This paper proposes Temporally Decomposable Image Representations (TDIR), a representation learning algorithm that decomposes historical photographs into separate date and content components through orthogonal subspaces, and defines and proves the conditions under which such a decomposition is achievable.
Abstract
While time evolves linearly, the geometry of neural embedding spaces is inherently multi-dimensional, often chaotic, and difficult to interpret. In principle, one could constrain an embedding space to a single temporal dimension; however, such a reduction would sacrifice performance on downstream tasks, as one-dimensional embeddings cannot retain sufficient expressive capacity. This paper asks whether it is possible to learn representations that preserve temporal structure while remaining effective for image and object retrieval, and answers this question by building the mathematical foundations of such a system. We propose Temporally Decomposable Image Representations (TDIR), a representation learning algorithm that decomposes historical photographs into separate date and content components through orthogonal subspaces. We define and prove the conditions under which such a decomposition is achievable, characterize the error incurred when those conditions are only partially met, and show that orthogonality between temporal and categorical subspaces emerges naturally from the joint optimization, without requiring it to be imposed explicitly. Beyond its geometric properties, TDIR enables a class of transitive operations on embedding spaces: the temporal information of one image can be extracted and injected into the representation of another, with no label supervision required. All theoretical properties are grounded and validated in the real-world problem of Composed Image Retrieval on historical photographs, where a query simultaneously specifies object content and a target time period, either through labels or through example images. This in-the-wild setting serves as a concrete backing for the propositions we derive, offering an intuitive and interpretable way to navigate photographic archives while maintaining competitive performance in both date estimation and object retrieval.
Scalable Vector Graphics are a fundamental medium for resolution-independent visual content, yet the deep learning community lacks a continuous, dense, and invertible latent space for vector representations, the kind of foundational building block that Variational Autoencoders and their descendants have long provided for raster images. We introduce SLS (SVG Latent Space), a Transformer-based autoencoder that learns compact dense representations of individual SVG paths, the atomic visual elements from which any SVG image can be composed. By modeling SVG commands, coordinate data, and visual properties within a unified BPE-based token vocabulary, SLS learns fixed-size latent representations that jointly capture structure and appearance, and can be decoded back into valid, style-consistent SVG paths with high fidelity. The resulting embedding space is robust, invertible, and structured: embeddings lie on a unit hypersphere, enabling efficient similarity search, composition, and downstream conditioning through simple vector-space operations. Finally, we demonstrate that SLS generalizes across diverse tasks reducing their FLOPs by over 150 times compared to token-based approaches, and establishing a general-purpose latent foundation for vector graphics research.
Leonardo Zini, Elia Frigieri, L. Baraldi· 0 citations
Multimodal embedding spaces in models like CLIP enable powerful capabilities such as semantic similarity retrieval and cross-modal zero-shot classification. These embeddings compress high-level semantics into a single vector, which comes at the cost of primarily expressing a dominant semantics like main object while suppressing other important attributes such as camera angle or color tone. We propose a text-conditioned transformation of visual embeddings that makes such attributes explicitly accessible. Given a natural language description of an attribute category (e.g.,"color"or"art style"), a network generates an affine transformation that emphasizes the specified attribute. Conditioning on text enables it to learn many attributes simultaneously, accessing them at inference time through an intuitive interface. The network is trained to align transformed embeddings with the frozen latent space, enabling retrieval using existing large-scale embeddings without any re-encoding. When applied to a full set, the same mechanism transforms the latent space for attribute disentanglement tasks such as multi-clustering. By operating directly in latent space, our method provides a unified and efficient framework for controlling embedding spaces, demonstrating state-of-the-art performance across both attribute-based retrieval and multi-attribute organization tasks with near-zero inference cost. Project page: https://joefioresi718.github.io/ControlEmbed_webpage/
Joseph Fioresi, Fabian Caba Heilbron, Pankaj Nathani et al.· 0 citations
The target representation defines the distribution an image generator must learn, yet it is often treated as an interchangeable interface. This assumption is particularly questionable for continuous masked generators, which combine contextual inference from visible tokens with conditional modeling of each missing token. We study raw pixels, SD-VAE latents and DINOv2 as well as MAE representation-autoencoder features within a unified masked autoregressive rectified-flow model. Under a shared ImageNet training budget, these spaces exhibit distinct optimization and inference regimes. DINOv2 converges fastest in both iterations and computation but benefits strongly from a wider local denoiser and direct context fusion. Pixels optimize substantially more slowly and require a different prediction, masking, and guidance configuration. MAE reconstructs images more faithfully and exhibits clear semantic clustering, yet produces generations substantially worse than DINOv2. The representations also respond differently to classifier-free guidance and occupy distinct precision-recall trade-offs. Together, our results show that compression, reconstruction fidelity, token dimensionality, and visible semantic clustering do not individually predict generative behavior. Instead, target representations redistribute difficulty across contextual modeling, per-token denoising, and inference-time distributional control.
