Daily Papers

Post-training compression of Transformer models commonly relies on truncated singular value decomposition (SVD). However, enforcing a single shared subspace can degrade accuracy even at moderate compression. Sparse dictionary learning provides a more flexible union-of-subspaces representation, but existing approaches often suffer from iterative dictionary and coefficient updates. We propose COMPOT (Calibration-Optimized Matrix Procrustes Orthogonalization for Transformers), a training-free compression framework that uses a small calibration dataset to estimate a sparse weight factorization. COMPOT employs orthogonal dictionaries that enable closed-form Procrustes updates for the dictionary and analytical single-step sparse coding for the coefficients, eliminating iterative optimization. To handle heterogeneous layer sensitivity under a global compression budget, COMPOT further introduces a one-shot dynamic allocation strategy that adaptively redistributes layer-wise compression rates. Extensive experiments across diverse architectures and tasks show that COMPOT consistently delivers a superior quality-compression trade-off over strong low-rank and sparse baselines, while remaining fully compatible with post-training quantization for extreme compression. Code is available https://github.com/mts-ai/COMPOT{here}.

3D Gaussian Splatting (3DGS) has emerged as a core technique for 3D representation. Its effectiveness largely depends on precise camera poses and accurate point cloud initialization, which are often derived from pretrained Multi-View Stereo (MVS) models. However, in unposed reconstruction task from hundreds of outdoor images, existing MVS models may struggle with memory limits and lose accuracy as the number of input images grows. To address this limitation, we propose a novel unposed 3DGS reconstruction framework that integrates pretrained MVS priors with the probabilistic Procrustes mapping strategy. The method partitions input images into subsets, maps submaps into a global space, and jointly optimizes geometry and poses with 3DGS. Technically, we formulate the mapping of tens of millions of point clouds as a probabilistic Procrustes problem and solve a closed-form alignment. By employing probabilistic coupling along with a soft dustbin mechanism to reject uncertain correspondences, our method globally aligns point clouds and poses within minutes across hundreds of images. Moreover, we propose a joint optimization framework for 3DGS and camera poses. It constructs Gaussians from confidence-aware anchor points and integrates 3DGS differentiable rendering with an analytical Jacobian to jointly refine scene and poses, enabling accurate reconstruction and pose estimation. Experiments on Waymo and KITTI datasets show that our method achieves accurate reconstruction from unposed image sequences, setting a new state of the art for unposed 3DGS reconstruction.

Training-free open-vocabulary semantic segmentation (OVSS) promises rapid adaptation to new label sets without retraining. Yet, many methods rely on heavy post-processing or handle text and vision in isolation, leaving cross-modal geometry underutilized. Others introduce auxiliary vision backbones or multi-model pipelines, which increase complexity and latency while compromising design simplicity. We present PEARL, \underline{P}rocrust\underline{e}s \underline{a}lignment with text-awa\underline{r}e \underline{L}aplacian propagation, a compact two-step inference that follows an align-then-propagate principle. The Procrustes alignment step performs an orthogonal projection inside the last self-attention block, rotating keys toward the query subspace via a stable polar iteration. The text-aware Laplacian propagation then refines per-pixel logits on a small grid through a confidence-weighted, text-guided graph solve: text provides both a data-trust signal and neighbor gating, while image gradients preserve boundaries. In this work, our method is fully training-free, plug-and-play, and uses only fixed constants, adding minimal latency with a small per-head projection and a few conjugate-gradient steps. Our approach, PEARL, sets a new state-of-the-art in training-free OVSS without extra data or auxiliary backbones across standard benchmarks, achieving superior performance under both with-background and without-background protocols.

