mean-accuracy gaps to BF16, respectively. AWSRC achieves the highest mean downstream accuracy in byte-matched residual-codec ablations and improves all metrics across model families with up to 32B parameters.

Muon motivates designing optimizer geometry around the function of each parameter block and uses the spectral norm for hidden linear layers. For the language-model head, the spectral norm is not a faithful measure of functional change. Softmax removes shared logit shifts, whereas the spectral norm can assign arbitrarily large size to updates that change no output probability. We therefore treat the LM head and softmax as one module and derive an update geometry for their composition. Hilbert's projective distance respects this invariance as it measures the largest change in pairwise log odds. For an update $S$ with token rows $s_i^\top$, we show that the largest Hilbert distance over $\left\lVert h\right\rVert_2\leq H$ is exactly $H D(S)$, where $D(S)=\max_{i<j}\left\lVert s_i - s_j\right\rVert_2$ is the Euclidean row diameter. This diameter replaces the spectral norm in the resulting Muon-style steepest descent problem. An exact solution is possible, but its direct formulation contains one $d$-dimensional vector variable for every token pair. For a vocabulary size of approximately $50$k, this means more than one billion token pairs, making the calculation impractical at every training step. We instead impose a stronger common-ball constraint and derive projected RowNorm as an $O(Vd)$ solution. For the exact RowNorm oracle, we prove that its first-order decrease is at least $1/\sqrt{2}$ of the exact diameter-constrained optimum. With Muon on the backbone, experiments across three seeds at 190M, 380M, and 640M parameters show that RowNorm reduces mean final step diameters and empirical Hilbert RMS perturbations by factors of $45$--$60$ and $12$--$15$, respectively, with only a $0.0057$--$0.0153$ increase in mean final validation loss.

A 4-bit quantized weight specifies a rounding cell rather than a single full-precision value. We introduce in-cell learning, a paradigm for writing new knowledge only within these cells, so that re-quantizing the served weights reproduces the released integer codes and scales exactly. CellFill implements this idea with bounded trainable positions inside frozen quantization cells and ships the update as a separate, subtractively revocable file. Across published NF4 and W4A16 releases of Qwen3 and Gemma from 1.7B to 32B parameters, CellFill writes 83-99% of a real-fact corpus while returning the stored code on every constrained weight. The injected facts generalize to paraphrases and composition, and answer 78-88% of selected PopQA questions that the released model misses. Sequential experiments show that rehearsal preserves earlier knowledge, whereas available room and new-task plasticity decline across updates. Consolidation re-quantizes the learned weights to produce a declared major version, restoring room at a measured capability cost. A six-task write-rehearse-consolidate cycle retains at least 92.8% of first learning in two 8B runs and records zero code violations over 6.9 billion constrained weights at every fold. These results define a version-management protocol in which minor updates preserve the released quantized artifact bitwise and major updates are explicit, measurable, and verifiable.

Open-weight language models are fine-tuned, quantized, pruned, and merged, yet their provenance is often undocumented. We study data-free white-box lineage verification: can weights alone reveal whether two compatible model checkpoints share ancestry? Residual training produces a shared identity-aligned component in branch products, so this structure alone cannot establish ancestry. We remove it and compare checkpoint-specific structure across residual blocks, yielding a symmetric lineage score calibrated against independent checkpoints. On residual-MLP and GPT-2 benchmarks, the score separates fine-tuned, LoRA-merged, pruned, and quantized descendants from independent and distilled models (AUROC=1.0), distinguishing weight ancestry from behavioral similarity. Under function-preserving checkpoint laundering experiments, weight-space baselines lose margin or fail; our score remains unchanged and runs 76x faster than the nearest robust baseline on GPT-2. The projection-pairing signal appears across six language-model families and beyond, and a case study correctly identifies 3 related and 7 unrelated LLaMA-2 public checkpoints. Collectively, these results establish a passive, data-free provenance signal for compatible open-weight language-model checkpoints

Transformer-based language models achieve strong performance but incur substantial inference cost due to repeated high-dimensional matrix multiplications. We propose Reduced Matrix Multiplication (RMM), a training-free, input-adaptive inference method that reduces Transformer matrix products by selecting informative slices along their contraction dimensions, without modifying model weights. Under a simple retention-ratio control, RMM provides a smooth and predictable accuracy-efficiency trade-off. Across language models ranging from 1B to 70B parameters, we find that reduction tolerance depends on the model family, task, component, and retention ratio, although it often improves with model scale. Under moderate reduction, RMM remains robust across the evaluated discriminative, autoregressive generation, and long-context settings. We further show that the same principle extends to multimodal vision-language inference. Mechanistic ablations reveal a structural asymmetry within Transformers: attention-side computations are substantially more reducible than MLP components. Finally, wall-clock benchmarks with custom kernels on an NVIDIA A100 show that these computational savings can translate into practical runtime gains, especially at longer sequence lengths. Together, these results position RMM as a scalable direction for input-adaptive inference-time optimization.

Supervised fine-tuning (SFT) is a standard approach for adapting LLMs to a target distribution, but in settings such as personalization, where each author requires separate weight access, optimization, storage, and retraining, its costs become prohibitive. We propose Weightless Fine-Tuning (WFT), a training-free decoding-time method that approximates the distributional effect of SFT without weight updates. WFT computes supervised residuals on an author's training sequence and transports them to the current prompt through a cross-prefix transport operator estimated from dropout-induced cross-covariance. The operator captures how a perturbation at one context propagates to predictions at another, replacing gradient-based parameter updates with logit-space corrections. On three LaMP personalization benchmarks, WFT achieves the best average performance across datasets, matches or exceeds SFT on individual tasks, and outperforms other lightweight baselines on average. In a budget-controlled comparison, WFT approaches SFT performance using less than 7% of the effective computation. Logit-level analysis shows a cosine similarity of 0.875 between the logit shifts induced by WFT and SFT over 95% of the next-token probability mass, suggesting that WFT captures the distributional effect of supervised adaptation without modifying model weights.

