Daily Papers

Complete orthogonal predictive coordinates do not by themselves bind a latent direction to a named intervention. We present a mathematical and synthetic audit motivated by vascular device-vessel suitcordance. Capacity-matched least-squares predictors were exactly equivalent under complete fixed output transforms, whereas an anchor-only observer recovered interpretations only within the span of known perturbation signatures. Six three-dimensional configurations across 64 seeds gave a maximum paired prediction discrepancy of 6.7e-15 but a median untransported edit error of 1.513. Coordinate transport removed that error. Noisy and weak anchors constrained calibration stability, and changing the representation basis required recalibration or verified transport. Across 256 additional fits in dimensions 3-24, prediction equivalence persisted within 4.0e-15. We then evaluated nine deliberate runnable fault classes across 64 seeds. All 576 faulty executions completed, but each violated at least one reconstruction, prediction, delivered-edit or scope contract; all 320 valid control records passed. Repeating a faulty implementation gave exact self-agreement despite error against the separately computed simulator expectation. For one omitted-direction defect, probe coverage followed its analytic law, and rank-aware abstention protected unsupported interpretations. Scalar-noise experiments exposed both missed weak faults and excessive rejection under narrow relative tolerances. These controls provide an executable separation of prediction, semantic support and scientific acceptance. They are synthetic numerical audits, not clinical validation, neural JEPA-Anything replication, agent learning or patient treatment-effect estimation.

Classical simulation of quantum physics is a central approach to investigating physical phenomena. Quantum computers enhance computational capabilities beyond those of classical resources, but it remains unclear to what extent existing limited quantum computers can contribute to this enhancement. In this work, we explore a new hybrid, efficient quantum-classical representation of quantum states, the multiple-basis representation. This representation consists of a linear combination of states that are sparse in some given and different bases, specified by quantum circuits. Such representation is particularly appealing when considering depth-limited quantum circuits within reach of current hardware. We analyze the expressivity of multiple-basis representation states depending on the classical simulability of their quantum circuits. In particular, we show that multiple-basis representation states include, but are not restricted to, both matrix-product states and stabilizer states. Furthermore, we find cases in which this representation can be used, namely approximation of ground states, simulation of deeper computations by specifying bases with shallow circuits, and a tomographical protocol to describe states as multiple-basis representations. We envision this work to open the path of simultaneous use of several hardware-friendly bases, a natural description of hybrid computational methods accessible for near-term hardware.

Recently, sophisticated deep learning-based approaches have been developed for generating efficient initial guesses to accelerate the convergence of density functional theory (DFT) calculations. While the actual initial guesses are often density matrices (DM), quantities that can convert into density matrices also qualify as alternative forms of initial guesses. Hence, existing works mostly rely on the prediction of the Hamiltonian matrix for obtaining high-quality initial guesses. However, the Hamiltonian matrix is both numerically difficult to predict and intrinsically non-transferable, hindering the application of such models in real scenarios. In light of this, we propose a method that constructs DFT initial guesses by predicting the electron density in a compact auxiliary basis representation using E(3)-equivariant neural networks. Trained on small molecules with up to 20 atoms, our model is able to achieve an average 33.3% self-consistent field (SCF) step reduction on systems up to 60 atoms, substantially outperforming Hamiltonian-centric and DM-centric models. Critically, this acceleration remains nearly constant with increasing system sizes and exhibits strong transferring behaviors across orbital basis sets and exchange-correlation (XC) functionals. To the best of our knowledge, this work represents the first and robust candidate for a universally transferable DFT acceleration method. We are also releasing the SCFbench dataset and its accompanying code to facilitate future research in this promising direction.

We introduce 3DShape2VecSet, a novel shape representation for neural fields designed for generative diffusion models. Our shape representation can encode 3D shapes given as surface models or point clouds, and represents them as neural fields. The concept of neural fields has previously been combined with a global latent vector, a regular grid of latent vectors, or an irregular grid of latent vectors. Our new representation encodes neural fields on top of a set of vectors. We draw from multiple concepts, such as the radial basis function representation and the cross attention and self-attention function, to design a learnable representation that is especially suitable for processing with transformers. Our results show improved performance in 3D shape encoding and 3D shape generative modeling tasks. We demonstrate a wide variety of generative applications: unconditioned generation, category-conditioned generation, text-conditioned generation, point-cloud completion, and image-conditioned generation.

We show how the Schur-Weyl duality that exists between the partition algebra and the symmetric group results in a stronger theoretical foundation for characterising all of the possible permutation equivariant neural networks whose layers are some tensor power of the permutation representation M_n of the symmetric group S_n. In doing so, we unify two separate bodies of literature, and we correct some of the major results that are now widely quoted by the machine learning community. In particular, we find a basis of matrices for the learnable, linear, permutation equivariant layer functions between such tensor power spaces in the standard basis of M_n by using an elegant graphical representation of a basis of set partitions for the partition algebra and its related vector spaces. Also, we show how we can calculate the number of weights that must appear in these layer functions by looking at certain paths through the McKay quiver for M_n. Finally, we describe how our approach generalises to the construction of neural networks that are equivariant to local symmetries.

Synthesizing whole-body manipulation of articulated objects, including body motion, hand motion, and object motion, is a critical yet challenging task with broad applications in virtual humans and robotics. The core challenges are twofold. First, achieving realistic whole-body motion requires tight coordination between the hands and the rest of the body, as their movements are interdependent during manipulation. Second, articulated object manipulation typically involves high degrees of freedom and demands higher precision, often requiring the fingers to be placed at specific regions to actuate movable parts. To address these challenges, we propose a novel coordinated diffusion noise optimization framework. Specifically, we perform noise-space optimization over three specialized diffusion models for the body, left hand, and right hand, each trained on its own motion dataset to improve generalization. Coordination naturally emerges through gradient flow along the human kinematic chain, allowing the global body posture to adapt in response to hand motion objectives with high fidelity. To further enhance precision in hand-object interaction, we adopt a unified representation based on basis point sets (BPS), where end-effector positions are encoded as distances to the same BPS used for object geometry. This unified representation captures fine-grained spatial relationships between the hand and articulated object parts, and the resulting trajectories serve as targets to guide the optimization of diffusion noise, producing highly accurate interaction motion. We conduct extensive experiments demonstrating that our method outperforms existing approaches in motion quality and physical plausibility, and enables various capabilities such as object pose control, simultaneous walking and manipulation, and whole-body generation from hand-only data.

Neural fields such as DeepSDF and Neural Radiance Fields have recently revolutionized novel-view synthesis and 3D reconstruction from RGB images and videos. However, achieving high-quality representation, reconstruction, and rendering requires deep neural networks, which are slow to train and evaluate. Although several acceleration techniques have been proposed, they often trade off speed for memory. Gaussian splatting-based methods, on the other hand, accelerate the rendering time but remain costly in terms of training speed and memory needed to store the parameters of a large number of Gaussians. In this paper, we introduce a novel neural representation that is fast, both at training and inference times, and lightweight. Our key observation is that the neurons used in traditional MLPs perform simple computations (a dot product followed by ReLU activation) and thus one needs to use either wide and deep MLPs or high-resolution and high-dimensional feature grids to parameterize complex nonlinear functions. We show in this paper that by replacing traditional neurons with Radial Basis Function (RBF) kernels, one can achieve highly accurate representation of 2D (RGB images), 3D (geometry), and 5D (radiance fields) signals with just a single layer of such neurons. The representation is highly parallelizable, operates on low-resolution feature grids, and is compact and memory-efficient. We demonstrate that the proposed novel representation can be trained for 3D geometry representation in less than 15 seconds and for novel view synthesis in less than 15 mins. At runtime, it can synthesize novel views at more than 60 fps without sacrificing quality.

We present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear kernels for interpolating features at continuous query points. The spatial positions of their neural features are fixed on grid nodes and cannot well adapt to target signals. Our method instead builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals. To further improve the channel-wise capacity of radial basis functions, we propose to compose them with multi-frequency sinusoid functions. This technique extends a radial basis to multiple Fourier radial bases of different frequency bands without requiring extra parameters, facilitating the representation of details. Moreover, by marrying adaptive radial bases with grid-based ones, our hybrid combination inherits both adaptivity and interpolation smoothness. We carefully designed weighting schemes to let radial bases adapt to different types of signals effectively. Our experiments on 2D image and 3D signed distance field representation demonstrate the higher accuracy and compactness of our method than prior arts. When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.

Modern retrieval system often requires recomputing the representation of every piece of data in the gallery when updating to a better representation model. This process is known as backfilling and can be especially costly in the real world where the gallery often contains billions of samples. Recently, researchers have proposed the idea of Backward Compatible Training (BCT) where the new representation model can be trained with an auxiliary loss to make it backward compatible with the old representation. In this way, the new representation can be directly compared with the old representation, in principle avoiding the need for any backfilling. However, followup work shows that there is an inherent tradeoff where a backward compatible representation model cannot simultaneously maintain the performance of the new model itself. This paper reports our ``not-so-surprising'' finding that adding extra dimensions to the representation can help here. However, we also found that naively increasing the dimension of the representation did not work. To deal with this, we propose Backward-compatible Training with a novel Basis Transformation (BT^2). A basis transformation (BT) is basically a learnable set of parameters that applies an orthonormal transformation. Such a transformation possesses an important property whereby the original information contained in its input is retained in its output. We show in this paper how a BT can be utilized to add only the necessary amount of additional dimensions. We empirically verify the advantage of BT^2 over other state-of-the-art methods in a wide range of settings. We then further extend BT^2 to other challenging yet more practical settings, including significant change in model architecture (CNN to Transformers), modality change, and even a series of updates in the model architecture mimicking the evolution of deep learning models.

A fuzzy theoretic analytical approach was recently introduced that leads to efficient and robust models while addressing automatically the typical issues associated to parametric deep models. However, a formal conceptualization of the fuzzy theoretic analytical deep models is still not available. This paper introduces using measure theoretic basis the notion of membership-mapping for representing data points through attribute values (motivated by fuzzy theory). A property of the membership-mapping, that can be exploited for data representation learning, is of providing an interpolation on the given data points in the data space. An analytical approach to the variational learning of a membership-mappings based data representation model is considered.

Natural language understanding (NLU) is an essential branch of natural language processing, which relies on representations generated by pre-trained language models (PLMs). However, PLMs primarily focus on acquiring lexico-semantic information, while they may be unable to adequately handle the meaning of constructions. To address this issue, we introduce construction grammar (CxG), which highlights the pairings of form and meaning, to enrich language representation. We adopt usage-based construction grammar as the basis of our work, which is highly compatible with statistical models such as PLMs. Then a HyCxG framework is proposed to enhance language representation through a three-stage solution. First, all constructions are extracted from sentences via a slot-constraints approach. As constructions can overlap with each other, bringing redundancy and imbalance, we formulate the conditional max coverage problem for selecting the discriminative constructions. Finally, we propose a relational hypergraph attention network to acquire representation from constructional information by capturing high-order word interactions among constructions. Extensive experiments demonstrate the superiority of the proposed model on a variety of NLU tasks.

We study neural image compression based on the Sparse Visual Representation (SVR), where images are embedded into a discrete latent space spanned by learned visual codebooks. By sharing codebooks with the decoder, the encoder transfers integer codeword indices that are efficient and cross-platform robust, and the decoder retrieves the embedded latent feature using the indices for reconstruction. Previous SVR-based compression lacks effective mechanism for rate-distortion tradeoffs, where one can only pursue either high reconstruction quality or low transmission bitrate. We propose a Masked Adaptive Codebook learning (M-AdaCode) method that applies masks to the latent feature subspace to balance bitrate and reconstruction quality. A set of semantic-class-dependent basis codebooks are learned, which are weighted combined to generate a rich latent feature for high-quality reconstruction. The combining weights are adaptively derived from each input image, providing fidelity information with additional transmission costs. By masking out unimportant weights in the encoder and recovering them in the decoder, we can trade off reconstruction quality for transmission bits, and the masking rate controls the balance between bitrate and distortion. Experiments over the standard JPEG-AI dataset demonstrate the effectiveness of our M-AdaCode approach.

Human perception is structured around objects which form the basis for our higher-level cognition and impressive systematic generalization abilities. Yet most work on representation learning focuses on feature learning without even considering multiple objects, or treats segmentation as an (often supervised) preprocessing step. Instead, we argue for the importance of learning to segment and represent objects jointly. We demonstrate that, starting from the simple assumption that a scene is composed of multiple entities, it is possible to learn to segment images into interpretable objects with disentangled representations. Our method learns -- without supervision -- to inpaint occluded parts, and extrapolates to scenes with more objects and to unseen objects with novel feature combinations. We also show that, due to the use of iterative variational inference, our system is able to learn multi-modal posteriors for ambiguous inputs and extends naturally to sequences.

Kolmogorov-Arnold Networks (KANs) have inspired numerous works exploring their applications across a wide range of scientific problems, with the potential to replace Multilayer Perceptrons (MLPs). While many KANs are designed using basis and polynomial functions, such as B-splines, ReLU-KAN utilizes a combination of ReLU functions to mimic the structure of B-splines and take advantage of ReLU's speed. However, ReLU-KAN is not built for multiple inputs, and its limitations stem from ReLU's handling of negative values, which can restrict feature extraction. To address these issues, we introduce Activation Function-Based Kolmogorov-Arnold Networks (AF-KAN), expanding ReLU-KAN with various activations and their function combinations. This novel KAN also incorporates parameter reduction methods, primarily attention mechanisms and data normalization, to enhance performance on image classification datasets. We explore different activation functions, function combinations, grid sizes, and spline orders to validate the effectiveness of AF-KAN and determine its optimal configuration. In the experiments, AF-KAN significantly outperforms MLP, ReLU-KAN, and other KANs with the same parameter count. It also remains competitive even when using fewer than 6 to 10 times the parameters while maintaining the same network structure. However, AF-KAN requires a longer training time and consumes more FLOPs. The repository for this work is available at https://github.com/hoangthangta/All-KAN.