The Platonic Representation Hypothesis suggests that independently trained neural networks converge to increasingly similar latent spaces. However, current strategies for mapping these representations are inherently pairwise, scaling quadratically with the number of models and failing to yield a consistent global reference. In this paper, we study the alignment of M ge 3 models. We first adapt Generalized Procrustes Analysis (GPA) to construct a shared orthogonal universe that preserves the internal geometry essential for tasks like model stitching. We then show that strict isometric alignment is suboptimal for retrieval, where agreement-maximizing methods like Canonical Correlation Analysis (CCA) typically prevail. To bridge this gap, we finally propose Geometry-Corrected Procrustes Alignment (GCPA), which establishes a robust GPA-based universe followed by a post-hoc correction for directional mismatch. Extensive experiments demonstrate that GCPA consistently improves any-to-any retrieval while retaining a practical shared reference space.

Chain-of-thought (CoT) supervised fine-tuning (SFT) is widely adopted to improve reasoning ability, yet we find that it systematically degrades long-context recall in hybrid linear-attention models. Across architectures including HypeNet and Jet-Nemotron, retrieval performance on Needle-In-A-Haystack (NIAH) deteriorates substantially after CoT-SFT, and the degradation becomes more severe under harder retrieval settings and longer context windows. For example, HypeNet-9B on NIAH-S2@256K decreases from 67.2% to 9.4%. We attribute this to CoT-SFT biasing attention gradients toward short-range patterns, disrupting query-key projections (W_Q, W_K) that are responsible for long-range routing. Motivated by this observation, we propose QK-Restore, a training-free method that restores only W_Q and W_K from the pre-SFT checkpoint while preserving all other post-SFT parameters. We further introduce a Procrustes variant to balance routing preservation and reasoning adaptation. Across architectures, QK-Restore consistently restores long-context capability at zero training cost while preserving reasoning performance; for instance, on HypeNet-5B it improves S3@256K from 65.4% to 76.4% while maintaining strong reasoning performance.

Multimodal representations enable zero-shot classification and retrieval, but aligning independently trained models usually requires large amounts of paired data. Yet, the Platonic Representation Hypothesis suggests that models trained on different modalities may converge spontaneously toward a shared representation geometry. But then, do we even need paired examples for cross-modal alignment? Remarkably, we show that paired examples are unnecessary for coarse cross-modal alignment. Our simple Wasserstein Procrustes method with a coarse geometric initialization aligns two disjoint embedding sets by estimating a single orthogonal map without seeing any pairs. Across datasets, modalities, and unimodal models, we show that we can consistently align independently trained representations without pairs, and standard geometric alignment metrics accurately predict when this is possible. Nevertheless, we can naturally benefit from paired examples. In the very few-pair regime, our method substantially outperforms existing ones, while staying competitive with pair-based methods with more added examples. Finally, we demonstrate that the resulting alignments can enable text-to-image generation without paired examples. These results show that independently trained models often share enough geometry to establish cross-modal correspondence with little or no paired data.

Foundation models remain vulnerable to spurious correlations and ``Clever Hans'' strategies. Explainable machine learning can find and remove such strategies for classifiers without metadata. For foundation models, no such option exists yet. We propose Disentangled Diffusion Autoencoders (DiDAE). DiDAE wraps a frozen foundation model in a conditional diffusion decoder. A counterfactual is one closed-form edit along a direction of a disentangled dictionary, followed by decoding. The dictionary can be supervised (Procrustes) or unsupervised (Singular Value Decomposition, Sparse Autoencoders). No gradients are needed, so DiDAE is up to 2000 times faster than the state of the art. We evaluate on six datasets, two synthetic and four real-world. In a desiderata-driven benchmark on three of them, its counterfactuals are on par with or better than the state of the art, and they repair downstream classifiers through Counterfactual Knowledge Distillation (CFKD), where they beat metadata-based correction. The same machinery can rank a pretrained dictionary against a trained classifier. It returns the few directions the classifier actually reads, each causally verified by a counterfactual that flips the decision, and repairs the classifier along those a teacher marks spurious. The workflow is plug-and-play in our open-source Peal library we publish alongside the paper. With a public dictionary and a pretrained decoder, all that remains is a cheap linear distillation of the classifier and its own fine-tuning.