We introduce cut-cell skinning, a geometric prior designed to augment data-driven skinning weight generation. While data-driven methods show promise in producing high-quality skinning weights, they often lack the generalizability of classic geometric approaches. To bridge this gap, we propose a geometric prior that can be robustly computed for in-the-wild meshes and is efficient for large-scale machine learning workflows. The key idea of our cut-cell skinning is a fast graph-based approximation of the volumetric geodesics distances, motivated by their importance in classic skinning weight computation. Our method achieves orders of magnitude speedup compared to optimization-based solvers and remains resilient to topological artifacts common in cage- or voxel-based alternatives. We demonstrate the efficacy of the cut-cell skinning prior by integrating it into recent neural skinning models, showing consistent improvements across existing methods and achieving state-of-the-art results. Project page: https://wenchao-m.github.io/CutCell.github.io/

Reinforcement learning with verifiable rewards yields no group-relative signal when rollout groups are uniformly correct or uniformly wrong, which account for 63.0-68.0% of groups in our experiments. We propose SKALD (Skill-Anchored Latent Distillation), an on-policy self-distillation framework that uses two context views of the same Qwen3-Base model: a question-only student and a teacher conditioned on an abstract, explicit-answer-filtered skill card. The student is trained on its own prefixes, transferring the skill-induced advantage into shared parameters without privileged input at test time. To stabilize context-induced distribution mismatch, SKALD employs an annealed exponentially tilted objective that downweights teacher-preferred tokens with very low student likelihood; as the tilt vanishes, it converges to teacher cross-entropy and recovers the forward-KL student gradient. An empirical gate activates distillation only when verified rollouts estimate a positive teacher advantage. Across five held-out mathematics benchmarks, SKALD improves overall avg@8 over GRPO by +2.46, +4.85, and +12.01 at 0.6B, 1.7B, and 4B, respectively. At 1.7B, zero-variance-only distillation recovers 84.7% of the full gain, while SKALD remains +4.06 above FLOP-matched GRPO and exceeds contextual skill exposure by +3.77. These results show that abstract skills provide dense supervision where group-relative rewards become uninformative.

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.

We present \LegoLM{}, a structured weight-sharing compression framework for large language models grounded in a systematic study of why global weight sharing fails and how to fix it. We identify two distinct failure modes. Distributional mismatch: for vector blocks of dimension d <= 2, transformer layers with heterogeneous weight scales impose a scale-mismatch penalty that grows linearly with d and cannot be resolved by increasing K, producing perplexity in the millions.Outlier dominance: for scalar blocks, a fraction ~1/K of weights lies beyond the outermost Lloyd-Max decision threshold and cannot be represented by any centroid; their misrepresentation accumulates across layers, causing catastrophic quality loss. \LegoLM{} resolves both failure modes via three data-free adaptations: 1 scalar-block encoding to eliminate the $d$-linear mismatch component, 2 percentile-selective replacement that identifies and preserves outlier weights verbatim, and 3 boundary-layer protection for the first and last transformer blocks. Across GPT-2 small (124M) and Mistral-7B, \LegoLM{} achieves +0.03% PPL degradation at 4.41X compression on Mistral-7B - outperforming PTQ-8bit in both quality and compression ratio - and -0.02% at 2.67X. Downstream evaluation on LAMBADA and HellaSwag confirms that \LegoLM{} at K=64, p=99% preserves accuracy within noise at 5.12 X compression, exceeding PTQ-8bit's compression ratio while matching its accuracy. We further discover that outlier dominance grows with model scale: full replacement at K=128 degrades GPT-2 small by only +23% but catastrophically degrades Mistral-7B by +1,134,279%, while selective replacement at p=99% rescues both models to under +15%. A controlled ablation confirms that selective replacement is the dominant mechanism: adding it to per-layer K-means also yields near-lossless quality, matching \LegoLM{} within 0.02%.

Structured output, where an LLM populates a predefined JSON schema, has become a default mechanism for data labeling and information extraction, but it also introduces a second instruction channel through schema descriptions. We tested whether classification-label definitions are better placed in the system prompt, user prompt, or schema description using a single-field classification task with nonce labels across ten model configurations from two vendors. Schema descriptions did not consistently outperform prompt-based placement; for GPT-4.1 and GPT-5.4 without reasoning, schema placement underperformed system prompts by 11-13 percentage points. Yet schemas are not inert metadata: when prompts and schemas conflicted, incorrect schema instructions caused accuracy drops of 5-45 points, with Claude Haiku 4.5 falling from 52.5% to 7%, indicating that schema instructions can override prompt instructions, and GPT-5.5 falling from 100% to 73%. Further, adding a required intermediate reasoning field before the label field improved schema-only accuracy by 15-24 points when headroom existed, exceeding system-prompt-only performance in every case tested. The effect held even for Claude Sonnet 4.6 at medium reasoning, where extended thinking alone did not produce a comparable gain. This suggests that schema design can affect how effectively models use information encoded in field descriptions. Overall, these results indicate that schema influence is model-dependent. In practice, the system prompt remains a safe default for definitions, but the bigger discipline is maintaining a single source of truth and preventing prompt/schema drift. More importantly, schema design itself may be a stronger lever than instruction placement. Practitioners should treat prompts and schemas as a unified instruction surface and empirically validate both placement and field design for their target model.