Mixture of Experts (MoE) models scale capacity but often suffer from representation collapse and gradient instability. We propose Dynamic Subspace Composition (DSC), a framework that approximates context-dependent weights via a state-dependent, sparse expansion of a shared basis bank. Formally, DSC models the weight update as a residual trajectory within a Star- Shaped Domain, employing a Magnitude-Gated Simplex Interpolation to ensure continuity at the identity. Unlike standard Mixture-of-LoRAs, which incurs O(M rd) parameter complexity by retrieving independent rank-r matrices, DSC constructs a compositional rank-K approximation from decoupled unit-norm basis vectors. This reduces parameter complexity to O(M d) and memory traffic to O(Kd), while Frame-Theoretic regularization and spectral constraints provide rigorous worst-case bounds on the dynamic update. The code is available at https://github. com/VladimerKhasia/DSC

The demand for high-quality medical imaging in clinical practice and assisted diagnosis has made 3D image reconstruction in radiological imaging a key research focus. Artificial intelligence (AI) has emerged as a promising approach for improving reconstruction accuracy while reducing acquisition and processing time, thereby minimizing patient radiation exposure and discomfort and ultimately benefiting clinical diagnosis. This review surveys state-of-the-art AI-based 3D reconstruction algorithms in radiological imaging and organizes them into four representation families according to how the reconstructed target is parameterized: discrete grid representations, explicit basis expansion representations, explicit primitive representations, and implicit neural representations. In particular, the review clarifies the relationships among these representation forms and highlights radiance field methods as a specialized subtype of implicit neural representation. In addition, we summarize commonly used evaluation metrics and benchmark datasets for radiological image reconstruction. Finally, we discuss the current state of development, major challenges, and future research directions in this rapidly evolving field. Our project is available at: https://github.com/Bean-Young/AI4Radiology.

Vector Quantization (VQ) is a widely used method for converting continuous representations into discrete codes, which has become fundamental in unsupervised representation learning and latent generative models. However, VQ models are often hindered by the problem of representation collapse in the latent space, which leads to low codebook utilization and limits the scalability of the codebook for large-scale training. Existing methods designed to mitigate representation collapse typically reduce the dimensionality of latent space at the expense of model capacity, which do not fully resolve the core issue. In this study, we conduct a theoretical analysis of representation collapse in VQ models and identify its primary cause as the disjoint optimization of the codebook, where only a small subset of code vectors are updated through gradient descent. To address this issue, we propose SimVQ, a novel method which reparameterizes the code vectors through a linear transformation layer based on a learnable latent basis. This transformation optimizes the entire linear space spanned by the codebook, rather than merely updating the code vector selected by the nearest-neighbor search in vanilla VQ models. Although it is commonly understood that the multiplication of two linear matrices is equivalent to applying a single linear layer, our approach works surprisingly well in resolving the collapse issue in VQ models with just one linear layer. We validate the efficacy of SimVQ through extensive experiments across various modalities, including image and audio data with different model architectures. Our code is available at https://github.com/youngsheen/SimVQ.

The proliferation of short video and live-streaming platforms has revolutionized how consumers engage in online shopping. Instead of browsing product pages, consumers are now turning to rich-content e-commerce, where they can purchase products through dynamic and interactive media like short videos and live streams. This emerging form of online shopping has introduced technical challenges, as products may be presented differently across various media domains. Therefore, a unified product representation is essential for achieving cross-domain product recognition to ensure an optimal user search experience and effective product recommendations. Despite the urgent industrial need for a unified cross-domain product representation, previous studies have predominantly focused only on product pages without taking into account short videos and live streams. To fill the gap in the rich-content e-commerce area, in this paper, we introduce a large-scale cRoss-dOmain Product Ecognition dataset, called ROPE. ROPE covers a wide range of product categories and contains over 180,000 products, corresponding to millions of short videos and live streams. It is the first dataset to cover product pages, short videos, and live streams simultaneously, providing the basis for establishing a unified product representation across different media domains. Furthermore, we propose a Cross-dOmain Product rEpresentation framework, namely COPE, which unifies product representations in different domains through multimodal learning including text and vision. Extensive experiments on downstream tasks demonstrate the effectiveness of COPE in learning a joint feature space for all product domains.

We address the problem of video representation learning without human-annotated labels. While previous efforts address the problem by designing novel self-supervised tasks using video data, the learned features are merely on a frame-by-frame basis, which are not applicable to many video analytic tasks where spatio-temporal features are prevailing. In this paper we propose a novel self-supervised approach to learn spatio-temporal features for video representation. Inspired by the success of two-stream approaches in video classification, we propose to learn visual features by regressing both motion and appearance statistics along spatial and temporal dimensions, given only the input video data. Specifically, we extract statistical concepts (fast-motion region and the corresponding dominant direction, spatio-temporal color diversity, dominant color, etc.) from simple patterns in both spatial and temporal domains. Unlike prior puzzles that are even hard for humans to solve, the proposed approach is consistent with human inherent visual habits and therefore easy to answer. We conduct extensive experiments with C3D to validate the effectiveness of our proposed approach. The experiments show that our approach can significantly improve the performance of C3D when applied to video classification tasks. Code is available at https://github.com/laura-wang/video_repres_mas.

Few Shot Class Incremental Learning (FSCIL) with few examples per class for each incremental session is the realistic setting of continual learning since obtaining large number of annotated samples is not feasible and cost effective. We present the framework MASIL as a step towards learning the maximal separable classifier. It addresses the common problem i.e forgetting of old classes and over-fitting to novel classes by learning the classifier weights to be maximally separable between classes forming a simplex Equiangular Tight Frame. We propose the idea of concept factorization explaining the collapsed features for base session classes in terms of concept basis and use these to induce classifier simplex for few shot classes. We further adds fine tuning to reduce any error occurred during factorization and train the classifier jointly on base and novel classes without retaining any base class samples in memory. Experimental results on miniImageNet, CIFAR-100 and CUB-200 demonstrate that MASIL outperforms all the benchmarks.

Recent advances in implicit neural representation have demonstrated the ability to recover detailed geometry and material from multi-view images. However, the use of simplified lighting models such as environment maps to represent non-distant illumination, or using a network to fit indirect light modeling without a solid basis, can lead to an undesirable decomposition between lighting and material. To address this, we propose a fully differentiable framework named neural ambient illumination (NeAI) that uses Neural Radiance Fields (NeRF) as a lighting model to handle complex lighting in a physically based way. Together with integral lobe encoding for roughness-adaptive specular lobe and leveraging the pre-convoluted background for accurate decomposition, the proposed method represents a significant step towards integrating physically based rendering into the NeRF representation. The experiments demonstrate the superior performance of novel-view rendering compared to previous works, and the capability to re-render objects under arbitrary NeRF-style environments opens up exciting possibilities for bridging the gap between virtual and real-world scenes. The project and supplementary materials are available at https://yiyuzhuang.github.io/NeAI/.

Anti-money laundering (AML) regulations mandate financial institutions to deploy AML systems based on a set of rules that, when triggered, form the basis of a suspicious alert to be assessed by human analysts. Reviewing these cases is a cumbersome and complex task that requires analysts to navigate a large network of financial interactions to validate suspicious movements. Furthermore, these systems have very high false positive rates (estimated to be over 95\%). The scarcity of labels hinders the use of alternative systems based on supervised learning, reducing their applicability in real-world applications. In this work we present LaundroGraph, a novel self-supervised graph representation learning approach to encode banking customers and financial transactions into meaningful representations. These representations are used to provide insights to assist the AML reviewing process, such as identifying anomalous movements for a given customer. LaundroGraph represents the underlying network of financial interactions as a customer-transaction bipartite graph and trains a graph neural network on a fully self-supervised link prediction task. We empirically demonstrate that our approach outperforms other strong baselines on self-supervised link prediction using a real-world dataset, improving the best non-graph baseline by 12 p.p. of AUC. The goal is to increase the efficiency of the reviewing process by supplying these AI-powered insights to the analysts upon review. To the best of our knowledge, this is the first fully self-supervised system within the context of AML detection.

This paper presents an efficient and lightweight multi-branch deep architecture to improve vehicle re-identification (V-ReID). While most V-ReID work uses a combination of complex multi-branch architectures to extract robust and diversified embeddings towards re-identification, we advocate that simple and lightweight architectures can be designed to fulfill the Re-ID task without compromising performance. We propose a combination of Grouped-convolution and Loss-Branch-Split strategies to design a multi-branch architecture that improve feature diversity and feature discriminability. We combine a ResNet50 global branch architecture with a BotNet self-attention branch architecture, both designed within a Loss-Branch-Split (LBS) strategy. We argue that specialized loss-branch-splitting helps to improve re-identification tasks by generating specialized re-identification features. A lightweight solution using grouped convolution is also proposed to mimic the learning of loss-splitting into multiple embeddings while significantly reducing the model size. In addition, we designed an improved solution to leverage additional metadata, such as camera ID and pose information, that uses 97% less parameters, further improving re-identification performance. In comparison to state-of-the-art (SoTA) methods, our approach outperforms competing solutions in Veri-776 by achieving 85.6% mAP and 97.7% CMC1 and obtains competitive results in Veri-Wild with 88.1% mAP and 96.3% CMC1. Overall, our work provides important insights into improving vehicle re-identification and presents a strong basis for other retrieval tasks. Our code is available at the https://github.com/videturfortuna/vehicle_reid_itsc2023.

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing signals such as images, audio, and 3D scenes. However, existing INR frameworks -- including MLPs with Fourier features, SIREN, and multiresolution hash grids -- implicitly assume a global and stationary spectral basis. This assumption is fundamentally misaligned with real-world signals whose frequency characteristics vary significantly across space, exhibiting local high-frequency textures, smooth regions, and frequency drift phenomena. We propose Neural Spectral Transport Representation (NSTR), the first INR framework that explicitly models a spatially varying local frequency field. NSTR introduces a learnable frequency transport equation, a PDE that governs how local spectral compositions evolve across space. Given a learnable local spectrum field S(x) and a frequency transport network F_θ enforcing nabla S(x) approx F_θ(x, S(x)), NSTR reconstructs signals by spatially modulating a compact set of global sinusoidal bases. This formulation enables strong local adaptivity and offers a new level of interpretability via visualizing frequency flows. Experiments on 2D image regression, audio reconstruction, and implicit 3D geometry show that NSTR achieves significantly better accuracy-parameter trade-offs than SIREN, Fourier-feature MLPs, and Instant-NGP. NSTR requires fewer global frequencies, converges faster, and naturally explains signal structure through spectral transport fields. We believe NSTR opens a new direction in INR research by introducing explicit modeling of space-varying spectrum.

Learning feature representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work mostly embeds coordinates using sine and cosine projections based on Double Fourier Sphere (DFS) features -- these embeddings assume a rectangular data domain even on global data, which can lead to artifacts, especially at the poles. At the same time, relatively little attention has been paid to the exact design of the neural network architectures these functional embeddings are combined with. This work proposes a novel location encoder for globally distributed geographic data that combines spherical harmonic basis functions, natively defined on spherical surfaces, with sinusoidal representation networks (SirenNets) that can be interpreted as learned Double Fourier Sphere embedding. We systematically evaluate the cross-product of positional embeddings and neural network architectures across various classification and regression benchmarks and synthetic evaluation datasets. In contrast to previous approaches that require the combination of both positional encoding and neural networks to learn meaningful representations, we show that both spherical harmonics and sinusoidal representation networks are competitive on their own but set state-of-the-art performances across tasks when combined. We provide source code at www.github.com/marccoru/locationencoder

We present GB-LSR (Global-Bandwidth Local Spectral Representation), a fixed-grid local spectral representation for continuous image reconstruction. The image domain is partitioned into non-overlapping square patches, each carrying coefficients for a truncated Fourier basis predicted from shared convolutional-encoder features. A single trainable scalar bandwidth is shared globally across all patches and images, and reconstruction at any continuous coordinate is a fixed-size basis contraction whose cost is independent of image size. We study three bandwidth-handling variants: a trainable global scalar (main), a fixed global scalar, and a per-patch bandwidth field. On a standardized native-reconstruction benchmark across Kodak, Set14, and Urban100, the main variant outperforms matched-budget amortized LIIF / LTE / WIRE re-implementations by 2.8-3.6 dB PSNR and 0.11-0.15 LPIPS, while running at roughly one-quarter of the slowest baseline's inference cost. The single global scalar suffices empirically: per-patch adaptive-bandwidth alternatives do not improve over it on either a closed-form locality diagnostic or an end-to-end ablation. In a separate arbitrary-scale super-resolution (ASR) extension, GB-LSR achieves competitive PSNR-Y under a canonical-style SR protocol and runs 1.44x faster than LIIF-RDN and 3.25x faster than LTE-SwinIR at x4; within the same extension, a variant trained and evaluated without 4-corner local-ensemble averaging gives a 1.77x speedup with 35% lower peak memory and negligible PSNR change, while additionally widening the RDN encoder from 64 to 96 channels gives a small positive PSNR shift with a 1.58x speedup and 31% lower peak memory. Native-reconstruction claims are scoped to the matched-budget amortized protocol, and ASR claims are scoped to a separate canonical-style SR protocol.

Learning a dense 3D model with fine-scale details from a single facial image is highly challenging and ill-posed. To address this problem, many approaches fit smooth geometries through facial prior while learning details as additional displacement maps or personalized basis. However, these techniques typically require vast datasets of paired multi-view data or 3D scans, whereas such datasets are scarce and expensive. To alleviate heavy data dependency, we present a robust texture-guided geometric detail recovery approach using only a single in-the-wild facial image. More specifically, our method combines high-quality texture completion with the powerful expressiveness of implicit surfaces. Initially, we inpaint occluded facial parts, generate complete textures, and build an accurate multi-view dataset of the same subject. In order to estimate the detailed geometry, we define an implicit signed distance function and employ a physically-based implicit renderer to reconstruct fine geometric details from the generated multi-view images. Our method not only recovers accurate facial details but also decomposes normals, albedos, and shading parts in a self-supervised way. Finally, we register the implicit shape details to a 3D Morphable Model template, which can be used in traditional modeling and rendering pipelines. Extensive experiments demonstrate that the proposed approach can reconstruct impressive facial details from a single image, especially when compared with state-of-the-art methods trained on large datasets.