Gait recognition is a significant biometric technique for person identification, particularly in scenarios where other physiological biometrics are impractical or ineffective. In this paper, we address the challenges associated with gait recognition and present a novel approach to improve its accuracy and reliability. The proposed method leverages advanced techniques, including sequential gait landmarks obtained through the Mediapipe pose estimation model, Procrustes analysis for alignment, and a Siamese biGRU-dualStack Neural Network architecture for capturing temporal dependencies. Extensive experiments were conducted on large-scale cross-view datasets to demonstrate the effectiveness of the approach, achieving high recognition accuracy compared to other models. The model demonstrated accuracies of 95.7%, 94.44%, 87.71%, and 86.6% on CASIA-B, SZU RGB-D, OU-MVLP, and Gait3D datasets respectively. The results highlight the potential applications of the proposed method in various practical domains, indicating its significant contribution to the field of gait recognition.

Merging finetuned Large Language Models (LLMs) has become increasingly important for integrating diverse capabilities into a single unified model. However, prevailing model merging methods rely on linear arithmetic in Euclidean space, which often destroys the intrinsic geometric properties of pretrained weights, such as hyperspherical energy. To address this, we propose Orthogonal Model Merging (OrthoMerge), a method that performs merging operations on the Riemannian manifold formed by the orthogonal group to preserve the geometric structure of the model's weights. By mapping task-specific orthogonal matrices learned by Orthogonal Finetuning (OFT) to the Lie algebra, OrthoMerge enables a principled yet efficient integration that takes into account both the direction and intensity of adaptations. In addition to directly leveraging orthogonal matrices obtained by OFT, we further extend this approach to general models finetuned with non-OFT methods (i.e., low-rank finetuning, full finetuning) via an Orthogonal-Residual Decoupling strategy. This technique extracts the orthogonal components of expert models by solving the orthogonal Procrustes problem, which are then merged on the manifold of the orthogonal group, while the remaining linear residuals are processed through standard additive merging. Extensive empirical results demonstrate the effectiveness of OrthoMerge in mitigating catastrophic forgetting and maintaining model performance across diverse tasks.

This paper reveals a novel linear characteristic exclusive to transformer decoders, including models such as GPT, LLaMA, OPT, BLOOM and others. We analyze embedding transformations between sequential layers, uncovering a near-perfect linear relationship (Procrustes similarity score of 0.99). However, linearity decreases when the residual component is removed due to a consistently low output norm of the transformer layer. Our experiments show that removing or linearly approximating some of the most linear blocks of transformers does not affect significantly the loss or model performance. Moreover, in our pretraining experiments on smaller models we introduce a cosine-similarity-based regularization, aimed at reducing layer linearity. This regularization improves performance metrics on benchmarks like Tiny Stories and SuperGLUE and as well successfully decreases the linearity of the models. This study challenges the existing understanding of transformer architectures, suggesting that their operation may be more linear than previously assumed.

Tracking semantic change in low-resource languages across extensive historical timelines presents significant challenges due to data scarcity and the limitations of static embedding alignments. This study investigates the diachronic evolution of the Sinhala language from the 13th to the 20th century using a multi-stage computational framework. We first align century-specific Word2Vec and FastText embeddings using Similarity Matrix Based Alignment (SMA) and Orthogonal Procrustes (OP) techniques, finding that OP alignment provides more stable neighbourhood tracking for identifying temporal similarity dips. To move beyond aggregate measures, we introduce a Bidirectional Semantic Impact Pruning approach using contextualised embeddings from a fine-tuned Llama-3.1-8B. By applying Leave-One-Out (LOO) diagnostics, we attempt to isolate influential sentences to distinguish between systemic semantic shifts and transient polysemic expansion. Our results show that semantic drift in the fine-tuned Llama-3.1-8B is not evenly distributed across all usages. Instead, a significant part of the change is driven by a smaller set of high-impact contextual instances, rather than gradual and uniform change across all occurrences. This work provides a preliminary framework for diachronic analysis in low-resource contexts, highlighting the trade-offs between model sensitivity and data availability.