Post-training quantization reduces the deployment cost of large language models, yet how severely a quantized model degrades is not determined by bit-width alone. We systematically study weight-only post-training quantization across bit-widths, quantization methods, model scales and downstream tasks on multiple model families. We observe that such degradation varies substantially across these factors: 4-bit quantization usually preserves performance, 2-bit often causes broad degradation, and at 3-bit, degradation becomes apparent but varies markedly with task type, quantization method and model scale. To explain this variability, we use the signal-to-noise ratio (SNR) to measure how strongly quantization perturbs full-precision representations. We trace degradation back to two linked processes: how quantization errors arise within individual modules, and how they accumulate across layers. First, a source SNR decomposition shows that newly introduced errors depend on three factors: the magnitude of the weight error, the strength of the task-specific signal, and how strongly the quantization error aligns with task-specific activations. Different factors affect these components in distinct ways. Second, a cross-layer propagation analysis shows that these errors can be attenuated, preserved, or amplified as they pass across layers, and that larger models benefit from weaker error amplification. Together, these results establish that quantization degradation is governed by how errors are introduced at the source and how they accumulate across the network.

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.

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.

The acquisition of multispectral imagery via small satellites (e.g., CubeSats) presents significant data downlink challenges due to high data volumes and restricted communication windows. While onboard image compression is critical to address this bottleneck, traditional methods often struggle to adapt to the nonlinear statistics of multi-band, multi-resolution data. To overcome these limitations, we propose ELMZip, a novel framework based on Extreme Learning Machines (ELM) and domain decomposition strategies for efficient, resolution-free onboard neural representation. ELMZip formulates the fitting process as a convex least-squares problem using random-feature single-layer networks, thereby eliminating the need for computationally expensive backpropagation. By adopting an asymmetric transmission protocol that sends only the compact output weights, the proposed method significantly reduces the downlink payload. Unlike previous neural representation approaches that rely on iterative optimization and require transmitting full network parameters, ELMZip achieves significant compression efficiency while maintaining high reconstruction fidelity. This capability enables immediate image reconstruction for analysis, allowing resource-constrained platforms to maximize data return and advancing real-time AI-powered Earth observation.

Weight quantization for large-language-model inference must balance adaptive reconstruction levels with representations regular enough for efficient GPU execution. Uniform integers constrain each group to a linear grid. Low-bit floating-point formats use a fixed exponent-mantissa structure, while learned codebooks gain flexibility at the cost of irregular decoding and additional metadata. We introduce CubicQuant, a parametric non-uniform scalar format that preserves a dense integer code stream while adapting reconstruction levels within each weight group. A monotonic cubic curve, specified by two shape parameters and one scale, maps uniformly spaced magnitude codes to non-uniform levels. The family spans 1-8-bit weight payloads, contains symmetric uniform integer quantization as an exact special case, and has effective width B + 64/G bits per weight for payload width B and group size G. We derive population distortion under Uniform, Gaussian, and Laplace distributions, formulate continuous and Dynamic-A8-carrier-aware fitting objectives, and describe direct packed-weight GPU execution. For finite groups of G=128 with 15,360 samples per distribution, W4 CubicQuant reduced reconstruction RMSE relative to optimally clipped four-bit uniform integer quantization by 3.90% on Uniform, 13.49% on Gaussian, and 28.14% on Laplace samples. Relative to the best enumerated four-bit finite floating-point format, the reductions were 3.90%, 9.44%, and 6.27%. Preliminary H200 kernel measurements show a workload-dependent crossover: model-dtype execution is faster for narrow GEMV, while Dynamic A8 becomes favorable as row count grows. The results establish the format's representational promise and direct executability; downstream model quality and cross-device end-to-end performance remain open evaluation questions.

Character image animation remains a foundational yet challenging task in computer vision. Existing approaches can be broadly categorized into three paradigms: methods based on explicit motion representations suffer from extraction errors and identity drift; methods based on implicit motion features lose fine-grained dynamics through compression; and in-context learning approaches avoid intermediate representations but incur prohibitive computational costs. Furthermore, all current systems are designed for offline synthesis, unable to meet the real-time requirements of interactive applications such as digital avatars and live-streaming hosts. To address these limitations, we present Wan-Animate-2, an end-to-end character animation framework that directly consumes the driving video within a redesigned Diffusion Transformer. Our architecture achieves superior motion fidelity and identity preservation by eliminating intermediate motion extractors entirely. We further introduce text driven viewpoint control that decouples the output camera perspective from the driving video--a capability rarely supported by prior character animation methods that rely on explicit motion representations. Beyond generation quality, we present Wan-Animate-2-Lite, an efficient variant that reduces inference latency to real-time thresholds through a three-stage training paradigm: teacher forcing pretraining with error buffer mechanism, and Self-Forcing distillation with chunk-wise backpropagation. This enables streaming character animation for interactive applications, opening new deployment scenarios that were previously infeasible. Qualitative evaluations and user studies demonstrate that Wan-Animate-2 achieves high-fidelity animation results across diverse characters and motion patterns. To foster further research and community development, we will release the Wan-Animate-2-Base model weights to the public.

Muon is a recent optimizer that orthogonalizes the update to each weight matrix with a Newton-Schulz iteration, which performs steepest descent under the spectral norm. Almost all the evidence for it comes from Transformer models, and its behavior on state-space models is largely unreported. We compare Muon with AdamW on Mamba-2 130M under a controlled protocol that varies only which weight groups are trained with Muon. The benefit is localized. Muon on the output projection alone beats Muon on the input projection or on both. The advantage is mainly one of token efficiency. It holds on two corpora and two token budgets, and persists when training continues well past the compute-optimal point. Conditioning does not explain the gain. Muon lowers the condition number of whichever projection it trains, but the better-conditioned input projection is not the one that helps.