The pre-trained image-text models, like CLIP, have demonstrated the strong power of vision-language representation learned from a large scale of web-collected image-text data. In light of the well-learned visual features, some existing works transfer image representation to video domain and achieve good results. However, how to utilize image-language pre-trained model (e.g., CLIP) for video-language pre-training (post-pretraining) is still under explored. In this paper, we investigate two questions: 1) what are the factors hindering post-pretraining CLIP to further improve the performance on video-language tasks? and 2) how to mitigate the impact of these factors? Through a series of comparative experiments and analyses, we find that the data scale and domain gap between language sources have great impacts. Motivated by these, we propose a Omnisource Cross-modal Learning method equipped with a Video Proxy mechanism on the basis of CLIP, namely CLIP-ViP. Extensive results show that our approach improves the performance of CLIP on video-text retrieval by a large margin. Our model also achieves SOTA results on a variety of datasets, including MSR-VTT, DiDeMo, LSMDC, and ActivityNet. We will release our code and pre-trained CLIP-ViP models at https://github.com/microsoft/XPretrain/tree/main/CLIP-ViP.

This paper presents the Visual Place Cell Encoding (VPCE) model, a biologically inspired computational framework for simulating place cell-like activation using visual input. Drawing on evidence that visual landmarks play a central role in spatial encoding, the proposed VPCE model activates visual place cells by clustering high-dimensional appearance features extracted from images captured by a robot-mounted camera. Each cluster center defines a receptive field, and activation is computed based on visual similarity using a radial basis function. We evaluate whether the resulting activation patterns correlate with key properties of biological place cells, including spatial proximity, orientation alignment, and boundary differentiation. Experiments demonstrate that the VPCE can distinguish between visually similar yet spatially distinct locations and adapt to environment changes such as the insertion or removal of walls. These results suggest that structured visual input, even in the absence of motion cues or reward-driven learning, is sufficient to generate place-cell-like spatial representations and support biologically inspired cognitive mapping.

We consider a family of linear systems A_mu alpha=C with system matrix A_mu depending on a parameter mu and for simplicity parameter-independent right-hand side C. These linear systems typically result from the finite-dimensional approximation of a parameter-dependent boundary-value problem. We derive a procedure based on the Empirical Interpolation Method to obtain a separated representation of the system matrix in the form A_muapproxsum_{m}beta_m(mu)A_{mu_m} for some selected values of the parameter. Such a separated representation is in particular useful in the Reduced Basis Method. The procedure is called nonintrusive since it only requires to access the matrices A_{mu_m}. As such, it offers a crucial advantage over existing approaches that instead derive separated representations requiring to enter the code at the level of assembly. Numerical examples illustrate the performance of our new procedure on a simple one-dimensional boundary-value problem and on three-dimensional acoustic scattering problems solved by a boundary element method.

Manipulating latent code in generative adversarial networks (GANs) for facial image synthesis mainly focuses on continuous attribute synthesis (e.g., age, pose and emotion), while discrete attribute synthesis (like face mask and eyeglasses) receives less attention. Directly applying existing works to facial discrete attributes may cause inaccurate results. In this work, we propose an innovative framework to tackle challenging facial discrete attribute synthesis via semantic decomposing, dubbed SD-GAN. To be concrete, we explicitly decompose the discrete attribute representation into two components, i.e. the semantic prior basis and offset latent representation. The semantic prior basis shows an initializing direction for manipulating face representation in the latent space. The offset latent presentation obtained by 3D-aware semantic fusion network is proposed to adjust prior basis. In addition, the fusion network integrates 3D embedding for better identity preservation and discrete attribute synthesis. The combination of prior basis and offset latent representation enable our method to synthesize photo-realistic face images with discrete attributes. Notably, we construct a large and valuable dataset MEGN (Face Mask and Eyeglasses images crawled from Google and Naver) for completing the lack of discrete attributes in the existing dataset. Extensive qualitative and quantitative experiments demonstrate the state-of-the-art performance of our method. Our code is available at: https://github.com/MontaEllis/SD-GAN.

Versatile and adaptive semantic understanding would enable autonomous systems to comprehend and interact with their surroundings. Existing fixed-class models limit the adaptability of indoor mobile and assistive autonomous systems. In this work, we introduce LEXIS, a real-time indoor Simultaneous Localization and Mapping (SLAM) system that harnesses the open-vocabulary nature of Large Language Models (LLMs) to create a unified approach to scene understanding and place recognition. The approach first builds a topological SLAM graph of the environment (using visual-inertial odometry) and embeds Contrastive Language-Image Pretraining (CLIP) features in the graph nodes. We use this representation for flexible room classification and segmentation, serving as a basis for room-centric place recognition. This allows loop closure searches to be directed towards semantically relevant places. Our proposed system is evaluated using both public, simulated data and real-world data, covering office and home environments. It successfully categorizes rooms with varying layouts and dimensions and outperforms the state-of-the-art (SOTA). For place recognition and trajectory estimation tasks we achieve equivalent performance to the SOTA, all also utilizing the same pre-trained model. Lastly, we demonstrate the system's potential for planning.

Mechanistic Interpretability aims to reverse engineer the algorithms implemented by neural networks by studying their weights and activations. An obstacle to reverse engineering neural networks is that many of the parameters inside a network are not involved in the computation being implemented by the network. These degenerate parameters may obfuscate internal structure. Singular learning theory teaches us that neural network parameterizations are biased towards being more degenerate, and parameterizations with more degeneracy are likely to generalize further. We identify 3 ways that network parameters can be degenerate: linear dependence between activations in a layer; linear dependence between gradients passed back to a layer; ReLUs which fire on the same subset of datapoints. We also present a heuristic argument that modular networks are likely to be more degenerate, and we develop a metric for identifying modules in a network that is based on this argument. We propose that if we can represent a neural network in a way that is invariant to reparameterizations that exploit the degeneracies, then this representation is likely to be more interpretable, and we provide some evidence that such a representation is likely to have sparser interactions. We introduce the Interaction Basis, a tractable technique to obtain a representation that is invariant to degeneracies from linear dependence of activations or Jacobians.

Neural Radiance Fields (NeRFs) have proven to be powerful 3D representations, capable of high quality novel view synthesis of complex scenes. While NeRFs have been applied to graphics, vision, and robotics, problems with slow rendering speed and characteristic visual artifacts prevent adoption in many use cases. In this work, we investigate combining an autoencoder (AE) with a NeRF, in which latent features (instead of colours) are rendered and then convolutionally decoded. The resulting latent-space NeRF can produce novel views with higher quality than standard colour-space NeRFs, as the AE can correct certain visual artifacts, while rendering over three times faster. Our work is orthogonal to other techniques for improving NeRF efficiency. Further, we can control the tradeoff between efficiency and image quality by shrinking the AE architecture, achieving over 13 times faster rendering with only a small drop in performance. We hope that our approach can form the basis of an efficient, yet high-fidelity, 3D scene representation for downstream tasks, especially when retaining differentiability is useful, as in many robotics scenarios requiring continual learning.

Parametric body models offer expressive 3D representation of humans across a wide range of poses, shapes, and facial expressions, typically derived by learning a basis over registered 3D meshes. However, existing human mesh modeling approaches struggle to capture detailed variations across diverse body poses and shapes, largely due to limited training data diversity and restrictive modeling assumptions. Moreover, the common paradigm first optimizes the external body surface using a linear basis, then regresses internal skeletal joints from surface vertices. This approach introduces problematic dependencies between internal skeleton and outer soft tissue, limiting direct control over body height and bone lengths. To address these issues, we present ATLAS, a high-fidelity body model learned from 600k high-resolution scans captured using 240 synchronized cameras. Unlike previous methods, we explicitly decouple the shape and skeleton bases by grounding our mesh representation in the human skeleton. This decoupling enables enhanced shape expressivity, fine-grained customization of body attributes, and keypoint fitting independent of external soft-tissue characteristics. ATLAS outperforms existing methods by fitting unseen subjects in diverse poses more accurately, and quantitative evaluations show that our non-linear pose correctives more effectively capture complex poses compared to linear models.

Long-horizon agents accumulate progress in persistent task state, yet repeatedly process interaction histories describing how that progress was achieved. This raises a natural question: can long-horizon context instead be organized around reusable progress rather than the history that produced it? In this paper, we introduce CarryOn, an object-oriented context runtime that organizes continuation around reusable task objects. Rather than treating compressed histories or reconstructed accounts of progress as the primary basis for continuation, CarryOn builds a context view from continuation carriers, complementary execution context, and a live tail of recent interactions. A core challenge is keeping this reusable basis valid after its surrounding history is retired: how can CarryOn update the basis without reconstructing the full representation at every fold? CarryOn maintains carrier records across folds, revising affected records against bound evidence and applicable environment checks while carrying forward unaffected records and jointly updating execution context. Experiments on OSWorld 2.0 and BrowseComp-Plus show improved gains of 5.8% and 7.0% while reducing total token usage by 51.9% and 22.9%, respectively. Project page: https://ethannju.github.io/carryon

Post-training compression of large language models (LLMs) largely relies on low-rank weight approximation, which represents each column of a weight matrix in a shared low-dimensional subspace. While this is a computationally efficient strategy, the imposed structural constraint is rigid and can lead to a noticeable model accuracy drop. In this work, we propose CoSpaDi (Compression via Sparse Dictionary Learning), a novel training-free compression framework that replaces low-rank decomposition with a more flexible structured sparse factorization in which each weight matrix is represented with a dense dictionary and a column-sparse coefficient matrix. This formulation enables a union-of-subspaces representation: different columns of the original weight matrix are approximated in distinct subspaces spanned by adaptively selected dictionary atoms, offering greater expressiveness than a single invariant basis. Crucially, CoSpaDi leverages a small calibration dataset to optimize the factorization such that the output activations of compressed projection layers closely match those of the original ones, thereby minimizing functional reconstruction error rather than mere weight approximation. This data-aware strategy preserves better model fidelity without any fine-tuning under reasonable compression ratios. Moreover, the resulting structured sparsity allows efficient sparse-dense matrix multiplication and is compatible with post-training quantization for further memory and latency gains. We evaluate CoSpaDi across multiple Llama and Qwen models under per-layer and per-group settings at 20-50\% compression ratios, demonstrating consistent superiority over state-of-the-art data-aware low-rank methods both in accuracy and perplexity. Our results establish structured sparse dictionary learning as a powerful alternative to conventional low-rank approaches for efficient LLM deployment.

Speech tokenization is the task of representing speech signals as a sequence of discrete units. Such representations can be later used for various downstream tasks including automatic speech recognition, text-to-speech, etc. More relevant to this study, such representation serves as the basis of Speech Language Models. In this work, we tackle the task of speech tokenization under the noisy setup and present NAST: Noise Aware Speech Tokenization for Speech Language Models. NAST is composed of three main components: (i) a predictor; (ii) a residual encoder; and (iii) a decoder. We evaluate the efficiency of NAST considering several spoken language modeling tasks and show that NAST is superior to the evaluated baselines across all setups. Lastly, we analyze NAST and show its disentanglement properties and robustness to signal variations in the form of noise, reverberation, pitch-shift, and time-stretch. Code and pre-trained models are available at https://github.com/ShovalMessica/NAST.

What audio embedding approach generalizes best to a wide range of downstream tasks across a variety of everyday domains without fine-tuning? The aim of the HEAR benchmark is to develop a general-purpose audio representation that provides a strong basis for learning in a wide variety of tasks and scenarios. HEAR evaluates audio representations using a benchmark suite across a variety of domains, including speech, environmental sound, and music. HEAR was launched as a NeurIPS 2021 shared challenge. In the spirit of shared exchange, each participant submitted an audio embedding model following a common API that is general-purpose, open-source, and freely available to use. Twenty-nine models by thirteen external teams were evaluated on nineteen diverse downstream tasks derived from sixteen datasets. Open evaluation code, submitted models and datasets are key contributions, enabling comprehensive and reproducible evaluation, as well as previously impossible longitudinal studies. It still remains an open question whether one single general-purpose audio representation can perform as holistically as the human ear.

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs). However, standard MLP-based PINNs often fail to converge when dealing with complex initial value problems, leading to solutions that violate causality and suffer from a spectral bias towards low-frequency components. To address these issues, we introduce NeuSA (Neuro-Spectral Architectures), a novel class of PINNs inspired by classical spectral methods, designed to solve linear and nonlinear PDEs with variable coefficients. NeuSA learns a projection of the underlying PDE onto a spectral basis, leading to a finite-dimensional representation of the dynamics which is then integrated with an adapted Neural ODE (NODE). This allows us to overcome spectral bias, by leveraging the high-frequency components enabled by the spectral representation; to enforce causality, by inheriting the causal structure of NODEs, and to start training near the target solution, by means of an initialization scheme based on classical methods. We validate NeuSA on canonical benchmarks for linear and nonlinear wave equations, demonstrating strong performance as compared to other architectures, with faster convergence, improved temporal consistency and superior predictive accuracy. Code and pretrained models are available in https://github.com/arthur-bizzi/neusa.

Understanding spatial location and relationships is a fundamental capability for modern artificial intelligence systems. Insights from human spatial cognition provide valuable guidance in this domain. Neuroscientific discoveries have highlighted the role of grid cells as a fundamental neural component for spatial representation, including distance computation, path integration, and scale discernment. In this paper, we introduce a novel positional encoding scheme inspired by Fourier analysis and the latest findings in computational neuroscience regarding grid cells. Assuming that grid cells encode spatial position through a summation of Fourier basis functions, we demonstrate the translational invariance of the grid representation during inner product calculations. Additionally, we derive an optimal grid scale ratio for multi-dimensional Euclidean spaces based on principles of biological efficiency. Utilizing these computational principles, we have developed a Grid-cell inspired Positional Encoding technique, termed GridPE, for encoding locations within high-dimensional spaces. We integrated GridPE into the Pyramid Vision Transformer architecture. Our theoretical analysis shows that GridPE provides a unifying framework for positional encoding in arbitrary high-dimensional spaces. Experimental results demonstrate that GridPE significantly enhances the performance of transformers, underscoring the importance of incorporating neuroscientific insights into the design of artificial intelligence systems.

