Latent Space Alignment

Unsupervised representational alignment recovers a stimulus-by-stimulus correspondence from geometry alone, but the automorphism group of the stimulus geometry bounds what any such alignment can identify, before data exist. The obvious diagnostic for this degeneracy, the cheapest non-identity relabelling, ranks two published designs in the wrong order, because dense sampling creates near-duplicates whose transposition is nearly free. We turn this known invariance (Demetci et al., 2024) into a design-time diagnostic and intervention. In colour, where candidate geometries have closed form, we show that the failure is structural: sixty-four times the restart budget leaves a symmetric design unmoved while an asymmetric set at the same N recovers every time. Discriminating representational models and recovering a correspondence are essentially uncorrelated objectives (r = -0.02 over 3,000 subsets). Choosing nine colours by this diagnostic alone, without consulting any learned representation, moves all 93 model representations away from the degenerate point and cuts catastrophic alignment failures from 75% to 2% with the models, the layers, N and the solver all held fixed. The same risk arises wherever a regular design meets its candidate geometry's isometry group, including evenly spaced orientations, tones, or motion directions, and the check costs one function call before data collection.

Human Activity Recognition (HAR) using inertial measurement units (IMUs) enables a wide range of applications, yet the field still lacks a unified model that can generalize across diverse subjects, devices, and activities. Training such a model is difficult due to two key challenges: sensing heterogeneity -- differences in sampling rates, channel configurations, and sensor placements -- and poor generalization to unseen activities and label vocabularies. We introduce HALO (Heterogeneity-Aware Language-aligned Open-set model), a domain-specific IMU foundation model that addresses both challenges through a two-stage training framework. Stage 1 pretrains the IMU encoder with heterogeneity-aware self-supervised learning, including adaptive-pooling tokenization, channel-independent feature extraction, and contextualized sensor conditioning that injects natural-language sensor descriptions into each channel embedding. Stage 2 aligns this IMU encoder with text embeddings via synonym-aware soft contrastive learning, enabling open-set recognition via cosine-similarity retrieval without per-dataset classifiers. Trained on 10 public HAR datasets and evaluated on 7 held-out datasets, HALO outperforms five state-of-the-art baselines on all 8 aggregate metrics, and still leads on 3 of 4 settings under baseline-matched inputs. Despite using only ~35M trainable parameters -- 10x fewer than the latest foundation model MOMENT (341.2M) -- HALO improves zero-shot open-set accuracy, measured over all 87 training labels, by 13.7 percentage points. On two further datasets with severe distribution shift, every model including HALO collapses zero-shot. A video demonstration of HALO's performance in real world is available at https://youtu.be/rooVKragtFU

Accurate visual decoding can reveal how the brain represents visual information and recover perceived content from neural signals such as electroencephalography (EEG), with potential for neural communication. However, current EEG-to-image retrieval methods perform far below their within-subject counterparts for new users without labeled calibration, limiting real-world deployment. To understand this gap, we analyze EEG features across subjects and find that different subjects preserve similar relationships among concepts but express them along different coordinate directions. We therefore propose Subject Coordinate Recovery (SCORE), a target label-free framework combining recovery-aware source training with coordinate alignment at deployment. During training, SCORE aligns source subject EEG with a common image space and simulates unseen-subject recovery through source-only episodes. At deployment, with both encoders frozen, SCORE selects reliable EEG-image landmarks through hubness-corrected matching and estimates an orthogonal transformation to recover target EEG coordinates without source data or target labels. In 200-way retrieval on two public benchmarks, SCORE outperforms the unadapted baseline for every target subject and achieves the best overall accuracy. It reaches 53.23%/83.55% and 12.01%/32.16% Top-1/Top-5 on THINGS-EEG2 and Alljoined-1.6M, respectively, surpassing the strongest baselines by 17.45/15.70 and 3.08/4.62 percentage points. Without target labels or encoder updates, SCORE brings brain-based visual decoding closer to robust, practical, low-latency deployment across users.