Dense pretrained transformers do not naturally expose interpretable units for circuit extraction. Existing approaches obtain such units by learning auxiliary sparse representations or training sparse models, incurring substantial additional computation while potentially introducing a fidelity gap between the representation being analyzed and the original pretrained model. We propose Sparse Weight Decomposition (SWD), which reparameterizes pretrained linear projections by factorizing each weight matrix into two sparse factors whose shared intermediate coordinates serve as individually addressable circuit units. Without training a separate replacement network, this parametric representation supports the same scoring, selection, and ablation circuit extraction workflow used for methods that learn sparse features. Across single-matrix replacements, SWD matches the held-out fidelity achieved by Transcoder and other strong baselines while using less than 1% of the data that those baselines use to train their replacements. For matched replacement fidelity, SWD reaches the same circuit sufficiency and necessity targets with fewer active read/write edges and selected units across tasks on GPT-2, Qwen2.5, and Qwen3.5-27B. We further show that SWD remains effective for full-model replacement of all attention and MLP weight matrices after fine-tuning the nonzero factor values. Finally, SWD also features a zero-data variant, allowing broader use of mechanistic interpretability analysis (e.g., per-step analysis).

Fine-tuning a large language model on new data degrades what it previously learned. We present Omega-S, a drop-in penalty computed from the weight matrix alone: it needs no previous-task data, no Fisher matrix and no stored copy of the old weights. It is three lines in an existing training loop and adds under 4% to the cost of a step. Retention. On Llama-3-8B with LoRA, fine-tuned from code to prose and measured by HumanEval over ten seeds, Omega-S retains more of the original capability than no regularisation on 9 of 10 seeds (0.173 -> 0.238 absolute pass@1; sign test one-sided p=0.011, Wilcoxon p=0.006), as a retention ratio, 62.9% -> 84.1%. It also beats tuned weight decay on 10 of 10 seeds (p=0.002) and tuned EWC on 8 of 10 (p=0.014), every arm re-measured in the same session. Mechanism, measured rather than asserted. Omega-S is topological by construction, its objective built from Tr(A^3), but we measured which of its four factors actually moves and three do not: their elasticity with respect to the weights is at or below 1e-4, against 9e-3 for the degree-variance term. As implemented, the composite reduces to a penalty on the variance of node degrees, which means row magnitude in square modules and directional alignment in non-square ones. We report this because a method whose name promises one thing and whose gradient does another should say so. We also enumerate the open design choices, including a contrast-preserving construction that does what it was designed to do and makes retention worse on all ten seeds. Repeating an identical configuration, same seed and same hardware, gives a standard deviation of 0.104 in retention ratio. We have not found this quantified for low-rank fine-tuning of language models, and it bounds every seed-paired comparison in this literature, ours included. Code, per-seed results and the full record of negative results are available.

Matrix spectral optimizers reshape weight-update spectra but usually delegate vector-valued biases to a separate optimizer. We study whether this separation is neutral. We formulate each affine layer as a joint momentum matrix $A=[M_W,αm_b]$ and apply a capped regularized-inverse spectral map to the complete matrix, producing both the weight and physical bias updates. A strict five-seed ablation on a four-layer BERT-mini trained from scratch on IMDb compares exact-SVD Muon, weight-only inverse shaping, affine-probe inverse shaping, and the proposed joint regularized inverse (JRI). Weight-only inverse shaping raises validation-loss-selected test accuracy from $84.903\pm0.242\%$ to $85.562\pm0.308\%$ and lowers selected test loss from $0.3479$ to $0.3345$. Allowing bias to alter the joint SVD while retaining an independent Adam bias update does not improve over weight-only inverse shaping. Using the transformed bias jointly raises selected test accuracy to $85.738\pm0.180\%$ and lowers test loss to $0.3291$, with all five seeds improving relative to the probe baseline. During the peak-performance window, JRI preserves the eligible weight-update norm while reducing the bias-update norm from $0.02095$ to $0.00301$, lowers boundary-function share from $86.58\%$ to $78.97\%$, and changes the cosine between weight-induced boundary motion and explicit bias from $+0.030$ to $-0.137$. An independent 22-seed replication yields $85.743\pm0.203\%$ selected test accuracy. These results identify joint affine spectral allocation as a small but consistent extension to weight-only spectral optimization.

Language models often complete an underspecified reference to a city with unstated assumptions about urban size, form, infrastructure, environment, and function. We measure those assumptions without naming places. Ten open-weight checkpoints rate anonymized profiles derived from real morphological urban centres across 40 audited indicators and seven domains. The design combines constrained probability-based ratings, prespecified reliability screens, lineage-aware aggregation, multiple population weightings, an independent replication sample, and whole-profile validation. The clearest shared tendency favours urban profiles with larger developed area, faster recent growth, greater mapped infrastructure and non-residential capacity, and less sparse form. Most eligible directions recur in the replication data, and direct ratings of complete profiles show moderate agreement with the indicator-wise construction. Geographic differences shrink after accounting for city scale and development, while reliably measured paired tasks indicate that typicality and desirability are often closely aligned. The framework makes an otherwise vague notion of what models regard as an ordinary city empirically traceable. The resulting evidence delineates a shared yet model-dependent portrait of the city through the lens of language models.

Model families are typically trained size by size, each from scratch. Can apretrained large model instead be converted into a smaller sibling? Wecharacterize the 1.4B->410M conversion in the Pythia family end to end.Representations align strongly across sizes (ridge R^2=0.84) while parametersalign weakly. Dense weight projection is functionally destructive, and abit-exact reconstruction control shows this is not an assembly artifact: basismixing breaks rotary, per-head, GELU, and LayerNorm structure. After the best-fitlinear operator, weight residuals are statistically indistinguishable from noiseunder shuffle controls. Conversion value therefore lives in initialization. Inmatched-budget continued pre-training we decompose conversion into twoindependent levers: least-squares compensation (a function lever, best zero-shot)and variance-preserving rescale (a dynamics lever, best endpoints). Compensationis a token-efficient, low-budget win rather than a universal one. At 30M tokens itbeats the strongest subcloning variant on both a width-reduced pair (84.0 +/- 1.8vs. 89.7 +/- 3.7, 3/3 seeds) and a held-out depth-reduced pair (109.3 vs. 117.9,3/3 seeds), reaching a given quality with fewer tokens. At a 33x larger budget thetwo converge to parity (40.0 vs. 40.0), both far ahead of from-scratch, whichtransfer initialization always beats: by up to 18x at low budget, with the marginnarrowing at convergence and at the largest scale. We also map the method'sboundary. At about 5x the donor scale (6.9B->1.4B) stacking both leversover-corrects, consistent with ill-conditioning of the compensation solve at largewidth, which points to dimension-aware regularization as a fix. At matched budgetour initialization also beats structured pruning with distillation, the standardpipeline for this task, and improves further when combined with it. Code,checkpoints, and the frozen evaluation corpus are released.