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.

Code intelligence leverages machine learning techniques to extract knowledge from extensive code corpora, with the aim of developing intelligent tools to improve the quality and productivity of computer programming. Currently, there is already a thriving research community focusing on code intelligence, with efforts ranging from software engineering, machine learning, data mining, natural language processing, and programming languages. In this paper, we conduct a comprehensive literature review on deep learning for code intelligence, from the aspects of code representation learning, deep learning techniques, and application tasks. We also benchmark several state-of-the-art neural models for code intelligence, and provide an open-source toolkit tailored for the rapid prototyping of deep-learning-based code intelligence models. In particular, we inspect the existing code intelligence models under the basis of code representation learning, and provide a comprehensive overview to enhance comprehension of the present state of code intelligence. Furthermore, we publicly release the source code and data resources to provide the community with a ready-to-use benchmark, which can facilitate the evaluation and comparison of existing and future code intelligence models (https://xcodemind.github.io). At last, we also point out several challenging and promising directions for future research.

Computed tomography (CT) serves as an effective tool for lung cancer screening, diagnosis, treatment, and prognosis, providing a rich source of features to quantify temporal and spatial tumor changes. Nonetheless, the diversity of CT scanners and customized acquisition protocols can introduce significant inconsistencies in texture features, even when assessing the same patient. This variability poses a fundamental challenge for subsequent research that relies on consistent image features. Existing CT image standardization models predominantly utilize GAN-based supervised or semi-supervised learning, but their performance remains limited. We present DiffusionCT, an innovative score-based DDPM model that operates in the latent space to transform disparate non-standard distributions into a standardized form. The architecture comprises a U-Net-based encoder-decoder, augmented by a DDPM model integrated at the bottleneck position. First, the encoder-decoder is trained independently, without embedding DDPM, to capture the latent representation of the input data. Second, the latent DDPM model is trained while keeping the encoder-decoder parameters fixed. Finally, the decoder uses the transformed latent representation to generate a standardized CT image, providing a more consistent basis for downstream analysis. Empirical tests on patient CT images indicate notable improvements in image standardization using DiffusionCT. Additionally, the model significantly reduces image noise in SPAD images, further validating the effectiveness of DiffusionCT for advanced imaging tasks.

Text-to-image (T2I) generation aims at producing realistic images corresponding to text descriptions. Generative Adversarial Network (GAN) has proven to be successful in this task. Typical T2I GANs are 2 phase methods that first pretrain an inter-modal representation from aligned image-text pairs and then use GAN to train image generator on that basis. However, such representation ignores the inner-modal semantic correspondence, e.g. the images with same label. The semantic label in priory describes the inherent distribution pattern with underlying cross-image relationships, which is supplement to the text description for understanding the full characteristics of image. In this paper, we propose a framework leveraging both inter- and inner-modal correspondence by label guided supervised contrastive learning. We extend the T2I GANs to two parameter-sharing contrast branches in both pretraining and generation phases. This integration effectively clusters the semantically similar image-text pair representations, thereby fostering the generation of higher-quality images. We demonstrate our framework on four novel T2I GANs by both single-object dataset CUB and multi-object dataset COCO, achieving significant improvements in the Inception Score (IS) and Frechet Inception Distance (FID) metrics of imagegeneration evaluation. Notably, on more complex multi-object COCO, our framework improves FID by 30.1%, 27.3%, 16.2% and 17.1% for AttnGAN, DM-GAN, SSA-GAN and GALIP, respectively. We also validate our superiority by comparing with other label guided T2I GANs. The results affirm the effectiveness and competitiveness of our approach in advancing the state-of-the-art GAN for T2I generation

Unsupervised learning of object-centric representations in dynamic visual scenes is challenging. Unlike most previous approaches that learn to decompose 2D images, we present DynaVol, a 3D scene generative model that unifies geometric structures and object-centric learning in a differentiable volume rendering framework. The key idea is to perform object-centric voxelization to capture the 3D nature of the scene, which infers the probability distribution over objects at individual spatial locations. These voxel features evolve over time through a canonical-space deformation function, forming the basis for global representation learning via slot attention. The voxel features and global features are complementary and are both leveraged by a compositional NeRF decoder for volume rendering. DynaVol remarkably outperforms existing approaches for unsupervised dynamic scene decomposition. Once trained, the explicitly meaningful voxel features enable additional capabilities that 2D scene decomposition methods cannot achieve: it is possible to freely edit the geometric shapes or manipulate the motion trajectories of the objects.

With the advancement of diffusion models (DMs) and the substantially increased computational requirements, quantization emerges as a practical solution to obtain compact and efficient low-bit DMs. However, the highly discrete representation leads to severe accuracy degradation, hindering the quantization of diffusion models to ultra-low bit-widths. In this paper, we propose BinaryDM, a novel accurate quantization-aware training approach to push the weights of diffusion models towards the limit of 1-bit. Firstly, we present a Learnable Multi-basis Binarizer (LMB) to recover the representations generated by the binarized DM, which improves the information in details of representations crucial to the DM. Secondly, a Low-rank Representation Mimicking (LRM) is applied to enhance the binarization-aware optimization of the DM, alleviating the optimization direction ambiguity caused by fine-grained alignment. Moreover, a progressive initialization strategy is applied to training DMs to avoid convergence difficulties. Comprehensive experiments demonstrate that BinaryDM achieves significant accuracy and efficiency gains compared to SOTA quantization methods of DMs under ultra-low bit-widths. As the first binarization method for diffusion models, BinaryDM achieves impressive 16.0 times FLOPs and 27.1 times storage savings with 1-bit weight and 4-bit activation, showcasing its substantial advantages and potential for deploying DMs on resource-limited scenarios.

Establishing a universal benchmark for tactile representation learning in robotic manipulation remains challenging due to the diversity of tactile sensor designs, data formats, and robot embodiments. Rather than seeking to establish such, we explore a scalable and promising direction for future development: egocentric vision paired with full-hand tactile data. To this end, we introduce HT-Bench, a large-scale multi-task benchmark for dexterous full-hand tactile sensing, comprising 10M RGB frames and 7.8M tactile frames collected across 226 tasks. HT-Bench evaluates tactile representations from three key perspectives: whether they encode meaningful contact geometry, whether they can align tactile observations with visual information, and whether they generalize to unseen tasks. To assess these capabilities, HT-Bench includes four tasks: fine-grained tactile similarity retrieval, masked tactile inpainting, vision-to-tactile synthesis, and multimodal tactile frame prediction. We further propose HandTouch, a vector-quantized vision--tactile encoder that learns tactile representations through progressive spatial, cross-modal, and temporal training. Across HT-Bench, HandTouch consistently outperforms representative tactile encoder baselines, improving Recall@5 on fine-grained tactile similarity retrieval from 74.65\% to 85.23\%, reducing RMSE on masked tactile inpainting from 0.022 to 0.010, and increasing OOD cIoU on vision-to-tactile synthesis from 0.628 to 0.705. These results demonstrate the effectiveness of HandTouch and suggest that large-scale egocentric full-hand tactile data provides a scalable basis for evaluating and advancing tactile representation learning in dexterous manipulation.

We propose Super-resolution Neural Operator (SRNO), a deep operator learning framework that can resolve high-resolution (HR) images at arbitrary scales from the low-resolution (LR) counterparts. Treating the LR-HR image pairs as continuous functions approximated with different grid sizes, SRNO learns the mapping between the corresponding function spaces. From the perspective of approximation theory, SRNO first embeds the LR input into a higher-dimensional latent representation space, trying to capture sufficient basis functions, and then iteratively approximates the implicit image function with a kernel integral mechanism, followed by a final dimensionality reduction step to generate the RGB representation at the target coordinates. The key characteristics distinguishing SRNO from prior continuous SR works are: 1) the kernel integral in each layer is efficiently implemented via the Galerkin-type attention, which possesses non-local properties in the spatial domain and therefore benefits the grid-free continuum; and 2) the multilayer attention architecture allows for the dynamic latent basis update, which is crucial for SR problems to "hallucinate" high-frequency information from the LR image. Experiments show that SRNO outperforms existing continuous SR methods in terms of both accuracy and running time. Our code is at https://github.com/2y7c3/Super-Resolution-Neural-Operator

Reliably reconstructing physical fields from sparse sensor data is a challenge that frequently arises in many scientific domains. In practice, the process generating the data often is not understood to sufficient accuracy. Therefore, there is a growing interest in using the deep neural network route to address the problem. This work presents a novel approach that learns a continuous representation of the physical field using implicit neural representations (INRs). Specifically, after factorizing spatiotemporal variability into spatial and temporal components using the separation of variables technique, the method learns relevant basis functions from sparsely sampled irregular data points to develop a continuous representation of the data. In experimental evaluations, the proposed model outperforms recent INR methods, offering superior reconstruction quality on simulation data from a state-of-the-art climate model and a second dataset that comprises ultra-high resolution satellite-based sea surface temperature fields.

Spelling error correction is an important yet challenging task because a satisfactory solution of it essentially needs human-level language understanding ability. Without loss of generality we consider Chinese spelling error correction (CSC) in this paper. A state-of-the-art method for the task selects a character from a list of candidates for correction (including non-correction) at each position of the sentence on the basis of BERT, the language representation model. The accuracy of the method can be sub-optimal, however, because BERT does not have sufficient capability to detect whether there is an error at each position, apparently due to the way of pre-training it using mask language modeling. In this work, we propose a novel neural architecture to address the aforementioned issue, which consists of a network for error detection and a network for error correction based on BERT, with the former being connected to the latter with what we call soft-masking technique. Our method of using `Soft-Masked BERT' is general, and it may be employed in other language detection-correction problems. Experimental results on two datasets demonstrate that the performance of our proposed method is significantly better than the baselines including the one solely based on BERT.

Automatic recognition of insect sound could help us understand changing biodiversity trends around the world -- but insect sounds are challenging to recognize even for deep learning. We present a new dataset comprised of 26399 audio files, from 459 species of Orthoptera and Cicadidae. It is the first large-scale dataset of insect sound that is easily applicable for developing novel deep-learning methods. Its recordings were made with a variety of audio recorders using varying sample rates to capture the extremely broad range of frequencies that insects produce. We benchmark performance with two state-of-the-art deep learning classifiers, demonstrating good performance but also significant room for improvement in acoustic insect classification. This dataset can serve as a realistic test case for implementing insect monitoring workflows, and as a challenging basis for the development of audio representation methods that can handle highly variable frequencies and/or sample rates.

Reservoir computing offers a lightweight framework for forecasting dynamical systems but may struggle to capture long-range dependencies due to limited representational capacity. Conventional reservoir computing recurrently uses trainable reservoirs with hyperparameter sensitivity, while the next-generation reservoir computing removes recurrence at the cost of rapidly growing feature dimensions. Here, we develop Kolmogorov-Arnold Reservoir Computing (KARC), which replaces reservoirs with explicit basis-function expansions inspired by the Kolmogorov-Arnold representation theorem. We rigorously show that KARC is a lightweight design of Kolmogorov-Arnold networks (KANs), preserving the potential expressive capacity of KANs while admitting efficient closed-form training of reservoir computing. At comparable cost, KARC outperforms existing reservoir computing methods on challenging benchmarks including partial differential equations. It can also be integrated with generative diffusion models for text-to-image generation. This work thus establishes a principled bridge between reservoir computing and KANs, enabling efficient and high-fidelity dynamical system forecasting.

Omni-directional (360°) cameras provide embodied agents with a holistic view of their surroundings, making them suited for directional reasoning in tasks such as navigation and object search. Existing Vision Language Models (VLMs) project 360° observations to 2D equirectangular projection (ERP) images and process them using architectures designed for perspective images. However, they ignore the spherical nature of 360° observations, where each pixel represents a viewing direction relative to the agent. Consequently, their direction estimates often become inconsistent under camera view transformations caused by agent motion. This limitation is particularly critical for map-free navigation, where the agent must continuously estimate the target direction in its egocentric frame. We propose EAGOR, a training-free, geometry-aware framework for embodied 360° directional reasoning. Instead of predicting target directions as ERP image coordinates, EAGOR formulates directional reasoning as recursive Bayesian estimation directly on the sphere. It maintains a continuous belief over target directions and propagates it equivariantly under agent motion without training the backbone VLMs. To achieve this, we introduce the Spherical Harmonic Belief Field (SH-BF), whose spherical harmonic representation provides a globally defined, rotation-aware basis for directional estimation on the spherical manifold. This formulation eliminates ERP seam discontinuities, latitude distortions, and interpolation errors. We evaluate EAGOR on two benchmark datasets and real-world experiments with a legged robot across directional reasoning tasks. EAGOR consistently outperforms existing methods, achieving average relative gains of +34.4% and +45.6% on HOS and OSR-Bench, respectively, while improving navigation success by +14.6%, reducing step count by 17.7%, and lowering mean angular error by 24.5%.

Patterns and textures are defining characteristics of many natural objects: a shirt can be striped, the wings of a butterfly can be veined, and the skin of an animal can be scaly. Aiming at supporting this analytical dimension in image understanding, we address the challenging problem of describing textures with semantic attributes. We identify a rich vocabulary of forty-seven texture terms and use them to describe a large dataset of patterns collected in the wild.The resulting Describable Textures Dataset (DTD) is the basis to seek for the best texture representation for recognizing describable texture attributes in images. We port from object recognition to texture recognition the Improved Fisher Vector (IFV) and show that, surprisingly, it outperforms specialized texture descriptors not only on our problem, but also in established material recognition datasets. We also show that the describable attributes are excellent texture descriptors, transferring between datasets and tasks; in particular, combined with IFV, they significantly outperform the state-of-the-art by more than 8 percent on both FMD and KTHTIPS-2b benchmarks. We also demonstrate that they produce intuitive descriptions of materials and Internet images.