With the rapid advancement of large language models, brain-language decoding has achieved remarkable progress. However, it remains unclear whether decoded content genuinely reflects neural representations or is largely reconstructed by the language model itself. This ambiguity limits interpretability and hinders the investigation of intrinsic brain-language correspondence. To address this challenge, we propose MD-SigLIP. This margin-regularized structured semantic alignment framework directly aligns brain embeddings with text embeddings in a shared semantic space, enabling retrieval-based decoding. This formulation enables explicit modeling of the correspondence between neural representations and language semantics. Building upon duplicate-aware sigmoid contrastive learning, we introduce a listwise margin-regularized term that enforces structured ranking constraints between positive semantic clusters and negative samples. By modeling multi-positive semantic structure and margin-based ordering simultaneously, the method captures the manifold organization of language embeddings reflected in neural signals. Experiments demonstrate state-of-the-art retrieval performance under both full-vocabulary and subset evaluation settings.

Disentangled representation learning seeks latent representations whose indicidual dimensions each align with a distinct covariate. Unsupervised approaches typically target latent dimension independence, yet this gives no guarantee that the resulting dimensions align with semantically meaningful covariates. Supervised approaches structure the latent space using observed covariates, but under correlated covariates they cannot simultaneously control one-to-one latent-covariate alignment and latent independence. We introduce a unified, supervised framework that couples latent dimension-covariate dependence with constraints on the latent structure. Within this framework, we show an inherent trade-off, where enforcing latent independence or exclusive one-to-one latent-covariate dependence comes at a provable cost in latent-covariate alignment. We prove that the resulting disentanglement regimes are ordered by the strength of that alignment. Each regime admits a closed-form transformation of the latent space. We apply these transformations post-hoc to realign the representations of pretrained models such as CLIP, DINOv2, and ViT, and we fold them into the inference of informed factor analysis (iFA), a probabilistic model with covariate-informed factors. On simulated and real multi-omics data, we show that both post-hoc alignment and iFA enable controllability of structured latent representations.

Robot sensor designs, particularly tactile sensors, are highly diverse and evolve rapidly. Modeling each sensor in simulation demands substantial domain expertise and computational approximations can degrade the fidelity of the simulated signals. We propose Sim2Real via Bottlenecked Latent Reconstruction (SBLR), a framework that avoids sensor-specific simulation entirely by (1) training policies on a simulator-native oracle sensor that is easy to construct without modeling any particular sensor (e.g. we use a point-cloud and finger-tip forces as a tactile oracle), and (2) aligning real sensor latent embeddings to those of the oracle sensor at inference time. Policy training proceeds in two-stage: the policy first learns from the oracle sensor latents, then a bottlenecked latent reconstruction adapts it to the information loss expected when using the real sensor instead of the oracle. The alignment between oracle and real sensor is learned from unpaired random-play data collected in both simulation and the real world, using rectified-flow-based transformation networks trained on nearest-neighbor pseudo-pairs. Simulation experiments on three contact-rich tasks show that SBLR matches or approaches the performance of an oracle with direct access to tactile simulation. Hardware experiments on Peg Insertion and Gear Meshing with GelSight Mini and DIGIT sensors demonstrate 85-97.5% zero-shot success without requiring any sensor-specific modeling or calibration, outperforming a physics-based tactile simulation baseline by 7.5-15%.

We investigate whether simple transformations can translate representations across heterogeneous text embedding models. Understanding how independently trained models organize semantic information is an enabler for AI-to-AI latent communication without decoding into human-readable text. Focusing on lightweight translators such as linear mappings, we test the literature hypothesis of latent universality in a realistic text setting beyond simplified benchmarks. Across nine embedding models differing in architecture, pooling strategy, and training objective, we evaluate compatibility using CKA, downstream transfer, fidelity, and retrieval. Simple translators recover meaningful shared structure and support transfer for some compatible pairs, but fail sharply for others. Compatibility depends jointly on architecture, training objective, pooling, and data distribution. Overall, the results show that heterogeneous embedding spaces are not universally related by simple mappings as often suggested in some literature.