Robot learning is splitting into two bets: policies that bake competence into frozen weights (vision-language-action, or VLA, models), and agents that write and refine their own executable skills as code. This survey organises the field around that axis of weights versus skills. Its central analytical contribution is a deep-dive that arranges code-as-policy methods by their degree of self-improvement, from zero-shot program synthesis, through closed-loop self-repair and persistent skill memory, to the sparsely populated cell in which execution feedback, skill memory, and evolutionary search combine into one open-ended loop; only a few very recent systems (for example ASPIRE, ENPIRE, and RoboClaw) occupy that cell. We map the complementary "skills" pole, from unsupervised reinforcement-learning skill discovery to large-language-model skill libraries, and show that the word "skill" is used in at least five distinct senses, of which only the code sense self-improves without gradient updates. We then connect the taxonomy to the emerging skill economy: commercial robot-skill marketplaces now distribute one-tap skills across robots but ship only static playback, which surfaces open problems of adaptation, cross-embodiment portability, provenance, safety verification, composition, and standardisation. This is a deliberately focused survey. Rather than cataloguing the field exhaustively, it examines 77 representative systems across six technique families through one taxonomy and a set of contrast tables, and it supplies operational definitions of the self-improvement mechanisms together with a statement of what each family cannot do.

Adapting a language model to a task no longer requires training all of its weights, and a line of parameter-efficient methods has driven the trainable count from billions down to a handful of scalars. Gradient-free adaptation, which samples random weight perturbations and keeps the ones that score well, has not followed that trajectory and still perturbs every entry of the weight tensor. It is unknown whether that full-weight search is necessary, and more fundamentally which property of a perturbation makes it work at all, because existing methods vary the search space, the perturbation scale, and the aggregation together. We resolve this by intervening on one factor at a time inside a fixed pipeline, holding candidate scoring and voting constant while we vary the search dimension, the subspace that carries the perturbation, and its norm. Perturbing a frozen frame of 12 to 16 scalars stays 1.8 accuracy points behind full-weight search on average across 49 model-benchmark cells, trailing it in 36 of them. Neither the dimension nor the choice of basis explains that performance. A random frame whose Grassmann overlap with the SVD frame is at chance level performs identically once a single scale factor is matched, and at large scales the SVD directions collapse first. What survives is the perturbation norm, whose usable range closes within a factor of five across seven models and stays flat inside. The perturbation norm is therefore the one factor with a failure mode, and its safe region transfers across scale and family. The design question narrows from which subspace to perturb to how hard to shake.

Vector symbolic architectures (VSA) are widely used for reasoning in neuro-symbolic (NeSy) AI, yet high-dimensional codebooks often create severe memory bottlenecks that limit scalability and deployment. In this paper, we propose Gram-Space, a compression framework that applies Gram-Schmidt orthogonalization to represent codebook vectors in a compact orthonormal coordinate system. Gram-Space preserves the dot-product structure required by matrix-based VSA operators, which supports numerically equivalent execution of matrix similarity, probability vectorization, and attention score computations. We provide a correctness analysis showing that inner products are preserved under the orthonormal basis representation. Using modern GPU hardware, we benchmark the Gram-Space framework on standard neuro-symbolic reasoning datasets. Experimental evaluations across state-of-the-art VSA models show that Gram-Space reduces model-level GPU memory usage by up to 15.75x and improves inference latency by up to 3.62x. Profiling results further indicate that Gram-Space reduces allocation-heavy overhead in codebook-associated stages and improves hardware utilization for NeSy workloads.

The cost of storing and transmitting a trained neural network scales with its parameter count, a bottleneck for over-the-air updates, on-device libraries, and other bandwidth-bound deployments. We study an extreme form of model compression in which the deployable artifact is not the weights but a short recipe for regenerating them. Building on Mapping Networks, which express a network's weights as a nonlinear function of a compact trainable latent and a fixed random basis, we observe that only the latent need be stored, because the basis and initialization center are reproducible from an integer seed. A model becomes a seed together with a quantized latent, whose size is set by the latent dimension and bit width rather than the parameter count. We formalize this artifact and introduce a seeded block-wise basis that scales to networks whose projection cannot be held in memory. In our experiments, a mapped model is as accurate as the same network quantized aggressively to a few bits per weight, while taking far fewer bytes to store. Reaching the most aggressive bit widths depends on fine-tuning the latent with quantization in the loop. The results do not depend on the particular random basis, and a structured basis lets the weights be regenerated almost for free even for large networks.

Implicit Neural Representations (INRs) encode signals as the weights of a coordinate-based neural network and have recently been proposed as an alternative domain for downstream learning. While promising, classification directly in weight space remains challenging due to the high dimensionality and complex structure of INR parameters. Furthermore, the way discriminative information is distributed across INR weights remains poorly understood. We propose a hierarchical Mixture-of-Experts (HMoE) Transformer that processes INR weights using conditional computation aligned with the structure of the underlying implicit network. Coupled with a meta-learning framework that shapes INR parameters for downstream tasks, our model achieves state-of-the-art accuracy across standard benchmarks, ranging from low-resolution datasets to high-resolution ImageNet-1K. To gain insight into how INRs encode discriminative information, we develop weight-space attribution and pruning methods that identify parameters most relevant for classification. These analyses reveal how class-specific structure emerges within INR layers and support the suitability of MoE architectures for weight-space learning. Our approach advances both the performance and interpretability of weight-space classifiers.