Mechanistic interpretability research on emotion in large language models -- linear probing, activation patching, sparse autoencoder (SAE) feature analysis, causal ablation, steering vector extraction -- depends on stimuli that contain the words for the emotions they test. When a probe fires on "I am furious", it is unclear whether the model has detected anger or detected the word "furious". The two readings have very different consequences for every downstream claim about emotion circuits, features, and interventions. We release AIPsy-Affect, a 480-item clinical stimulus battery that removes the confound at the stimulus level: 192 keyword-free vignettes evoking each of Plutchik's eight primary emotions through narrative situation alone, 192 matched neutral controls that share characters, setting, length, and surface structure with the affect surgically removed, plus moderate-intensity and discriminant-validity splits. The matched-pair structure supports linear probing, activation patching, SAE feature analysis, causal ablation, and steering vector extraction under a strong methodological guarantee: any internal representation that distinguishes a clinical item from its matched neutral cannot be doing so on the basis of emotion-keyword presence. A three-method NLP defense battery -- bag-of-words sentiment, an emotion-category lexicon, and a contextual transformer classifier -- confirms the property: bag-of-words methods see only situational vocabulary, and a contextual classifier detects affect (p < 10^-15) but cannot identify the category (5.2% top-1 vs. 82.5% on a keyword-rich control). AIPsy-Affect extends our earlier 96-item battery (arXiv:2603.22295) by a factor of four and is released openly under MIT license.

We present RegHead, a framework for constructing semantic blendshape sets for animatable non-humanoid head avatars. With a fixed expression vocabulary, semantic blendshapes provide a low-dimensional and interpretable animation interface and support cross-identity retargeting. Building such blendshape sets remains expensive because (i) expression-consistent supervision is scarce, (ii) generated 4D assets typically lack correspondence, and (iii) facial motion is highly localized. We propose (1) a large-scale dataset of non-humanoid identities paired with a shared expression vocabulary, obtained by expanding a small artist-rigged library via fine-tuned image editing; (2) a dense stochastic anchor motion representation tailored to localized facial deformations; and (3) a fast feed-forward registration model that converts unregistered expression meshes into a corresponded blendshape basis by predicting anchor-based deformations from the neutral shape. Experiments show that our approach produces higher-fidelity expression meshes than baselines, while running orders of magnitude faster than optimization. We further demonstrate real-time retargeting from human face tracking signals to non-humanoid characters, capturing both head pose and localized facial motions. Our project page is available at https://snap-research.github.io/RegHead/.

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by millions of parameters, but valuable because it increases our ability to understand current models and create improved versions of them. In this paper we investigate the extent to which neural networks exhibit what we call convergent learning, which is when the representations learned by multiple nets converge to a set of features which are either individually similar between networks or where subsets of features span similar low-dimensional spaces. We propose a specific method of probing representations: training multiple networks and then comparing and contrasting their individual, learned representations at the level of neurons or groups of neurons. We begin research into this question using three techniques to approximately align different neural networks on a feature level: a bipartite matching approach that makes one-to-one assignments between neurons, a sparse prediction approach that finds one-to-many mappings, and a spectral clustering approach that finds many-to-many mappings. This initial investigation reveals a few previously unknown properties of neural networks, and we argue that future research into the question of convergent learning will yield many more. The insights described here include (1) that some features are learned reliably in multiple networks, yet other features are not consistently learned; (2) that units learn to span low-dimensional subspaces and, while these subspaces are common to multiple networks, the specific basis vectors learned are not; (3) that the representation codes show evidence of being a mix between a local code and slightly, but not fully, distributed codes across multiple units.

We provide a construction for categorical representation learning and introduce the foundations of "categorifier". The central theme in representation learning is the idea of everything to vector. Every object in a dataset S can be represented as a vector in R^n by an encoding map E: Obj(S)toR^n. More importantly, every morphism can be represented as a matrix E: Hom(S)toR^{n}_{n}. The encoding map E is generally modeled by a deep neural network. The goal of representation learning is to design appropriate tasks on the dataset to train the encoding map (assuming that an encoding is optimal if it universally optimizes the performance on various tasks). However, the latter is still a set-theoretic approach. The goal of the current article is to promote the representation learning to a new level via a category-theoretic approach. As a proof of concept, we provide an example of a text translator equipped with our technology, showing that our categorical learning model outperforms the current deep learning models by 17 times. The content of the current article is part of the recent US patent proposal (patent application number: 63110906).

To make claims about representations that generalize beyond a particular trained model, we need to specify when two representations should count as equivalent. The Linear Representation Hypothesis is often discussed without making this equivalence explicit. Different notions of equivalence preserve different structures, so metrics, probes, and interventions that appear to study the same representation may in fact correspond to different hypotheses. We therefore argue that the Linear Representation Hypothesis is not one hypothesis but a family of claims distinguished by representation equivalence. We formalize this idea using group actions, specifying the representation object, the procedure that produces it, and the property ultimately asserted, while accounting for equivalences imposed by the model architecture. This framework clarifies how assumptions can change across metrics, reading points, and analysis stages, and we use it to audit common representation quantities and recent interpretability analyses.

Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Although modern models are trained on massive datasets, they still cover only a tiny fraction of the combinatorial space of possible inputs, raising the question of what structure representations must have to support generalization to unseen combinations. We formalize three desiderata for compositional generalization under standard training (divisibility, transferability, stability) and show they impose necessary geometric constraints: representations must decompose linearly into per-concept components, and these components must be orthogonal across concepts. This provides theoretical grounding for the Linear Representation Hypothesis: the linear structure widely observed in neural representations is a necessary consequence of compositional generalization. We further derive dimension bounds linking the number of composable concepts to the embedding geometry. Empirically, we evaluate these predictions across modern vision models (CLIP, SigLIP, DINO) and find that representations exhibit partial linear factorization with low-rank, near-orthogonal per-concept factors, and that the degree of this structure correlates with compositional generalization on unseen combinations. As models continue to scale, these conditions predict the representational geometry they may converge to. Code is available at https://github.com/oshapio/necessary-compositionality.

Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear representation" actually mean? And, how do we make sense of geometric notions (e.g., cosine similarity or projection) in the representation space? To answer these, we use the language of counterfactuals to give two formalizations of "linear representation", one in the output (word) representation space, and one in the input (sentence) space. We then prove these connect to linear probing and model steering, respectively. To make sense of geometric notions, we use the formalization to identify a particular (non-Euclidean) inner product that respects language structure in a sense we make precise. Using this causal inner product, we show how to unify all notions of linear representation. In particular, this allows the construction of probes and steering vectors using counterfactual pairs. Experiments with LLaMA-2 demonstrate the existence of linear representations of concepts, the connection to interpretation and control, and the fundamental role of the choice of inner product.

For nonconvex optimization in machine learning, this article proves that every local minimum achieves the globally optimal value of the perturbable gradient basis model at any differentiable point. As a result, nonconvex machine learning is theoretically as supported as convex machine learning with a handcrafted basis in terms of the loss at differentiable local minima, except in the case when a preference is given to the handcrafted basis over the perturbable gradient basis. The proofs of these results are derived under mild assumptions. Accordingly, the proven results are directly applicable to many machine learning models, including practical deep neural networks, without any modification of practical methods. Furthermore, as special cases of our general results, this article improves or complements several state-of-the-art theoretical results on deep neural networks, deep residual networks, and overparameterized deep neural networks with a unified proof technique and novel geometric insights. A special case of our results also contributes to the theoretical foundation of representation learning.

The standard basis of transformer hidden states is a training-free, architecture-general feature basis for detecting concepts and, in language models, steering them; with no learned dictionary. Individual dimensions act as binary registers read one at a time: their signs (+/-1) encode content, their magnitudes strength. A feature is just a subset of dimensions with a consistent sign pattern, read by counting sign agreements. We validate this Bag of Dims (BoD) framework across seven models spanning language, vision, and audio; reading dimensions one at a time loses nothing, as a full-capacity MLP adds zero AUC over per-dim reading. The same per-dimension signs appear in every modality, so they reflect transformer training itself, not the language objective. Sign alone carries predictive content: setting all magnitudes to unity preserves 60-93% top-5 next-token accuracy through the LM head. From a single-token cache (one forward pass per token, no labels) we detect 175 categories at AUC 0.97-0.99 by counting sign agreements, and from random seeds alone discovery scales to 1500 features per model. A trained probe adds only +0.018 AUC and converges to axis-aligned weights: the rotation dictionaries learn buys little. Signs are causally operative: they survive the attention projections, and flipping a concept's sign pattern in the live forward pass suppresses it. Reading and steering are separate roles in the same basis: a concept's reader dimensions are not its writer dimensions. The writer target is just as cheap, the sign of the summed unembedding rows over a few seeds, no training. Injected through the attention output pathway under closed-loop control, it steers concepts into fluent text on four language models (62-92% of twelve concepts). The signs were in the standard basis all along; the open problem is no longer finding the right rotation but cataloging what each dimension encodes.

State representation learning, or the ability to capture latent generative factors of an environment, is crucial for building intelligent agents that can perform a wide variety of tasks. Learning such representations without supervision from rewards is a challenging open problem. We introduce a method that learns state representations by maximizing mutual information across spatially and temporally distinct features of a neural encoder of the observations. We also introduce a new benchmark based on Atari 2600 games where we evaluate representations based on how well they capture the ground truth state variables. We believe this new framework for evaluating representation learning models will be crucial for future representation learning research. Finally, we compare our technique with other state-of-the-art generative and contrastive representation learning methods. The code associated with this work is available at https://github.com/mila-iqia/atari-representation-learning

Few shot classification aims to learn to recognize novel categories using only limited samples per category. Most current few shot methods use a base dataset rich in labeled examples to train an encoder that is used for obtaining representations of support instances for novel classes. Since the test instances are from a distribution different to the base distribution, their feature representations are of poor quality, degrading performance. In this paper we propose to make use of the well-trained feature representations of the base dataset that are closest to each support instance to improve its representation during meta-test time. To this end, we propose BaseTransformers, that attends to the most relevant regions of the base dataset feature space and improves support instance representations. Experiments on three benchmark data sets show that our method works well for several backbones and achieves state-of-the-art results in the inductive one shot setting. Code is available at github.com/mayug/BaseTransformers

A key requirement for the development of effective learning representations is their evaluation and comparison to representations we know to be effective. In natural sensory domains, the community has viewed the brain as a source of inspiration and as an implicit benchmark for success. However, it has not been possible to directly test representational learning algorithms directly against the representations contained in neural systems. Here, we propose a new benchmark for visual representations on which we have directly tested the neural representation in multiple visual cortical areas in macaque (utilizing data from [Majaj et al., 2012]), and on which any computer vision algorithm that produces a feature space can be tested. The benchmark measures the effectiveness of the neural or machine representation by computing the classification loss on the ordered eigendecomposition of a kernel matrix [Montavon et al., 2011]. In our analysis we find that the neural representation in visual area IT is superior to visual area V4. In our analysis of representational learning algorithms, we find that three-layer models approach the representational performance of V4 and the algorithm in [Le et al., 2012] surpasses the performance of V4. Impressively, we find that a recent supervised algorithm [Krizhevsky et al., 2012] achieves performance comparable to that of IT for an intermediate level of image variation difficulty, and surpasses IT at a higher difficulty level. We believe this result represents a major milestone: it is the first learning algorithm we have found that exceeds our current estimate of IT representation performance. We hope that this benchmark will assist the community in matching the representational performance of visual cortex and will serve as an initial rallying point for further correspondence between representations derived in brains and machines.

We introduce an axiomatic evaluation framework for latent thought representations in LLMs, comprising metrics that are independent of downstream benchmark scores and reveal representational failures that benchmark accuracy masks. Existing evaluations conflate representation quality with model capacity. Therefore, failures cannot be attributed to the representation rather than to the model that processes it. We formalize four functional axioms (Causality, Minimality, Separability, and Stability) and define a quantitative measure for each, computed directly on the representation independently of downstream accuracy. We audit open-weight LLMs across 23 reasoning tasks (e.g., Spatial Reasoning, Factual QA). We find that no candidate satisfies all four axioms simultaneously, that the representations distinguish task type reliably but cannot distinguish between two questions within the same task, and that the representations encode little information beyond what is already present in the input embedding. The failure is consistent across dense, reasoning-distilled, and RL-trained model families, indicating that the gap is structural rather than a property of model size or training procedure.

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning.

Given the importance of remote sensing, surprisingly little attention has been paid to it by the representation learning community. To address it and to establish baselines and a common evaluation protocol in this domain, we provide simplified access to 5 diverse remote sensing datasets in a standardized form. Specifically, we investigate in-domain representation learning to develop generic remote sensing representations and explore which characteristics are important for a dataset to be a good source for remote sensing representation learning. The established baselines achieve state-of-the-art performance on these datasets.

Set representation has become ubiquitous in deep learning for modeling the inductive bias of neural networks that are insensitive to the input order. DeepSets is the most widely used neural network architecture for set representation. It involves embedding each set element into a latent space with dimension L, followed by a sum pooling to obtain a whole-set embedding, and finally mapping the whole-set embedding to the output. In this work, we investigate the impact of the dimension L on the expressive power of DeepSets. Previous analyses either oversimplified high-dimensional features to be one-dimensional features or were limited to analytic activations, thereby diverging from practical use or resulting in L that grows exponentially with the set size N and feature dimension D. To investigate the minimal value of L that achieves sufficient expressive power, we present two set-element embedding layers: (a) linear + power activation (LP) and (b) linear + exponential activations (LE). We demonstrate that L being poly(N, D) is sufficient for set representation using both embedding layers. We also provide a lower bound of L for the LP embedding layer. Furthermore, we extend our results to permutation-equivariant set functions and the complex field.