Modern one-step diffusion models achieve impressive quality through distribution-based timestep distillation. Yet, they rely on a critical assumption: Teacher and Student must inhabit the same latent space. This Shared-Space constraint prevents knowledge transfer from modern high-capacity Teachers (e.g., SD 3.5 and Flux) into compact, deployment-friendly Students such as SD 1.5, whose latent resolution and VAE parameterization differ from the Teacher. We formalize this overlooked regime as Cross-Space Distillation, where Teacher and Student differ in both latent resolution and VAE space. To enable distillation under this mismatch, we introduce the Bridge, a lightweight latent interface that maps Student latents into the Teacher space without modifying the Student backbone. Bridge combines a frozen Student VAE decoder as a spatial prior with a compact learnable projector, and is trained with latent reconstruction and attention fidelity objectives for stable Teacher-space alignment. Across diverse modern Teachers, Bridge enables substantial gains for compact one-step Students; for example, it improves SD 1.5 from 5.4 to 9.4 HPSv3 while preserving one-step inference, low latency, and broad ecosystem compatibility. These results show that heterogeneous large Teachers can be distilled into efficient, deployable backbones through a lightweight latent-space interface.

Generative models, particularly diffusion and score-based approaches, have recently achieved strong performance in speech enhancement, but their iterative sampling process limits real-time deployment. Flow Matching offers an efficient alternative by transporting noisy speech toward clean speech through an ordinary differential equation with few function evaluations. In this work, we propose a skip-free encoder-decoder backbone for flow-matching speech enhancement, guided by Latent Representation Alignment (LRA). Instead of relying on U-Net skip connections, which may transfer noise-correlated low-level features to the decoder, the proposed model aligns its bottleneck and decoder representations with clean latent features extracted from a frozen Descript Audio Codec encoder-decoder without quantization. This codec-aligned supervision promotes compact clean-speech representations while preserving efficient few-step inference. Experiments on WSJ0-CHiME3 and VoiceBank-DEMAND show improved PESQ and perceptual quality, especially on VoiceBank-DEMAND, using only five function evaluations.

Federated low-rank adaptation methods are attractive for fine-tuning large models under communication and privacy constraints, but heterogeneous client data can induce geometric misalignment between local low-rank updates. We study whether this subspace misalignment leads to destructive aggregation and slower convergence in LoRA-based federated learning. We propose a subspace-regularized federated LoRA objective that encourages local client updates to remain close to a shared global reference subspace. We present a complete empirical evaluation on two pretrained models, RoBERTa-large and SmolLM-360M, over HellaSwag in a non-IID 10-client federated setting, across 3 random seeds (42, 43, 44), yielding 24 total experimental runs (4 methods x 3 seeds x 2 models). On RoBERTa-large, Subspace-Reg achieves the strongest mean best accuracy (0.454 +/- 0.023), mean final accuracy (0.429 +/- 0.011), and lowest final loss (1.363) across all three seeds, outperforming FedAvg, SVD redistribution, and FedSVD baselines by a large margin. On SmolLM-360M, FedAvg leads on accuracy, revealing that accuracy gains are model-dependent. Crucially, Subspace-Reg achieves near-perfect basis overlap, approximately 0.9999, on both models and across all seeds, versus 0.958 to 0.991 for all baselines, providing robust support for the geometric alignment hypothesis. The code is publicly available at https://github.com/sadia-sigma-lab/Subspace-Constrained-Federated-learning-with-Lora.

Model merging has emerged as a training-free alternative to multi-task learning, aiming to combine multiple task-specific fine-tuned models into a single multi-task model. Most existing model merging approaches follow the Task Arithmetic paradigm, which decomposes fine-tuned weights into pre-trained parameters and task vectors, and performs merging exclusively in the task-vector space. The effectiveness of this paradigm implicitly relies on the assumption that task-specific knowledge is encoded solely within task vectors. We argue that this assumption generally does not hold due to the intrinsic task preferences of pre-trained models. Specifically, we identify Load-Bearing Wall (LBW) dimensions, namely some task-critical knowledge that remains embedded in the pre-trained weights rather than being fully transferred into task vectors. We characterize LBW dimensions from both scalar-weight and subspace perspectives, thereby covering the major paradigms of existing model merging methods. Our analysis reveals that, by ignoring LBW dimensions, task-vector-based approaches fail to fully resolve task conflicts and may inadvertently damage task-specific knowledge encoded in the pre-trained model, leading to degradation. To address this issue, we propose PACT, which preserves the anchored task-specific cores (i.e., LBW dimensions) within task vectors by aligning their orthogonal complements with the subspace of the pre-trained weights. These aligned subspace components are then removed from the task vectors before applying existing model merging algorithms. Furthermore, we develop an efficient variant based on randomized SVD to improve scalability. PACT can be seamlessly integrated with existing methods. Extensive experiments across multiple benchmarks demonstrate that PACT consistently enhances mainstream model merging approaches and establishes new state-of-the-art performance.