Generative UI (GenUI) lets large language models synthesize a complete, renderable interface directly from a natural-language instruction, but evaluating the quality of what they generate remains an open problem. Human evaluation is costly and rater-variant, while LLM-as-a-judge is scalable but reflects only a single implicit viewpoint, unable to capture how different populations of real users actually perceive the same interface. We propose the Evidence-Grounded, Social-Weighted Persona Panel (ESPP), a three-stage GenUI evaluation method in which a panel of psychologically diverse, evidence-grounded personas independently rates a screenshot, exchanges opinions under a trait-derived, semantically-gated bounded-confidence mechanism, and is aggregated via Delphi-inspired social weighting into a single judgment. ESPP tracks human judgment substantially more closely than a naive single-pass judge, raising Pearson $r$ from $0.716$ to $0.922$, and a prompt-ensemble control recovers only about a third of this gap, isolating genuine persona and evidence grounding as the dominant source of improvement. Beyond this fidelity gain, retaining each panelist's individual rating further reveals that user subgroups agree on overall model rankings yet diverge sharply on specific rating dimensions, a structural disagreement a single homogeneous judge would systematically erase. The codes are available at https://github.com/Wuzheng02/ESPP.

The performance of Large Language Models (LLMs) is fundamentally influenced by the distributional composition of multi-domain pre-training data. While manual heuristics were prevalent in early models, they increasingly fail to capture the intricate synergies between domains as data complexity grows. To overcome the issue, a dominant approach seeks to fit a proxy function mapping between domain weights and their corresponding validation losses, and then find the optimal domain weights to minimize validation losses. These methods rely on strong structural assumptions, such as rank invariance or scaling laws, which are often violated, resulting in non-negligible estimation bias. A promising approach is to directly optimize the weighting scheme from data. However, it suffers from unstable optimization trajectory and prohibitive computational overhead, limiting its potential to search better domain weights configurations. This paper presents a Bayesian domain weighting method to infer the weights from a Dirichlet distribution via introducing Gamma prior information learned from observations. Experimental results demonstrate that proposed method could achieve stable and efficient domain weights learning, and identifies optimal mixtures while consuming substantially less data than search-based function-fitting methods, revitalizing optimization-based domain weighting for large-scale applications.

A temporally drifting data stream may pass through discrete regimes rather than changing continuously. We ask whether such regimes are recoverable from the weights of models trained on the stream, using a hidden Markov model (HMM) fit to the chronologically ordered trajectory of those weights. We study this question in two domains known to drift over time: multimodal misinformation detection, using the Fakeddit dataset; and sentiment analysis, using the Yelp dataset. We train classifiers on consecutive temporal windows and fit an HMM to the trajectory of their aligned weights, recovering latent states that partition each timeline into coherent phases. On both datasets, classifiers generalize better to data from windows sharing the state of their training window than to windows across state boundaries. This within-state transfer advantage survives a control for temporal proximity and modestly exceeds the advantage recovered by a naive partition into contiguous states of equal size. Although the states are estimated solely from model weights, they correlate more strongly with shifts in the data's class distribution than with the weight-space geometry used to estimate them. After class divergence and lag are residualized out, the within-state advantage exceeds its permutation null on both tasks, indicating that the states recover structure relevant to transfer beyond the data distribution. Every effect replicates on both tasks but is attenuated on Yelp, whose label distribution is more temporally stable.

Deep off-policy reinforcement learning algorithms for continuous control typically rely on neural value function approximation to guide policy improvement. However, temporal-difference (TD) learning introduces noisy targets, resulting in non-stationary optimization, while greedy policy updates amplify early-stage estimation errors. The recursive propagation of such errors leads to persistent overestimation bias and degraded training stability in actor-critic methods. Existing approaches attempt to alleviate this issue via prioritized sampling or modified value learning objectives, but often overemphasize high-uncertainty transitions caused by limited data coverage or bootstrapping errors, thereby further amplifying bias.In this paper, we propose Collaborative Weighting Actor-Critic (CWAC), a unified framework that explicitly accounts for predictive uncertainty in value estimation. CWAC employs distributional critic to model return uncertainty and introduces a collaborative weighting mechanism that jointly reweights TD-errors and uncertainty, enabling robust learning from reliable samples while suppressing noisy updates. In addition, we incorporate a stochastic pessimistic value estimation scheme via sampling from the return distribution, which effectively mitigates error propagation during policy improvement. CWAC can be seamlessly integrated into existing off-policy algorithm frameworks such as SAC, TD3, and DDPG with minimal overhead. Empirical results demonstrate that our proposed method significantly enhances performance across a diverse range of simulated tasks. Our code is publicly available at https://anonymous.4open.science/r/CWAC-348E.

Low-rank adaptation (LoRA) fine-tuning has made it cheap and easy to customize open-weight image generation models for specific tasks, including the production of child sexual abuse material (CSAM). Existing moderation relies on metadata or generated outputs, but metadata can be deceptive and generating outputs may itself be unacceptable or illegal. We show that a safer signal lives in the weights. The top-left singular vectors of a LoRA's updates form a compact, inference-free fingerprint ($u_1$) of its strongest learned change. Using human-subject age as a benign proxy for CSAM, we find that $u_1$ identifies what a LoRA was trained on, generalizes across base models, and abstains on unrelated benign content. The signal is robust to additive weight noise, rescaling, and precision reduction. These results indicate that harmful LoRAs could be screened directly from their weights without relying on metadata or generating harmful outputs.