Learning compatible representations enables the interchangeable use of semantic features as models are updated over time. This is particularly relevant in search and retrieval systems where it is crucial to avoid reprocessing of the gallery images with the updated model. While recent research has shown promising empirical evidence, there is still a lack of comprehensive theoretical understanding about learning compatible representations. In this paper, we demonstrate that the stationary representations learned by the d-Simplex fixed classifier optimally approximate compatibility representation according to the two inequality constraints of its formal definition. This not only establishes a solid foundation for future works in this line of research but also presents implications that can be exploited in practical learning scenarios. An exemplary application is the now-standard practice of downloading and fine-tuning new pre-trained models. Specifically, we show the strengths and critical issues of stationary representations in the case in which a model undergoing sequential fine-tuning is asynchronously replaced by downloading a better-performing model pre-trained elsewhere. Such a representation enables seamless delivery of retrieval service (i.e., no reprocessing of gallery images) and offers improved performance without operational disruptions during model replacement. Code available at: https://github.com/miccunifi/iamcl2r.

Implicit neural representations (INRs) have arisen as useful methods for representing signals on Euclidean domains. By parameterizing an image as a multilayer perceptron (MLP) on Euclidean space, INRs effectively represent signals in a way that couples spatial and spectral features of the signal that is not obvious in the usual discrete representation, paving the way for continuous signal processing and machine learning approaches that were not previously possible. Although INRs using sinusoidal activation functions have been studied in terms of Fourier theory, recent works have shown the advantage of using wavelets instead of sinusoids as activation functions, due to their ability to simultaneously localize in both frequency and space. In this work, we approach such INRs and demonstrate how they resolve high-frequency features of signals from coarse approximations done in the first layer of the MLP. This leads to multiple prescriptions for the design of INR architectures, including the use of complex wavelets, decoupling of low and band-pass approximations, and initialization schemes based on the singularities of the desired signal.

Representation learning, and interpreting learned representations, are key areas of focus in machine learning and neuroscience. Both fields generally use representations as a means to understand or improve a system's computations. In this work, however, we explore surprising dissociations between representation and computation that may pose challenges for such efforts. We create datasets in which we attempt to match the computational role that different features play, while manipulating other properties of the features or the data. We train various deep learning architectures to compute these multiple abstract features about their inputs. We find that their learned feature representations are systematically biased towards representing some features more strongly than others, depending upon extraneous properties such as feature complexity, the order in which features are learned, and the distribution of features over the inputs. For example, features that are simpler to compute or learned first tend to be represented more strongly and densely than features that are more complex or learned later, even if all features are learned equally well. We also explore how these biases are affected by architectures, optimizers, and training regimes (e.g., in transformers, features decoded earlier in the output sequence also tend to be represented more strongly). Our results help to characterize the inductive biases of gradient-based representation learning. These results also highlight a key challenge for interpretability - or for comparing the representations of models and brains - disentangling extraneous biases from the computationally important aspects of a system's internal representations.

Medical vision-language models (VLMs) have shown increasing potential for radiological image interpretation. Medical VLMs encode radiological images into visual representations that capture both anatomical and phenotypic information for diagnosis. Existing approaches improve pathological phenotype representations through semantic-guided representation alignment. However, pathological phenotypes arise as lesion-specific visual changes superimposed on underlying normal anatomy. Such semantic alignment approaches fail to model the phenotype-specific increment relative to the corresponding normal anatomical representation. To address this gap, we propose ΔRepresentation, a visual phenotype representation learning framework based on counterfactual reasoning for medical VLMs. It comprises BaseAnatomy, a geometry-supervised representation learning module, and ΔPhenotype, a counterfactual incremental representation learning module. BaseAnatomy provides fine-grained geometric supervision through spatial relationships across and within anatomical structures. ΔPhenotype computes the representation increment between lesion representations and their corresponding normal anatomical representations, and supervises increments associated with the same phenotype to cluster in the representation space. Experiments on ReXGroundingCT and LIDC-IDRI demonstrate that ΔRepresentation effectively structures pathological phenotype representations and improves lesion grounding and phenotype characterization accuracy in medical VLMs. Code is available at https://anonymous.4open.science/r/deltarep-CF6D.

This paper describes pi2vec, a method for representing behaviors of black box policies as feature vectors. The policy representations capture how the statistics of foundation model features change in response to the policy behavior in a task agnostic way, and can be trained from offline data, allowing them to be used in offline policy selection. This work provides a key piece of a recipe for fusing together three modern lines of research: Offline policy evaluation as a counterpart to offline RL, foundation models as generic and powerful state representations, and efficient policy selection in resource constrained environments.

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate dimension reduction, typically achieved via basis expansions. Currently, these bases are chosen a priori without the information for the task at hand and thus may not be effective for the designated task. We instead propose to adaptively learn these bases in an end-to-end fashion. We introduce neural networks that employ a new Basis Layer whose hidden units are each basis functions themselves implemented as a micro neural network. Our architecture learns to apply parsimonious dimension reduction to functional inputs that focuses only on information relevant to the target rather than irrelevant variation in the input function. Across numerous classification/regression tasks with functional data, our method empirically outperforms other types of neural networks, and we prove that our approach is statistically consistent with low generalization error. Code is available at: https://github.com/jwyyy/AdaFNN.

Foundation models are high-capacity networks pretrained once on broad data and then reused across many tasks. This chapter introduces them through the idea of a transferable representation, the internal description a network forms during training, which, rather than the fitted task, is what carries over to new problems. We develop the idea from first principles for an astronomical reader, starting from why a representation matters and what makes one useful, and then surveying the architectures, self-supervised objectives, scaling, adaptation, and cross-modal learning that produce one. A theme throughout is the distinction between these methods and the goal they serve. The presence of a transformer, a self-supervised objective, and large-scale pretraining does not by itself make a model a foundation model, since the defining property is that the learned representation transfers, as tested by its ability to work on new tasks with little or no task-specific training data (few-shot and zero-shot learning). We then consider astronomy, where data are abundant but labels are scarce and simulations often stand in for ground truth. Here we offer a cautious reading of the current literature, in which many models adopt the architecture of foundation models while clear demonstrations of transfer across instruments, populations, and tasks remain comparatively rare. This is to be expected, since robust transfer beyond language is still uncommon even in vision and the wider physical sciences, and whether further scaling or a different account of representation will close the gap remains an open question. We close by placing the goal within the broader aim of machine intelligence and outlining the evidence that would mark real progress.

Representation learning has been a critical topic in machine learning. In Click-through Rate Prediction, most features are represented as embedding vectors and learned simultaneously with other parameters in the model. With the development of CTR models, feature representation learning has become a trending topic and has been extensively studied by both industrial and academic researchers in recent years. This survey aims at summarizing the feature representation learning in a broader picture and pave the way for future research. To achieve such a goal, we first present a taxonomy of current research methods on feature representation learning following two main issues: (i) which feature to represent and (ii) how to represent these features. Then we give a detailed description of each method regarding these two issues. Finally, the review concludes with a discussion on the future directions of this field.

In this study, we introduce FEET, a standardized protocol designed to guide the development and benchmarking of foundation models. While numerous benchmark datasets exist for evaluating these models, we propose a structured evaluation protocol across three distinct scenarios to gain a comprehensive understanding of their practical performance. We define three primary use cases: frozen embeddings, few-shot embeddings, and fully fine-tuned embeddings. Each scenario is detailed and illustrated through two case studies: one in sentiment analysis and another in the medical domain, demonstrating how these evaluations provide a thorough assessment of foundation models' effectiveness in research applications. We recommend this protocol as a standard for future research aimed at advancing representation learning models.

Model dimension (d_{model}) is a fundamental hyperparameter in transformer language models, yet its role in setting the geometric limits of feature representation remains under-explored. Grounded in the Linear Representation and Superposition Hypotheses - which propose that models encode features as near-orthogonal directions in latent space - we develop a framework for estimating how many such directions a model can support. We first establish the embedding matrix as a measurable proxy for near-orthogonality constraints across the latent space: the boundary between meaningful token relationships and incidental similarity in the pairwise cosine similarity distribution gives a concrete estimate of the model's accepted deviation varepsilon from perfect orthogonality. Applying this metric across dozens of open-source models reveals two classes: models with high varepsilon whose embeddings lack near-orthogonal structure, and models with low varepsilon that maintain it. We then show that the standard Johnson-Lindenstrauss lemma greatly underestimates the packing efficiency of trained representations, and derive an adjusted capacity formula in which the number of near-orthogonal directions depends on the ratio of vectors to dimensions (k/d) rather than the raw count - a single modification that cuts prediction error by two orders of magnitude with no extra parameters. Combining these results, we define representational capacity as an upper bound on the number of distinguishable directions available for features and embeddings in a model's latent space. Capacity is exponentially sensitive to varepsilon, and larger models favor tighter orthogonality constraints over maximizing raw capacity - a pattern compatible with several explanations (a stability-capacity trade-off, a ceiling on usable concepts, or confounds with model scale) that we leave to future work.

A central question for neuroscience is how to characterize brain representations of perceptual and cognitive content. An ideal characterization should distinguish different functional regions with robustness to noise and idiosyncrasies of individual brains that do not correspond to computational differences. Previous studies have characterized brain representations by their representational geometry, which is defined by the representational dissimilarity matrix (RDM), a summary statistic that abstracts from the roles of individual neurons (or responses channels) and characterizes the discriminability of stimuli. Here we explore a further step of abstraction: from the geometry to the topology of brain representations. We propose topological representational similarity analysis (tRSA), an extension of representational similarity analysis (RSA) that uses a family of geo-topological summary statistics that generalizes the RDM to characterize the topology while de-emphasizing the geometry. We evaluate this new family of statistics in terms of the sensitivity and specificity for model selection using both simulations and functional MRI (fMRI) data. In the simulations, the ground truth is a data-generating layer representation in a neural network model and the models are the same and other layers in different model instances (trained from different random seeds). In fMRI, the ground truth is a visual area and the models are the same and other areas measured in different subjects. Results show that topology-sensitive characterizations of population codes are robust to noise and interindividual variability and maintain excellent sensitivity to the unique representational signatures of different neural network layers and brain regions.

Existing object detection frameworks are usually built on a single format of object/part representation, i.e., anchor/proposal rectangle boxes in RetinaNet and Faster R-CNN, center points in FCOS and RepPoints, and corner points in CornerNet. While these different representations usually drive the frameworks to perform well in different aspects, e.g., better classification or finer localization, it is in general difficult to combine these representations in a single framework to make good use of each strength, due to the heterogeneous or non-grid feature extraction by different representations. This paper presents an attention-based decoder module similar as that in Transformer~vaswani2017attention to bridge other representations into a typical object detector built on a single representation format, in an end-to-end fashion. The other representations act as a set of key instances to strengthen the main query representation features in the vanilla detectors. Novel techniques are proposed towards efficient computation of the decoder module, including a key sampling approach and a shared location embedding approach. The proposed module is named bridging visual representations (BVR). It can perform in-place and we demonstrate its broad effectiveness in bridging other representations into prevalent object detection frameworks, including RetinaNet, Faster R-CNN, FCOS and ATSS, where about 1.5sim3.0 AP improvements are achieved. In particular, we improve a state-of-the-art framework with a strong backbone by about 2.0 AP, reaching 52.7 AP on COCO test-dev. The resulting network is named RelationNet++. The code will be available at https://github.com/microsoft/RelationNet2.

We consider representation misdirection (RM), a class of LLM unlearning methods that achieves forgetting by manipulating the forget-representations, that is, latent representations of forget samples. Despite being important, the roles of target vectors used in RM, however, remain underexplored. Here, we approach and revisit RM through the lens of the linear representation hypothesis. Specifically, if one can somehow identify a one-dimensional representation corresponding to a high-level concept, the linear representation hypothesis enables linear operations on this concept vector within the forget-representation space. Under this view, we hypothesize that, beyond forgetting, machine unlearning elicits controllable side behaviors and stronger side capabilities corresponding to the high-level concept. Our hypothesis is empirically validated across a wide range of tasks, including behavioral control (e.g., controlling unlearned models' truth, sentiment, and refusal) and capability enhancement (e.g., improving unlearned models' in-context learning capability). Our findings reveal that this fairly attractive phenomenon could be either a hidden risk if misused or a mechanism that can be harnessed for developing models that require stronger capabilities and controllable behaviors.

Representations are at the core of all deep reinforcement learning (RL) methods for both Markov decision processes (MDPs) and partially observable Markov decision processes (POMDPs). Many representation learning methods and theoretical frameworks have been developed to understand what constitutes an effective representation. However, the relationships between these methods and the shared properties among them remain unclear. In this paper, we show that many of these seemingly distinct methods and frameworks for state and history abstractions are, in fact, based on a common idea of self-predictive abstraction. Furthermore, we provide theoretical insights into the widely adopted objectives and optimization, such as the stop-gradient technique, in learning self-predictive representations. These findings together yield a minimalist algorithm to learn self-predictive representations for states and histories. We validate our theories by applying our algorithm to standard MDPs, MDPs with distractors, and POMDPs with sparse rewards. These findings culminate in a set of preliminary guidelines for RL practitioners.

Sofroniew et al. (2026) report that emotion concepts in Claude Sonnet 4.5 are represented as vectors whose geometry mirrors human affect psychology. We replicate the representational core of that study on the base pretrained model google/gemma-2-27b, inheriting every disclosed parameter, resolving unspecified steps by disclosed rules, and changing only the subject model. From 205,200 newly generated Claude Sonnet 4.5 stories matching the original corpus design, we extract 171 emotion vectors and recover the core results. The leading principal components form an affective circumplex (PC1 carries 26.7% of variance against the original study's ~27%, PC2 13.4% against ~14%), emotions cluster into similar intuitive families, and the geometry holds across a broad late-middle band. The valence axis aligns with human norms (r = 0.72, against 0.81) and is stable across scales and depth. Arousal aligns at r = 0.67 (against 0.66) but only at the full 171-emotion scale and late depth, so we do not classify it as replicated. Extending the original analysis, a 46-layer sweep locates a sharp seam at L22-26, where the geometry consolidates and the vocabulary readout becomes legible. An embedding-layer baseline finds much of the geometry already present in the static token embeddings, with arousal as the exception. On top-activating held-out text, the geometry predicts token-level co-activation at r = 0.907. At least 52% of vectors peak on structurally non-conceptual tokens, a measured floor for max-activation confounds. Even when a document contains the vector's emotion word, the peak lands on that word only 6.1% of the time. Because the subject is a base model and the stimuli are Claude-generated fiction, the recovered structure is a property of the pretrained representation of Claude-rendered emotion. The original's causal and assistant-facing analyses are out of scope. Code and data are released.