Cross-subject EEG decoding promises more training data, but it also exposes neural networks to strong inter-subject distribution shifts. We study whether task supervision and architecture alone can learn subject-aligned representations. We replace a shared EEG encoder with subject-specific encoders followed by a common classifier, and compare this hybrid model with standard EEGNet, AttentionBaseNet, and CTNet baselines with Euclidean Alignment (EA) on three motor-imagery datasets and one motor-execution dataset. EA improves shared encoders by recentering subject covariances, whereas the hybrid encoder reduces reliance on EA: removing EA has little effect on validation-loss dynamics or latent-space organization, and both hybrid variants consistently outperform non-aligned shared baselines. Subject-specific heads increase class distinctiveness and place each subject close to its own latent manifold while improving within-subject class separation. However, on cross-subject classification, subject-specific heads hinder direct parameter transfer to unseen subjects, motivating quantitative head selection and a brief calibration session. Although decoding gains depend on the dataset and backbone, our main findings concern that the sole use of architecture pressure promotes representation learning and alignment in a direction complementary to domain adaptation methods such as Euclidean Alignment. A per-subject low-rank adapter of only 2Cr parameters recover the full encoder's accuracy across five backbones and ranks $r=1$ to 16, so the per-subject module can be compressed by two to three orders of magnitude.

Aligning neural activity across subjects offers the promise of discovering shared computational principles and generalizable decoders. However, traditional alignment methods require shared stimuli across subjects, a constraint that limits applicability to naturalistic paradigms with limited or non-overlapping data. We introduce a Multi-Encoder-Decoder Variational Autoencoder (MED-VAE) that achieves cross-subject alignment without shared stimuli by anchoring representations to a common scaffold provided by a pretrained ANN. Using the Natural Scenes Dataset, we show that MED-VAE creates common latent spaces with superior semantic organisation, achieving higher cross-subject alignment than common methods while maintaining robust generalisation to held-out stimuli where traditional methods degrade. Reconstructing from these common spaces back to each subject's original neural space, MED-VAE preserves equal stimulus-driven signal in its cross-subject latent space. Finally, we show that this superior alignment directly enables cross-subject neural prediction, as demonstrated via cross-subject image decoding. In summary, we introduce a framework to identify generalisable common subspaces for cross-subject predictions and downstream tasks, demonstrated here for visual cortex responses to static images.

Latent visual reasoning (LVR) inserts supervised latent tokens between perception and answer generation in vision-language models (VLMs). The field uses alignment between these latents and their visual targets, i.e., cosine similarity or mean squared error (MSE), as both the training loss and the quality metric, assuming that better alignment yields a better answer. We test this with a designed matrix of five LVR variants and find the assumption inverted: cosine alignment is negatively correlated with accuracy across all five (r=-0.94). To explain this, we introduce PRISM, a pair of inference-time diagnostics: a linear probe that asks where the answer is decodable, and a corruption test that asks whether the latent is load-bearing. The supervised latents are largely bypassed. Corrupting them shifts accuracy by at most four points. The answer is decodable downstream of the latent but not at it, and the size of this decodability gap predicts how much each variant relies on its latent under perturbation. Consistent with an Information Bottleneck reading of the loss, the auxiliary objective reshapes the language model via shared parameters rather than via the latent variable it nominally optimizes.

Neural networks are known to develop latent representations that are $aligned$, namely structurally similar across networks trained with different architectures, training protocols, or training datasets. We study this phenomenon in a controlled setting, where we train an ensemble of networks on regression and classification tasks using training sets perturbed by independent realizations of a noise process. We show that the signal-to-noise ratio (SNR) and the training sample size influence the alignment in qualitatively similar ways in networks trained on real-world datasets and in an extremely simple $linear$ network with a single hidden layer, for which the alignment can be estimated analytically. Across linear and nonlinear networks, regression and classification tasks, and both synthetic and real-world data, we consistently observe that alignment varies monotonically with SNR but non-monotonically with training sample size. In particular, the alignment is minimized near the interpolation threshold, and a stronger alignment does not necessarily correspond to better generalization error. These findings reveal a non-trivial dependence of alignment on data quality and quantity, decoupled from generalization performance.