A person's physical characteristics such as weight and height are important indicators of his physical and mental health, daily life routines and finances. Body Mass Index (BMI) is a well known measure that encodes the characteristics of both the weight and the height. BMI has been used as a self-monitoring tool, and it has long-term implications on one's life. For example, it may help predicting the risk of various diseases and estimating longevity. Automatic BMI estimation using a single person image in the wild is a challenging task due to wide variations in human pose, camera geometry, personal appearance and distracting backgrounds. In this paper, we explore the performance of deep neural networks using single and multi-task learning by employing different modalities including RGB, depth-maps, pose-affinity maps, and edge-maps to predict BMI, weight, and height from daily life images available on social networking websites. Currently, no full body image dataset for BMI estimation is publicly available, therefore we propose a new dataset consisting of 6105 images with ground truth labels of height, weight and BMI. Our proposed dataset is collected in the wild containing images from various ethnicity and distributed over varying age groups and gender. It consists of frontal, back, full and half body, side poses, mirror selfies with varying backgrounds and scale variations and may contain artifacts hiding partial or full face. Extensive experimentation is performed using full body, half body and face images only using different CNN backbones including VGG, Densenet and ResNet. Our experimental results demonstrate that full body images have produced better results than the other half body and facial images in the wild.

Biomedical image analysis spans diverse modalities and tasks, yet real-world deployment is hindered by severe distribution shifts across scanners, protocols, and patient populations. High-performing models consequently require repeated domain-specific fine-tuning, which is a costly cycle that becomes impractical when labels are scarce or privacy constraints limit data sharing. We propose OPERA (Offline Policy-guided Expert Routing and Adaptation), a multi-agent ensemble framework that addresses this deployment bottleneck by treating expert weight assignment as an offline policy learning problem: a routing policy is learned from a small validation set without gradient updates to any expert agent, then deployed with test-time adaptation to handle distribution shift. OPERA coordinates heterogeneous specialist agents through complementary mechanisms. The expert profiling module learns selection policies offline, enabling informed allocation of expertise. Each agent undergoes confidence calibration through temperature adjustment, ensuring more reliable probabilistic outputs. OPERA also incorporates distribution aware adaptation, where class weights are dynamically adjusted at the batch level using statistics derived from unlabeled test data. Instance level routing assigns each sample to the most suitable expert by leveraging inter model agreement and predictive entropy. We evaluate OPERA on 9 datasets covering fundus photography, chest X-ray, CT, MRI, and multimodal diagnostic benchmarks, comparing against 30+ baselines across classification, segmentation, and multimodal settings. OPERA consistently improves performance and calibration quality, demonstrating that offline policy-guided expert agents coordination is a practical path to deployable biomedical AI without retraining. Code is on \href{https://github.com/HUANGLIZI/OPERA}{GitHub}.

We introduce Kimi K3, a 2.8T parameter Mixture-of-Experts model with 104 billion activated parameters, native vision capabilities, and a 1-million-token context window. Kimi K3 is built on Kimi Delta Attention and Attention Residuals, which improve information flow across sequence length and model depth. Together with Stable LatentMoE, which effectively activates 16 of 896 routed experts per token, and refined training and data recipes, these advances yield an approximately 2.5x improvement in overall scaling efficiency over Kimi K2. Post-training highlights reinforcement learning across general, agentic, and coding domains and multiple reasoning-effort levels, enabling compositional generalization and robust long-horizon execution. At 2.8T scale, Kimi K3 is supported by infrastructure advances in multiple areas: algorithm-system co-design for KDA, perfectly balanced expert-parallel training with efficient memory management, million-token agentic RL with persistent rollout and sandbox states, and deployment innovations. Extensive evaluations show that Kimi K3 achieves frontier-level performance across long-horizon coding, agentic, knowledge, reasoning, and vision tasks. While its overall performance still trails the most powerful proprietary models, namely Claude Fable 5 and GPT-5.6 Sol, Kimi K3 consistently outperforms other open and proprietary models evaluated in our suite. We release the full Kimi K3 model weights to facilitate future research and accelerate the broader deployment and adoption of frontier intelligence.

The discovery of scaling laws has motivated training neural networks on ever increasing quantities of data. This is typically done with a constant decoupled weight decay which causes the network weights to shrink steadily over the course of training. Taking inspiration from the Robbins--Monro conditions, we propose to scale weight decay by the fraction of the peak learning rate $η/η_{\max}$. We prove that this scaled weight decay preserves the asymptotic stationarity guarantees of the corresponding unregularized methods for both stochastic gradient descent and the non-Euclidean spectral optimizer Muon, thereby avoiding the additional asymptotic bias introduced by constant decoupled weight decay. This retains the stability benefits of weight decay without changing the asymptotic optimization target. Using a steady-state analysis, we explain why under standard weight decay the weight norm shrinks steadily as training proceeds, whereas under scaled weight decay it settles to a roughly constant value. When applied to the training of mixture-of-experts models, Muon with scaled weight decay (Muon-SW) consistently outpaces Muon with identical hyperparameters, reaching the same validation loss $\mathbf{30\%}$ faster at our largest scale across models from $72 - 930$ million parameters trained at $\sim 600$ tokens per active parameter. If this trend continues to hold, the method promises to substantially accelerate the pre-training of frontier models while requiring only a few lines of code to implement.