Representation alignment (REPA) guides generative training by distilling representations from a strong, pretrained vision encoder to intermediate diffusion features. We investigate a fundamental question: what aspect of the target representation matters for generation, its global semantic information (e.g., measured by ImageNet-1K accuracy) or its spatial structure (i.e. pairwise cosine similarity between patch tokens)? Prevalent wisdom holds that stronger global semantic performance leads to better generation as a target representation. To study this, we first perform a large-scale empirical analysis across 27 different vision encoders and different model scales. The results are surprising; spatial structure, rather than global performance, drives the generation performance of a target representation. To further study this, we introduce two straightforward modifications, which specifically accentuate the transfer of spatial information. We replace the standard MLP projection layer in REPA with a simple convolution layer and introduce a spatial normalization layer for the external representation. Surprisingly, our simple method (implemented in <4 lines of code), termed iREPA, consistently improves convergence speed of REPA, across a diverse set of vision encoders, model sizes, and training variants (such as REPA, REPA-E, Meanflow, JiT etc). %, etc. Our work motivates revisiting the fundamental working mechanism of representational alignment and how it can be leveraged for improved training of generative models. The code and project page are available at https://end2end-diffusion.github.io/irepa

In language models, what a representation encodes is determined by the geometry of its representation space: distances, not activations, carry meaning. Existing tools characterize the shape of this geometry but do not ask what that shape is organized for. We introduce Subspace PGA, a metric that tests whether a layer's distance structure aligns with the readout subspace of the unembedding matrix W_U more than with random subspaces of equal size. Across seven Pythia models (70M--6.9B) and three cross-family models, intermediate geometry is significantly organized for prediction (peak z = 9--24), but the degree is scale-dependent: small models (d leq 1024) progressively lose it at late layers during training -- even as loss keeps improving -- while large models (d geq 2048) preserve it throughout. We trace this to a capacity trade-off: a few dominant directions migrate away from W_U's readout, masking rather than destroying the predictive structure beneath, and removing them restores alignment. Neither spectral metrics nor loss curves capture this distinction. Scale thus determines not only how well a model predicts, but how its representation geometry is organized to do so.

Learned representations are a central component in modern ML systems, serving a multitude of downstream tasks. When training such representations, it is often the case that computational and statistical constraints for each downstream task are unknown. In this context rigid, fixed capacity representations can be either over or under-accommodating to the task at hand. This leads us to ask: can we design a flexible representation that can adapt to multiple downstream tasks with varying computational resources? Our main contribution is Matryoshka Representation Learning (MRL) which encodes information at different granularities and allows a single embedding to adapt to the computational constraints of downstream tasks. MRL minimally modifies existing representation learning pipelines and imposes no additional cost during inference and deployment. MRL learns coarse-to-fine representations that are at least as accurate and rich as independently trained low-dimensional representations. The flexibility within the learned Matryoshka Representations offer: (a) up to 14x smaller embedding size for ImageNet-1K classification at the same level of accuracy; (b) up to 14x real-world speed-ups for large-scale retrieval on ImageNet-1K and 4K; and (c) up to 2% accuracy improvements for long-tail few-shot classification, all while being as robust as the original representations. Finally, we show that MRL extends seamlessly to web-scale datasets (ImageNet, JFT) across various modalities -- vision (ViT, ResNet), vision + language (ALIGN) and language (BERT). MRL code and pretrained models are open-sourced at https://github.com/RAIVNLab/MRL.

We study the ability of foundation models to learn representations for classification that are transferable to new, unseen classes. Recent results in the literature show that representations learned by a single classifier over many classes are competitive on few-shot learning problems with representations learned by special-purpose algorithms designed for such problems. In this paper we provide an explanation for this behavior based on the recently observed phenomenon that the features learned by overparameterized classification networks show an interesting clustering property, called neural collapse. We demonstrate both theoretically and empirically that neural collapse generalizes to new samples from the training classes, and -- more importantly -- to new classes as well, allowing foundation models to provide feature maps that work well in transfer learning and, specifically, in the few-shot setting.

It is well noted that coordinate based MLPs benefit -- in terms of preserving high-frequency information -- through the encoding of coordinate positions as an array of Fourier features. Hitherto, the rationale for the effectiveness of these positional encodings has been solely studied through a Fourier lens. In this paper, we strive to broaden this understanding by showing that alternative non-Fourier embedding functions can indeed be used for positional encoding. Moreover, we show that their performance is entirely determined by a trade-off between the stable rank of the embedded matrix and the distance preservation between embedded coordinates. We further establish that the now ubiquitous Fourier feature mapping of position is a special case that fulfills these conditions. Consequently, we present a more general theory to analyze positional encoding in terms of shifted basis functions. To this end, we develop the necessary theoretical formulae and empirically verify that our theoretical claims hold in practice. Codes available at https://github.com/osiriszjq/Rethinking-positional-encoding.

Tabular representation learning has recently gained a lot of attention. However, existing approaches only learn a representation from a single table, and thus ignore the potential to learn from the full structure of relational databases, including neighboring tables that can contain important information for a contextualized representation. Moreover, current models are significantly limited in scale, which prevents that they learn from large databases. In this paper, we thus introduce our vision of relational representation learning, that can not only learn from the full relational structure, but also can scale to larger database sizes that are commonly found in real-world. Moreover, we also discuss opportunities and challenges we see along the way to enable this vision and present initial very promising results. Overall, we argue that this direction can lead to foundation models for relational databases that are today only available for text and images.

Task arithmetic, representing downstream tasks through linear operations on task vectors, has emerged as a simple yet powerful paradigm for transferring knowledge across diverse settings. However, maintaining a large collection of task vectors introduces scalability challenges in both storage and computation. We propose Task Vector Bases, a framework compressing T task vectors into M < T basis vectors while preserving the functionality of task arithmetic. By representing each task vector as a structured linear combination of basis atoms, our approach supports standard operations such as addition, negation, as well as more advanced arithmetic ones. The framework is orthogonal to other efficiency-oriented improvements in task arithmetic and can be used in combination with them. We provide theoretical analysis showing that basis compression retains addition generalization guarantees and enables principled unlearning, with error bounds depending on reconstruction quality. Empirically, our proposed basis construction methods consistently outperform heuristic basis construction baselines and, in some cases, even surpass the performance of full task vector collections across diverse downstream applications while reducing storage and computational requirements. The code is available at https://github.com/uiuctml/TaskVectorBasis.

Model merging enables powerful capabilities in neural networks without requiring additional training. In this paper, we introduce a novel perspective on model merging by leveraging the fundamental mechanisms of neural network representation. Our approach is motivated by the linear representation hypothesis, which states that neural networks encode information through linear combinations of feature vectors. We propose a method that superposes task-specific features from individual models into a merged model. Our approach specifically targets linear transformation matrices, which are crucial for feature activation and extraction in deep networks. By formulating the merging process as a linear system, we can preserve task-specific features from individual models and create merged models that effectively maintain multi-task capabilities compared to existing methods. Extensive experiments across diverse benchmarks and models demonstrate that our method outperforms existing techniques. Code is available at https://github.com/LARS-research/STF.

Understanding how semantic meaning is encoded in the representation spaces of large language models is a fundamental problem in interpretability. In this paper, we study the two foundational questions in this area. First, how are categorical concepts, such as {'mammal', 'bird', 'reptile', 'fish'}, represented? Second, how are hierarchical relations between concepts encoded? For example, how is the fact that 'dog' is a kind of 'mammal' encoded? We show how to extend the linear representation hypothesis to answer these questions. We find a remarkably simple structure: simple categorical concepts are represented as simplices, hierarchically related concepts are orthogonal in a sense we make precise, and (in consequence) complex concepts are represented as polytopes constructed from direct sums of simplices, reflecting the hierarchical structure. We validate these theoretical results on the Gemma large language model, estimating representations for 957 hierarchically related concepts using data from WordNet.

Representation learning seeks to expose certain aspects of observed data in a learned representation that's amenable to downstream tasks like classification. For instance, a good representation for 2D images might be one that describes only global structure and discards information about detailed texture. In this paper, we present a simple but principled method to learn such global representations by combining Variational Autoencoder (VAE) with neural autoregressive models such as RNN, MADE and PixelRNN/CNN. Our proposed VAE model allows us to have control over what the global latent code can learn and , by designing the architecture accordingly, we can force the global latent code to discard irrelevant information such as texture in 2D images, and hence the VAE only "autoencodes" data in a lossy fashion. In addition, by leveraging autoregressive models as both prior distribution p(z) and decoding distribution p(x|z), we can greatly improve generative modeling performance of VAEs, achieving new state-of-the-art results on MNIST, OMNIGLOT and Caltech-101 Silhouettes density estimation tasks.

High-throughput data generation methods and machine learning (ML) algorithms have given rise to a new era of computational materials science by learning relationships among composition, structure, and properties and by exploiting such relations for design. However, to build these connections, materials data must be translated into a numerical form, called a representation, that can be processed by a machine learning model. Datasets in materials science vary in format (ranging from images to spectra), size, and fidelity. Predictive models vary in scope and property of interests. Here, we review context-dependent strategies for constructing representations that enable the use of materials as inputs or outputs of machine learning models. Furthermore, we discuss how modern ML techniques can learn representations from data and transfer chemical and physical information between tasks. Finally, we outline high-impact questions that have not been fully resolved and thus, require further investigation.

Current foundation models exhibit impressive capabilities when prompted either with text only or with both image and text inputs. But do their capabilities change depending on the input modality? In this work, we propose IsoBench, a benchmark dataset containing problems from four major areas: math, science, algorithms, and games. Each example is presented with multiple isomorphic representations of inputs, such as visual, textual, and mathematical presentations. IsoBench provides fine-grained feedback to diagnose performance gaps caused by the form of the representation. Across various foundation models, we observe that on the same problem, models have a consistent preference towards textual representations. Most prominently, when evaluated on all IsoBench problems, Claude-3 Opus performs 28.7 points worse when provided with images instead of text; similarly, GPT-4 Turbo is 18.7 points worse and Gemini Pro is 14.9 points worse. Finally, we present two prompting techniques, IsoCombination and IsoScratchPad, which improve model performance by considering combinations of, and translations between, different input representations.

Coecke, Sadrzadeh, and Clark (arXiv:1003.4394v1 [cs.CL]) developed a compositional model of meaning for distributional semantics, in which each word in a sentence has a meaning vector and the distributional meaning of the sentence is a function of the tensor products of the word vectors. Abstractly speaking, this function is the morphism corresponding to the grammatical structure of the sentence in the category of finite dimensional vector spaces. In this paper, we provide a concrete method for implementing this linear meaning map, by constructing a corpus-based vector space for the type of sentence. Our construction method is based on structured vector spaces whereby meaning vectors of all sentences, regardless of their grammatical structure, live in the same vector space. Our proposed sentence space is the tensor product of two noun spaces, in which the basis vectors are pairs of words each augmented with a grammatical role. This enables us to compare meanings of sentences by simply taking the inner product of their vectors.

One of the decisions that arise when designing a neural network for any application is how the data should be represented in order to be presented to, and possibly generated by, a neural network. For audio, the choice is less obvious than it seems to be for visual images, and a variety of representations have been used for different applications including the raw digitized sample stream, hand-crafted features, machine discovered features, MFCCs and variants that include deltas, and a variety of spectral representations. This paper reviews some of these representations and issues that arise, focusing particularly on spectrograms for generating audio using neural networks for style transfer.

We provide a full characterisation of all of the possible group equivariant neural networks whose layers are some tensor power of R^{n} for three symmetry groups that are missing from the machine learning literature: O(n), the orthogonal group; SO(n), the special orthogonal group; and Sp(n), the symplectic group. In particular, we find a spanning set of matrices for the learnable, linear, equivariant layer functions between such tensor power spaces in the standard basis of R^{n} when the group is O(n) or SO(n), and in the symplectic basis of R^{n} when the group is Sp(n).

Recent advances in mechanistic interpretability have revealed that large language models (LLMs) develop internal representations corresponding not only to concrete entities but also distinct, human-understandable abstract concepts and behaviour. Moreover, these hidden features can be directly manipulated to steer model behaviour. However, it remains an open question whether this phenomenon is unique to models trained on inherently structured data (ie. language, images) or if it is a general property of foundation models. In this work, we investigate the internal representations of a large physics-focused foundation model. Inspired by recent work identifying single directions in activation space for complex behaviours in LLMs, we extract activation vectors from the model during forward passes over simulation datasets for different physical regimes. We then compute "delta" representations between the two regimes. These delta tensors act as concept directions in activation space, encoding specific physical features. By injecting these concept directions back into the model during inference, we can steer its predictions, demonstrating causal control over physical behaviours, such as inducing or removing some particular physical feature from a simulation. These results suggest that scientific foundation models learn generalised representations of physical principles. They do not merely rely on superficial correlations and patterns in the simulations. Our findings open new avenues for understanding and controlling scientific foundation models and has implications for AI-enabled scientific discovery.

Molecular representation is a foundational element in our understanding of the physical world. Its importance ranges from the fundamentals of chemical reactions to the design of new therapies and materials. Previous molecular machine learning models have employed strings, fingerprints, global features, and simple molecular graphs that are inherently information-sparse representations. However, as the complexity of prediction tasks increases, the molecular representation needs to encode higher fidelity information. This work introduces a novel approach to infusing quantum-chemical-rich information into molecular graphs via stereoelectronic effects. We show that the explicit addition of stereoelectronic interactions significantly improves the performance of molecular machine learning models. Furthermore, stereoelectronics-infused representations can be learned and deployed with a tailored double graph neural network workflow, enabling its application to any downstream molecular machine learning task. Finally, we show that the learned representations allow for facile stereoelectronic evaluation of previously intractable systems, such as entire proteins, opening new avenues of molecular design.