Independently trained transformers compute the same function in residual-stream bases that differ by a uniform random rotation on $\mathrm{SO}(d_{\mathrm{model}})$. We call this phenomenon polymorphism: same function, mutually unintelligible interior coordinates. One matrix multiplication per model pair removes it: an orthogonal Procrustes fit on a single batch of activations transfers sparse-autoencoder feature dictionaries and steering vectors between independently trained models, with no retraining. The phenomenon is invisible to the standard SAE universality metric. Decoder-column cosine similarity matches across seeds at 98%, the SAE-universality headline number, while an SAE trained on one seed reconstructs another seed's activations at negative explained variance, worse than predicting the constant mean. The decoder columns align; the encoder reads from a rotated frame. A single Procrustes rotation $R$ restores reconstruction to within 0.025 EV of the within-seed ceiling at every internal site. $R$ is Haar-distributed: $\|R - I\|_F$ matches the random-orthogonal prediction $\sqrt{2 d_{\mathrm{model}}}$ to 0.1% at $d_{\mathrm{model}} = 512$, and a Kolmogorov-Smirnov test of $R$'s eigenvalue spectrum against Haar $\mathrm{SO}(d_{\mathrm{model}})$ returns $p \approx 1.000$ pooled and per-pair. Diff-of-means steering vectors transfer in three regimes by alignment with $R$'s invariant subspace: clean when pinned by shared output weights, partial when overlapping the rotated subspace, inverted otherwise. With no shared I/O (Pythia), all three collapse to universally inverted. The same rotation account holds across training checkpoints within a single run. Validated on a 104k-parameter Dyck-3 transformer and nine independently-trained Pythia-70m seeds on The Pile, via a pre-registered four-bar operational framework. Frontier-scale (10B+) replication remains open.

Unified multimodal models (UMMs) achieve strong performance in both understanding and generation by learning a shared latent space, yet they often exhibit functional inconsistency between these two capabilities. We observe that this issue does not stem from a lack of shared representations, but from the absence of explicit alignment between the transformations that map into and out of the latent space. As a result, generation and re-encoding can follow inconsistent trajectories, leading to semantic drift under modality transitions. In this work, we propose LatentUMM, a framework that constructs an enhanced shared latent space to explicitly align these transformations and improve cross-modal consistency. LatentUMM consists of two stages. First, dual latent alignment enforces consistency at both the modality and capacity levels: cross-modal alignment uses a stronger embedding model to impose structured cross-modal semantics, while dual capacity alignment enforces bidirectional consistency under generation and re-encoding. Second, latent dynamics stabilization improves robustness via stochastic latent rollouts and preference optimization, favoring trajectories that better preserve semantic consistency. Experiments show that LatentUMM consistently improves multimodal consistency across diverse architectures. Code is available at: https://github.com/AIFrontierLab/TorchUMM/tree/main/src/umm/post_training/LatentUMM.

Latent representations learned by neural networks often exhibit semantic structure, where concept similarity is reflected by geometric proximity in embedding space. However, comparing such spaces across models remains difficult: changes in architecture, pretraining data, objective, or random seed can yield embeddings with similar content but incompatible geometry. This latent space alignment problem is central to interpretability, transfer and multimodal learning, federated systems, and semantic communication; however, progress remains limited by the lack of large-scale, model-diverse, and metadata-rich benchmarks. To address this gap, we introduce SEMASIA, a large-scale collection of latent representations extracted from approximately 1,700 pretrained vision models across eight standard image-classification benchmarks. SEMASIA pairs embeddings with structured metadata describing architectures, training regimes, pretraining sources, and model scale. We demonstrate three applications of the resource. First, we analyze the conceptual organization of individual latent spaces, showing consistent prototype-like clustering and hierarchical semantic neighborhoods across models and datasets. Second, we benchmark supervised alignment mappings between latent spaces using reconstruction error and downstream task performance. Third, we perform a large-scale regression analysis of how pretraining-data complexity, specialization, transfer learning, augmentation, and model scale relate to geometric and probing properties of embeddings. By coupling representational scale with standardized metadata, SEMASIA provides a reproducible foundation for studying latent geometry, evaluating alignment methods, and developing next-generation heterogeneous and interoperable AI systems.