Marcel Plocher, Bernhard Schölkopf, Andreas Geiger et al.· 0 citations
Contrastive Language-Image Pretraining (CLIP) representations form a semantic embedding space governed by cosine similarity, reflecting an intrinsic hyperspherical geometry. However, existing probabilistic interpretations typically rely on Gaussian assumptions, which fail to capture this directional and multimodal structure. We propose a principled density model for the CLIP latent space based on Mixtures of von Mises-Fisher (MovMF) distributions defined on the unit hypersphere. Using the Expectation-Maximization (EM) algorithm, we efficiently learn a probabilistic model in which each mixture component corresponds to a coherent semantic concept. This formulation yields a closed-form likelihood naturally aligned with hyperspherical geometry, enabling accurate and interpretable density estimation. Empirically, our model significantly improves long-tailed and out-of-distribution detection and provides a natural semantic decomposition, representing each embedding as a sparse probabilistic combination of interpretable concepts. These results suggest that CLIP latent space is more faithfully characterized as a hyperspherical semantic mixture rather than an isotropic Gaussian, establishing a simple and geometrically consistent probabilistic framework for modeling and understanding multimodal representations. Project page is available at https://xiaoyuzhizi.github.io/movmf-clip/.
Zijie Yu, Gaowen Liu, R. Kompella et al.· 0 citations
Recent works have highlighted the expressive limitations of embedding based retrieval models through both theoretical analyses and challenging benchmarks such as LIMIT. While multi-vector embeddings consistently outperform single-vector embeddings, the precise representational gap between them remains poorly understood. In this work, following Jayaram's work, we provide the first explicit family of query and document sets, together with their relevance matrices, for which single-vector embeddings that rank all relevant documents above irrelevant ones require exponential size, whereas polynomial-size multi-vector embeddings suffice. Our result establishes an exponential separation between the expressive power of single-vector and multi-vector embeddings for the task of ranking of documents as opposed to approximating numerical scores as in the work of Jayaram. Motivated by our theoretical construction, we introduce ANDOR, a new retrieval benchmark that naturally instantiates these hard examples. We show that state-of-the-art single-vector embedding models perform poorly on ANDOR in the zero-shot setting and exhibit only marginal improvements after fine-tuning, highlighting the inherent difficulty of the benchmark compared to prior work. In contrast, multi-vector models consistently outperform their single-vector counterparts and improve substantially with fine-tuning, closely aligning with our theoretical predictions.
Mihir Agarwal, Viraj Agrawal, Sabyasachi Basu et al.· 0 citations
DESS is introduced, a lightweight uncertainty layer that augments an existing embedding model with a predicted mean vector and an independent per-dimension spread vector that provides a modular, geometry-aware uncertainty layer for embedding-space models, provided its spread is calibrated to local embedding geometry.
Morten Grundetjern, J. Voigt, Per-Arne Andersen et al.· KI - Künstliche Intelligenz· 0 citations
Known for his clear and elegant writing style, Bertsekas shaped fields from control and optimization to large-scale computation and artificial intelligence.