The Linear Representation Hypothesis (LRH) states that neural networks learn to encode concepts as directions in activation space, and a strong version of the LRH states that models learn only such encodings. In this paper, we present a counterexample to this strong LRH: when trained to repeat an input token sequence, gated recurrent neural networks (RNNs) learn to represent the token at each position with a particular order of magnitude, rather than a direction. These representations have layered features that are impossible to locate in distinct linear subspaces. To show this, we train interventions to predict and manipulate tokens by learning the scaling factor corresponding to each sequence position. These interventions indicate that the smallest RNNs find only this magnitude-based solution, while larger RNNs have linear representations. These findings strongly indicate that interpretability research should not be confined by the LRH.

Self-supervised models have revolutionized speech processing, achieving new levels of performance in a wide variety of tasks with limited resources. However, the inner workings of these models are still opaque. In this paper, we aim to analyze the encoded contextual representation of these foundation models based on their inter- and intra-model similarity, independent of any external annotation and task-specific constraint. We examine different SSL models varying their training paradigm -- Contrastive (Wav2Vec2.0) and Predictive models (HuBERT); and model sizes (base and large). We explore these models on different levels of localization/distributivity of information including (i) individual neurons; (ii) layer representation; (iii) attention weights and (iv) compare the representations with their finetuned counterparts.Our results highlight that these models converge to similar representation subspaces but not to similar neuron-localized concepts\footnote{A concept represents a coherent fragment of knowledge, such as ``a class containing certain objects as elements, where the objects have certain properties. We made the code publicly available for facilitating further research, we publicly released our code.

Understanding how structured internal structure emerges during neural network training is central to the study of deep learning. We investigate this phenomenon through the group composition task, where a two-layer neural network is trained to predict g_1 star g_2 for elements of a finite group G. By lifting the projected gradient flow to the Fourier domain, we demonstrate that the training dynamics are governed by a Riemannian gradient ascent on a representation-theoretic energy functional. We prove that, under random initialization, this flow drives each neuron to converge almost surely toward a single irreducible representation, while the cross-layer Fourier coefficients achieve a rotational rank-one alignment. This framework provides a representation-theoretic account of feature learning and characterizes a novel low-rank compression phenomenon for matrix-valued group representations. Moreover, for Abelian groups, we provide a complete population-level description: random initialization promotes uniform diversification across nontrivial representations and induces Haar-uniform phases, jointly approximating the indicator via a majority-vote mechanism. We further prove that both phase alignment and representation competition emerge with exponential convergence rates.

Recent work has proposed the linear representation hypothesis: that language models perform computation by manipulating one-dimensional representations of concepts ("features") in activation space. In contrast, we explore whether some language model representations may be inherently multi-dimensional. We begin by developing a rigorous definition of irreducible multi-dimensional features based on whether they can be decomposed into either independent or non-co-occurring lower-dimensional features. Motivated by these definitions, we design a scalable method that uses sparse autoencoders to automatically find multi-dimensional features in GPT-2 and Mistral 7B. These auto-discovered features include strikingly interpretable examples, e.g. circular features representing days of the week and months of the year. We identify tasks where these exact circles are used to solve computational problems involving modular arithmetic in days of the week and months of the year. Finally, we provide evidence that these circular features are indeed the fundamental unit of computation in these tasks with intervention experiments on Mistral 7B and Llama 3 8B, and we find further circular representations by breaking down the hidden states for these tasks into interpretable components.

We propose a new representation for encoding 3D shapes as neural fields. The representation is designed to be compatible with the transformer architecture and to benefit both shape reconstruction and shape generation. Existing works on neural fields are grid-based representations with latents defined on a regular grid. In contrast, we define latents on irregular grids, enabling our representation to be sparse and adaptive. In the context of shape reconstruction from point clouds, our shape representation built on irregular grids improves upon grid-based methods in terms of reconstruction accuracy. For shape generation, our representation promotes high-quality shape generation using auto-regressive probabilistic models. We show different applications that improve over the current state of the art. First, we show results for probabilistic shape reconstruction from a single higher resolution image. Second, we train a probabilistic model conditioned on very low resolution images. Third, we apply our model to category-conditioned generation. All probabilistic experiments confirm that we are able to generate detailed and high quality shapes to yield the new state of the art in generative 3D shape modeling.

Adaptive sparse coding methods learn a possibly overcomplete set of basis functions, such that natural image patches can be reconstructed by linearly combining a small subset of these bases. The applicability of these methods to visual object recognition tasks has been limited because of the prohibitive cost of the optimization algorithms required to compute the sparse representation. In this work we propose a simple and efficient algorithm to learn basis functions. After training, this model also provides a fast and smooth approximator to the optimal representation, achieving even better accuracy than exact sparse coding algorithms on visual object recognition tasks.

We test the Platonic Representation Hypothesis (PRH) in astronomy by measuring representational convergence across a range of foundation models trained on different data types. Using spectroscopic and imaging observations from JWST, HSC, Legacy Survey, and DESI, we compare representations from vision transformers, self-supervised models, and astronomy-specific architectures via mutual k-nearest neighbour analysis. We observe consistent scaling: representational alignment generally increases with model capacity across our tested architectures, supporting convergence toward a shared representation of galaxy astrophysics. Our results suggest that astronomical foundation models can use pre-trained general-purpose architectures, allowing us to capitalise on the broader machine learning community's already-spent computational investment.

Does structure in representations imply structure in computation? We study how Llama-3.1-8B reasons over cyclic concepts (e.g., "what month is six months after August?"). Even though Llama-3.1-8B's representations for these concepts are circularly structured, we find that instead of directly computing modular addition in the period of the cyclic concept (e.g., 12 for months), the model re-uses a generic addition mechanism across tasks that operates independently of concept-specific geometry. First, it computes the sum of its two inputs using base-10 addition (six + August=14). Then, it maps this sum back to cyclic concept space (14->February). We show that Llama-3.1-8B uses task-agnostic Fourier features to compute these sums--in fact, these features have periods that respect standard base-10 addition, e.g., 2, 5, and 10, rather than the cyclic concept period (e.g., 12 for months). Furthermore, we identify a sparse set of 28 MLP neurons re-used across all tasks (approximately 0.2% of the MLP at layer 18) that can be partitioned into disjoint clusters, each computing the sum for a Fourier feature with a different period. Our work highlights how an interplay between causal abstraction and feature geometry can deepen our mechanistic understanding of LMs.

We demonstrate that a deep model can be reparametrized as a linear combination of several randomly initialized and frozen deep models in the weight space. During training, we seek local minima that reside within the subspace spanned by these random models (i.e., `basis' networks). Our framework, PRANC, enables significant compaction of a deep model. The model can be reconstructed using a single scalar `seed,' employed to generate the pseudo-random `basis' networks, together with the learned linear mixture coefficients. In practical applications, PRANC addresses the challenge of efficiently storing and communicating deep models, a common bottleneck in several scenarios, including multi-agent learning, continual learners, federated systems, and edge devices, among others. In this study, we employ PRANC to condense image classification models and compress images by compacting their associated implicit neural networks. PRANC outperforms baselines with a large margin on image classification when compressing a deep model almost 100 times. Moreover, we show that PRANC enables memory-efficient inference by generating layer-wise weights on the fly. The source code of PRANC is here: https://github.com/UCDvision/PRANC

The Boundary representation (B-rep) format is the de-facto shape representation in computer-aided design (CAD) to model solid and sheet objects. Recent approaches to generating CAD models have focused on learning sketch-and-extrude modeling sequences that are executed by a solid modeling kernel in postprocess to recover a B-rep. In this paper we present a new approach that enables learning from and synthesizing B-reps without the need for supervision through CAD modeling sequence data. Our method SolidGen, is an autoregressive neural network that models the B-rep directly by predicting the vertices, edges, and faces using Transformer-based and pointer neural networks. Key to achieving this is our Indexed Boundary Representation that references B-rep vertices, edges and faces in a well-defined hierarchy to capture the geometric and topological relations suitable for use with machine learning. SolidGen can be easily conditioned on contexts e.g., class labels, images, and voxels thanks to its probabilistic modeling of the B-rep distribution. We demonstrate qualitatively, quantitatively, and through perceptual evaluation by human subjects that SolidGen can produce high quality, realistic CAD models.

We present a representation-driven framework for reinforcement learning. By representing policies as estimates of their expected values, we leverage techniques from contextual bandits to guide exploration and exploitation. Particularly, embedding a policy network into a linear feature space allows us to reframe the exploration-exploitation problem as a representation-exploitation problem, where good policy representations enable optimal exploration. We demonstrate the effectiveness of this framework through its application to evolutionary and policy gradient-based approaches, leading to significantly improved performance compared to traditional methods. Our framework provides a new perspective on reinforcement learning, highlighting the importance of policy representation in determining optimal exploration-exploitation strategies.

Hyperdimensional computing (HDC) is a biologically-inspired framework which represents symbols with high-dimensional vectors, and uses vector operations to manipulate them. The ensemble of a particular vector space and a prescribed set of vector operations (including one addition-like for "bundling" and one outer-product-like for "binding") form a *vector symbolic architecture* (VSA). While VSAs have been employed in numerous applications and have been studied empirically, many theoretical questions about VSAs remain open. We analyze the *representation capacities* of four common VSAs: MAP-I, MAP-B, and two VSAs based on sparse binary vectors. "Representation capacity' here refers to bounds on the dimensions of the VSA vectors required to perform certain symbolic tasks, such as testing for set membership i in S and estimating set intersection sizes |X cap Y| for two sets of symbols X and Y, to a given degree of accuracy. We also analyze the ability of a novel variant of a Hopfield network (a simple model of associative memory) to perform some of the same tasks that are typically asked of VSAs. In addition to providing new bounds on VSA capacities, our analyses establish and leverage connections between VSAs, "sketching" (dimensionality reduction) algorithms, and Bloom filters.

Skills are a natural unit for describing what a language model can do and how its behavior can be changed. However, existing characterizations rely on human-written taxonomies, textual descriptions, or manual profiling pipelines--all external hypotheses about what matters that need not align with the model's internal representations. We argue that when the goal is to intervene on model behavior, skill characterization should be *model-native*: grounded in the model's own representations rather than imposed through external ontologies. We instantiate this view by recovering a compact orthogonal basis from sequence-level activations. The resulting basis is semantically interpretable but need not correspond to any predefined human ontology; instead, it captures axes of behavioral variation that the model itself organizes around. We validate this characterization on reasoning post-training, using the recovered basis for both SFT data selection and inference-time steering. We develop lightweight proxy interventions to identify which directions are most useful for a given model. Across Llama3-8B and Qwen2.5-3B, selecting data along those directions improves Pass@1 by up to 20% on MATH and 41% on AMC, outperforming data selection based on human-characterized skills. Because the basis lives in activation space, the same directions also serve as steering vectors at inference time, improving Pass@8 by up to 4.8% on MATH--an intervention that human-characterized skills cannot support. We further validate the characterization on safety alignment, where selecting adversarial training data for model-native skill coverage rather than textual diversity yields more sample-efficient learning. These results suggest that recovering skills from the model's own representations, rather than imposing them externally, provides a more effective foundation for intervening on model behavior. Codes are open-sourced.

Vectors are universal mathematical objects that can represent text, images, speech, or a mix of these data modalities. That happens regardless of whether data is represented by hand-crafted features or learnt embeddings. Collect a large enough quantity of such vectors and the question of retrieval becomes urgently relevant: Finding vectors that are more similar to a query vector. This monograph is concerned with the question above and covers fundamental concepts along with advanced data structures and algorithms for vector retrieval. In doing so, it recaps this fascinating topic and lowers barriers of entry into this rich area of research.

Recent developments in representational learning for information retrieval can be organized in a conceptual framework that establishes two pairs of contrasts: sparse vs. dense representations and unsupervised vs. learned representations. Sparse learned representations can further be decomposed into expansion and term weighting components. This framework allows us to understand the relationship between recently proposed techniques such as DPR, ANCE, DeepCT, DeepImpact, and COIL, and furthermore, gaps revealed by our analysis point to "low hanging fruit" in terms of techniques that have yet to be explored. We present a novel technique dubbed "uniCOIL", a simple extension of COIL that achieves to our knowledge the current state-of-the-art in sparse retrieval on the popular MS MARCO passage ranking dataset. Our implementation using the Anserini IR toolkit is built on the Lucene search library and thus fully compatible with standard inverted indexes.

Representational analysis explores how input data of a neural system are encoded in high dimensional spaces of its distributed neural activations, and how we can compare different systems, for instance, artificial neural networks and brains, on those grounds. While existing methods offer important insights, they typically do not account for local intrinsic geometrical properties within the high-dimensional representation spaces. To go beyond these limitations, we explore Ollivier-Ricci curvature and Ricci flow as tools to study the alignment of representations between humans and artificial neural systems on a geometric level. As a proof-of-principle study, we compared the representations of face stimuli between VGG-Face, a human-aligned version of VGG-Face, and corresponding human similarity judgments from a large online study. Using this discrete geometric framework, we were able to identify local structural similarities and differences by examining the distributions of node and edge curvature and higher-level properties by detecting and comparing community structure in the representational graphs.

Although disentangled representations are often said to be beneficial for downstream tasks, current empirical and theoretical understanding is limited. In this work, we provide evidence that disentangled representations coupled with sparse base-predictors improve generalization. In the context of multi-task learning, we prove a new identifiability result that provides conditions under which maximally sparse base-predictors yield disentangled representations. Motivated by this theoretical result, we propose a practical approach to learn disentangled representations based on a sparsity-promoting bi-level optimization problem. Finally, we explore a meta-learning version of this algorithm based on group Lasso multiclass SVM base-predictors, for which we derive a tractable dual formulation. It obtains competitive results on standard few-shot classification benchmarks, while each task is using only a fraction of the learned representations.