Recent progress in visual brain decoding from fMRI has been enabled by large-scale datasets such as the Natural Scenes Dataset (NSD) and powerful diffusion-based generative models. While current pipelines are primarily optimized for perception, their performance under mental-imagery remains less well understood. In this work, we study how a state-of-the-art (SOTA) perception decoder (DynaDiff) can be adapted to reconstruct imagined content from the NSD-Imagery benchmark. We propose a latent functional alignment (LFA) approach that maps imagery-evoked activity to the pretrained model's semantic content-enriched conditioning space, by adding a simple alignment module, while keeping the original remaining components frozen. To mitigate the limited amount of matched imagery-perception supervision, we further introduce a neural retrieval-based augmentation strategy that selects semantically related NSD perception trials from the same participants. Across four subjects, LFA consistently improves high-level semantic reconstruction metrics relative to the frozen pretrained baseline and a voxel-space ridge alignment baseline, and enables above-chance decoding from multiple cortical regions. These results suggest that semantic structure learned from perception can be leveraged to stabilize and improve visual imagery decoding under out-of-distribution conditions.

Automated face recognition has made rapid strides over the past decade due to the unprecedented rise of deep neural network (DNN) models that can be trained for domain-specific tasks. At the same time, large foundation models that are pretrained on broad vision or vision-language tasks have shown impressive generalization across diverse domains, including biometrics. This raises an important question: Do different DNN models---both domain-specific and foundation models---encode facial identity in similar ways, despite being trained on different datasets, loss functions, and architectures? In this regard, we directly analyze the geometric structure of embedding spaces imputed by different DNN models. Treating embeddings of face images as point clouds, we study whether simple affine transformations can align face representations of one model with another. Our findings reveal substantial cross-model compatibility: low-capacity linear mappings substantially improve cross-model face recognition over unaligned baselines for both identification and verification, including across foundation models never trained for face recognition. Alignment patterns generalize across datasets and vary systematically across model families, indicating representational convergence in facial identity encoding. These findings reframe independently trained templates as transferable rather than revocable, with implications for interoperability, ensemble design, and biometric template security.

Sequential Recommendation (SR) learns user preferences from their historical interaction sequences and provides personalized suggestions. In real-world scenarios, most items exhibit sparse interactions, known as the tail-item problem. This issue limits the model's ability to accurately capture item transition patterns. To tackle this, large language models (LLMs) offer a promising solution by capturing semantic relationships between items. Despite previous efforts to leverage LLM-derived embeddings for enriching tail items, they still face the following limitations: 1) They struggle to effectively fuse collaborative signals with semantic knowledge, leading to suboptimal item embedding quality. 2) Existing methods overlook the structural inconsistency between the ID and LLM embedding spaces, causing conflicting signals that degrade recommendation accuracy. In this work, we propose a Fusion and Alignment Enhancement framework with LLMs for Tail-item Sequential Recommendation (FAERec), which improves item representations by generating coherently-fused and structurally consistent embeddings. For the information fusion challenge, we design an adaptive gating mechanism that dynamically fuses ID and LLM embeddings. Then, we propose a dual-level alignment approach to mitigate structural inconsistency. The item-level alignment establishes correspondences between ID and LLM embeddings of the same item through contrastive learning, while the feature-level alignment constrains the correlation patterns between corresponding dimensions across the two embedding spaces. Furthermore, the weights of the two alignments are adjusted by a curriculum learning scheduler to avoid premature optimization of the complex feature-level objective. Extensive experiments across three widely used datasets with multiple representative SR backbones demonstrate the effectiveness and generalizability of our framework.

Dense retrieval systems increasingly face an asymmetry between complex instruction-like queries and relatively simple, static document collections. While stronger embedders can better understand such queries, re-embedding large corpora or fine-tuning large models is often impractical. We propose Efficient Retrieval Adapter (ERA), a query-side adapter learning framework for re-index-free retrieval adaptation. ERA first aligns the embedding spaces of a strong query embedder and a lightweight document embedder using unlabeled corpus documents, and then adapts the aligned query representation with a small number of labeled query-document pairs. Across 126 MAIR retrieval tasks from six domains, ERA improves average nDCG@10 by up to 8.2 points in symmetric settings and by more than 12 points in asymmetric settings, while using substantially fewer labels than supervised adapter training. These results show that retrieval systems can benefit from stronger query understanding without updating backbone embedders or rebuilding document indexes.