This onomasiological study uses diachronic word embeddings to explore how different words represented the same concepts over time, using historical word data from 1800 to 2000. We identify shifts in energy, transport, entertainment, and computing domains, revealing connections between language and societal changes. Our approach consisted in using diachronic word embeddings trained using word2vec with skipgram and aligning them using orthogonal Procrustes. We discuss possible difficulties linked to the relationships the method identifies. Moreover, we look at the ethical aspects of interpreting results, highlighting the need for expert insights to understand the method's significance.

We present 3DRegNet, a novel deep learning architecture for the registration of 3D scans. Given a set of 3D point correspondences, we build a deep neural network to address the following two challenges: (i) classification of the point correspondences into inliers/outliers, and (ii) regression of the motion parameters that align the scans into a common reference frame. With regard to regression, we present two alternative approaches: (i) a Deep Neural Network (DNN) registration and (ii) a Procrustes approach using SVD to estimate the transformation. Our correspondence-based approach achieves a higher speedup compared to competing baselines. We further propose the use of a refinement network, which consists of a smaller 3DRegNet as a refinement to improve the accuracy of the registration. Extensive experiments on two challenging datasets demonstrate that we outperform other methods and achieve state-of-the-art results. The code is available.

CLIP is a discriminative model trained to align images and text in a shared embedding space. Due to its multimodal structure, it serves as the backbone of many generative pipelines, where a decoder is trained to map from the shared space back to images. In this work, we show that image synthesis is nevertheless possible using CLIP alone -- without any decoder, training, or fine-tuning. Our approach optimizes a frequency-aware implicit neural representation that encourages coarse-to-fine generation by stratifying frequencies across network layers. To stabilize this inverse mapping, we introduce adversarially robust initialization, a lightweight Orthogonal Procrustes projection to align local text and image embeddings, and a blending loss that anchors outputs to natural image statistics. Without altering CLIP's weights, this framework unlocks capabilities such as text-to-image generation, style transfer, and image reconstruction. These findings suggest that discriminative models may hold untapped generative potential, hidden in plain sight.

Collecting large, aligned cross-modal datasets for music-flavor research is difficult because perceptual experiments are costly and small by design. We address this bottleneck through two complementary experiments. The first tests whether audio-flavor correlations, feature-importance rankings, and latent-factor structure transfer from an experimental soundtracks collection (257~tracks with human annotations) to a large FMA-derived corpus (sim49,300 segments with synthetic labels). The second validates computational flavor targets -- derived from food chemistry via a reproducible pipeline -- against human perception in an online listener study (49~participants, 20~tracks). Results from both experiments converge: the quantitative transfer analysis confirms that cross-modal structure is preserved across supervision regimes, and the perceptual evaluation shows significant alignment between computational targets and listener ratings (permutation p<0.0001, Mantel r=0.45, Procrustes m^2=0.51). Together, these findings support the conclusion that sonic seasoning effects are present in synthetic FMA annotations. We release datasets and companion code to support reproducible cross-modal AI research.

Reliable deployment of language models requires two capabilities that appear distinct but share a common geometric foundation: predicting whether a model will accept targeted behavioral control, and detecting when its internal structure degrades. We show that geometric stability, the consistency of a representation's pairwise distance structure, addresses both. Supervised Shesha variants that measure task-aligned geometric stability predict linear steerability with near-perfect accuracy (ρ= 0.89-0.97) across 35-69 embedding models and three NLP tasks, capturing unique variance beyond class separability (partial ρ= 0.62-0.76). A critical dissociation emerges: unsupervised stability fails entirely for steering on real-world tasks (ρapprox 0.10), revealing that task alignment is essential for controllability prediction. However, unsupervised stability excels at drift detection, measuring nearly 2times greater geometric change than CKA during post-training alignment (up to 5.23times in Llama) while providing earlier warning in 73\% of models and maintaining a 6times lower false alarm rate than Procrustes. Together, supervised and unsupervised stability form complementary diagnostics for the LLM deployment lifecycle: one for pre-deployment controllability assessment, the other for post-deployment monitoring.