Weights and biases are normally optimized as separate parameter tensors, yet they do not represent separate functions when the input to an affine layer has nonzero mean. For an affine map $z=Wx+b$ with input mean $μ$, a weight update contains a sample-independent displacement $ΔWμ$ that is functionally indistinguishable from a bias update. We call this hidden contribution \emph{boundary motion} and decompose each update into a centered, sample-varying \emph{shape} component and a shared \emph{boundary} component. On a four-layer Transformer trained from scratch on IMDb, the bias-like term $g_bμ^\top$ has a median norm equal to 0.664 of the raw weight-gradient norm across affine layers and training checkpoints. More strikingly, the median ratio $\norm{ΔWμ}/\norm{Δb}$ is 134.7, while $\norm{ΔWμ}/\norm{Δb+ΔWμ}$ is 0.994. Thus, under AdamW, the observed boundary motion is almost entirely realized through the weight matrix rather than the explicit bias. We implement a diagnostic optimizer, Shape--Boundary Orthogonal AdamW (SBO-AdamW), that optimizes $g_W-g_bμ^\top$ and $g_b$ with independent Adam states and compensates the weight-induced boundary displacement. In a single-seed experiment, SBO-AdamW raises validation accuracy from 81.68% to 85.81% and validation-selected test accuracy from 78.73% to 82.73%, with the best validation checkpoint occurring at step 800 instead of step 3000. However, the moving-batch-center compensation produces severe bias-coordinate drift and strongly reduces boundary energy. The present evidence therefore supports hidden boundary motion as an important optimization mechanism, but it does not yet establish a final general-purpose optimizer. A stable centered-affine parameterization is identified as the required next step.

Machine unlearning aims to remove the influence of specific training data while preserving model utility. Many state-of-the-art approaches pursue this goal by restricting the forgetting update to a subset of parameters selected through gradient-based saliency. Although such methods are widely adopted, the actual contribution of saliency-based weight selection to representation-level forgetting remains unclear. In this work, we perform the first controlled ablation of the saliency masking mechanism used by SalUn. Using a matched-compute experimental design on CIFAR-10 and CIFAR-100 with ResNet-18, we compare saliency-based masking against random masks of equal sparsity and unconstrained updates, while keeping the unlearning objective, optimization schedule, and computational budget fixed. Across multiple representation-level evaluations, including linear probing, prototype recovery, and layer-wise CKA, the three configurations exhibit statistically equivalent representation-level recoverability. We find that forget gradients are strongly concentrated in the final network layers (approximately 92% of the squared gradient energy on CIFAR-10) before any mask is applied, causing all masking strategies to operate within the same representational subspace. Furthermore, saliency masks show limited class specificity (specificity index 0.09-0.11), selecting highly overlapping parameter subsets across different forget classes. Our findings suggest that, in the studied setting, representation-level forgetting is primarily governed by gradient concentration and representation geometry rather than by the specific identity of saliency-selected weights. More broadly, the results support a growing body of evidence indicating that effective representation-level unlearning requires objectives that act directly on latent representations rather than on increasingly sophisticated weight-selection strategies.

Most explanations of training instability focus on \emph{learning-rate criticality}, typically characterized by the Edge of Stability, beyond which optimization becomes unstable. We argue that, in practical deep neural network training, there is an additional and often overlooked \emph{weight-norm criticality}. This criticality is induced by the interaction between normalization (which introduces scale-invariant components) and weight decay (which persistently shrinks parameter norms). As the weight decay coefficient increases, the norms of scale-invariant weights are progressively driven toward zero. Meanwhile, the sharpness of the loss landscape increases rapidly, destabilizing the optimization dynamics and resulting in abrupt loss spikes. This perspective provides a rationale for why weight penalties can improve generalization yet cannot be made arbitrarily strong: excessive decay drives scale-invariant weight norms past a critical boundary and destabilizes training. Our work provides a new mechanistic understanding of loss spikes through the lens of \emph{weight-norm criticality}. Moreover, \emph{weight-norm criticality} yields testable predictions that we validate empirically in networks with scale-invariant components, providing empirical support for the proposed mechanism.

Muon and related matrix-sign optimizers are increasingly used to pre-train large language models, but their effect on the internal geometry of individual weight matrices is not well understood. This preliminary report proposes a unified framework built on a single idealizing assumption -- exact scale invariance of the loss under weight rescaling, which holds approximately in normalization-heavy networks. Under this assumption, plain SGD carries a built-in 1/||W|| brake on its update size, whereas Muon's matrix-sign step removes that brake, so both the Frobenius and spectral norms drift outward faster (t^{1/2} versus t^{1/4}). We further observe that the spectral-norm perturbation has a non-negative second-order term. This implies that a lightweight "spectral cap" -- which projects out only the first-order growth of the single top singular direction from each update -- can control the output covariance W K_X W^T without freezing training: the weight keeps learning through non-top directions, top-direction rotation, and top switching. We relate this cap to the min-entropy (H-infinity) of the singular-value spectrum. We then study three systems trained with Muon: a nanoGPT feed-forward projection, a 64-expert mixture-of-experts router, and the query/key projections of a bf16 FlashAttention block. In each case the cap increases isotropy and, at the margins -- a router collapsing to a single expert, and the near-divergence of one attention head -- prevents a concrete failure, while leaving validation loss essentially unchanged. We emphasize that the scale-invariance assumption is strong and that these small-scale results are preliminary; comments are welcome.

Mixture-of-Experts (MoE) is a popular class of large language models (LLMs), offering high efficiency and accuracy. However, in KV-cache-intensive serving scenarios, MoEs often exhibit a tension between the GPU memory requirements of the model weights and the growing KV cache. We propose PagedWeight, a novel management method for MoE LLM serving that dynamically quantizes MoE model's weights at runtime and balances expert-weight precision with the KV cache sizes. PagedWeight exposes and effectively navigates the complex tradeoff between the model's task accuracy, memory consumption, and throughput/latency. Across several memory-sensitive MoE serving scenarios, PagedWeight improves the quality-memory tradeoff over several existing quantization baselines. PagedWeight achieves FP16-equivalent accuracy with up to 72.0% GPU memory savings and 1.94$\times$ throughput improvement, and improves quality over quantization methods by up to 39.3% at a similar memory budget with at most 4.1% throughput loss.