Adapting large-scale foundation models to new domains with limited supervision remains a fundamental challenge due to latent distribution mismatch, unstable optimization dynamics, and miscalibrated uncertainty propagation. This paper introduces an uncertainty-aware probabilistic latent transport framework that formulates domain adaptation as a stochastic geometric alignment problem in representation space. A Bayesian transport operator is proposed to redistribute latent probability mass along Wasserstein-type geodesic trajectories, while a PAC-Bayesian regularization mechanism constrains posterior model complexity to mitigate catastrophic overfitting. The proposed formulation yields theoretical guarantees on convergence stability, loss landscape smoothness, and sample efficiency under distributional shift. Empirical analyses demonstrate substantial reduction in latent manifold discrepancy, accelerated transport energy decay, and improved covariance calibration compared with deterministic fine-tuning and adversarial domain adaptation baselines. Furthermore, bounded posterior uncertainty evolution indicates enhanced probabilistic reliability during cross-domain transfer. By establishing a principled connection between stochastic optimal transport geometry and statistical generalization theory, the proposed framework provides new insights into robust adaptation of modern foundation architectures operating in heterogeneous environments. These findings suggest that uncertainty-aware probabilistic alignment constitutes a promising paradigm for reliable transfer learning in next-generation deep representation systems.

Generative models and vision encoders have largely advanced on separate tracks, optimized for different goals and grounded in different mathematical principles. Yet, they share a fundamental property: latent space Gaussianity. Generative models map Gaussian noise to images, while encoders map images to semantic embeddings whose coordinates empirically behave as Gaussian. We hypothesize that both are views of a shared latent source, the Universal Normal Embedding (UNE): an approximately Gaussian latent space from which encoder embeddings and DDIM-inverted noise arise as noisy linear projections. To test our hypothesis, we introduce NoiseZoo, a dataset of per-image latents comprising DDIM-inverted diffusion noise and matching encoder representations (CLIP, DINO). On CelebA, linear probes in both spaces yield strong, aligned attribute predictions, indicating that generative noise encodes meaningful semantics along linear directions. These directions further enable faithful, controllable edits (e.g., smile, gender, age) without architectural changes, where simple orthogonalization mitigates spurious entanglements. Taken together, our results provide empirical support for the UNE hypothesis and reveal a shared Gaussian-like latent geometry that concretely links encoding and generation. Code and data are available https://rbetser.github.io/UNE/

Brain encoding and decoding aims to understand the relationship between external stimuli and brain activities, and is a fundamental problem in neuroscience. In this article, we study latent embedding alignment for brain encoding and decoding, with a focus on improving sample efficiency under limited fMRI-stimulus paired data and substantial subject heterogeneity. We propose a lightweight alignment framework equipped with two statistical learning components: inverse semi-supervised learning that leverages abundant unpaired stimulus embeddings through inverse mapping and residual debiasing, and meta transfer learning that borrows strength from pretrained models across subjects via sparse aggregation and residual correction. Both methods operate exclusively at the alignment stage while keeping encoders and decoders frozen, allowing for efficient computation, modular deployment, and rigorous theoretical analysis. We establish finite-sample generalization bounds and safety guarantees, and demonstrate competitive empirical performance on the large-scale fMRI-image reconstruction benchmark data.

Vision-Language Models like CLIP are extensively used for inter-modal tasks which involve both visual and text modalities. However, when the individual modality encoders are applied to inherently intra-modal tasks like image-to-image retrieval, their performance suffers from the intra-modal misalignment. In this paper we study intra-modal misalignment in CLIP with a focus on the role of the projectors that map pre-projection image and text embeddings into the shared embedding space. By analyzing the form of the cosine similarity applied to projected features, and its interaction with the contrastive CLIP loss, we show that there is an inter-modal operator responsible for aligning the two modalities during training, and a second, intra-modal operator that only enforces intra-modal normalization but does nothing to promote intra-modal alignment. Via spectral analysis of the inter-modal operator, we identify an approximately isotropic subspace in which the two modalities are well-aligned, as well as anisotropic directions specific to each modality. We demonstrate that this aligned subspace can be directly obtained from the projector weights and that removing the anisotropic directions improves intra-modal alignment. Our experiments on intra-modal retrieval and classification benchmarks show that our training-free method reduces intra-modal misalignment, greatly lowers latency, and outperforms existing approaches across multiple pre-trained CLIP-like models. The code is publicly available at: https://github.com/simomagi/IsoCLIP.

Independently trained language models often learn compatible late-stage representations, despite differences in training objectives, architectures, and data modalities. We ask how far this compatibility extends: can a simple affine map let one model's hidden states be read directly by another model's output head? In this work, we learn affine transformations between the final hidden states of independent models and evaluate them across embedding classification, out-of-distribution detection, and autoregressive text generation. Across model pairs, we find that downstream performance is largely preserved under alignment, with linearly mapped source representations retaining both the decision boundaries and the confidence structure of a target model's classifier. Additionally, we show for the first time that linear alignment sometimes enables text generation across independently trained models, decoding one model's hidden states through another's frozen output head without fine-tuning. This capability is far from universal, and characterizing when it holds is a contribution of our work. We find that success is governed by two factors: tokenizer overlap, which correlates strongly with generation quality, and source-model scale, below which quality degrades sharply. Transfer is also asymmetric, with strong-to-weak mappings substantially outperforming weak-to-strong ones, indicating that source representational capacity, rather than the target head, is the limiting factor. Finally, we characterize where in the network this compatibility arises. A layer-wise analysis localizes this compatibility to the final one or two layers, indicating a late-stage, output-space phenomenon rather than evidence of shared reasoning.

We study a simple unsupervised regularization scheme for autoencoders called Manifold-Matching (MMAE): we align the pairwise distances in the latent space to those of the input data space by minimizing mean squared error. Because alignment occurs on pairwise distances rather than coordinates, it can also be extended to a lower-dimensional representation of the data, adding flexibility to the method. We find that this regularization outperforms similar methods on metrics based on preservation of nearest-neighbor distances and persistent homology-based measures. We also observe that MMAE provides a scalable approximation of Multi-Dimensional Scaling (MDS).

Variational Autoencoder (VAE) encoders play a critical role in modern generative models, yet their computational cost often motivates the use of knowledge distillation or quantification to obtain compact alternatives. Existing studies typically believe that the model work better on the samples closed to their training data distribution than unseen data distribution. In this work, we report a counter-intuitive phenomenon in VAE encoder distillation: a compact encoder distilled only at low resolutions exhibits poor reconstruction performance at its native resolution, but achieves dramatically improved results when evaluated at higher, unseen input resolutions. Despite never being trained beyond $256^2$ resolution, the distilled encoder generalizes effectively to $512^2$ resolution inputs, partially inheriting the teacher model's resolution preference.We further analyze latent distributions across resolutions and find that higher-resolution inputs produce latent representations more closely aligned with the teacher's manifold. Through extensive experiments on ImageNet-256, we show that simple resolution remapping-upsampling inputs before encoding and downsampling reconstructions for evaluation-leads to substantial gains across PSNR, MSE, SSIM, LPIPS, and rFID metrics. These findings suggest that VAE encoder distillation learns resolution-consistent latent manifolds rather than resolution-specific pixel mappings. This also means that the high training cost on memory, time and high-resolution datasets are not necessary conditions for distilling a VAE with high-resolution image reconstruction capabilities. On low resolution datasets, the distillation model still could learn the detailed knowledge of the teacher model in high-resolution image reconstruction.

Test-time adaptation (TTA) for image regression has received far less attention than its classification counterpart. Methods designed for classification often depend on classification-specific objectives and decision boundaries, making them difficult to transfer directly to continuous regression targets. Recent progress revisits regression TTA through subspace alignment, showing that simple source-guided alignment can be both practical and effective. Building on this line of work, we propose Predictive Spectral Calibration (PSC), a source-free framework that extends subspace alignment to block spectral matching. Instead of relying on a fixed support subspace alone, PSC jointly aligns target features within the source predictive support and calibrates residual spectral slack in the orthogonal complement. PSC remains simple to implement, model-agnostic, and compatible with off-the-shelf pretrained regressors. Experiments on multiple image regression benchmarks show consistent improvements over strong baselines, with particularly clear gains under severe distribution shifts.