Representation Learning

The human brain folds in utero, primarily during late gestation. Shortly after birth, cortical folding patterns are established and remain stable thereafter, making them promising early neurodevelopmental markers. Yet it is unclear whether the representations given by current neuroimaging foundation models capture cortical folding variability. Here, we introduce Champollion, a self-supervised learning framework that learns interpretable local representations of cortical folding from structural MRI. Optimized on representative folding-related tasks, Champollion accurately captures known folding patterns across cortical regions and external datasets. In a comprehensive benchmark, it consistently outperforms neuroimaging and general-purpose foundation models. Furthermore, Champollion reveals richer genetic associations than conventional morphometric descriptors and identifies localized folding signatures associated with incomplete hippocampal inversion, prematurity, and maternal smoking. These results establish cortical folding as a rich and largely untapped source of neurodevelopmental information, and Champollion provides a unified framework for discovering, localizing and interpreting long lasting cortical folding signatures.

Representation is a central concept in modern machine learning, where it usually refers to internal encodings that support learning and generalization. As models scale and their capabilities become increasingly human-level, this representational language sometimes shifts from an engineering context into the more philosophically loaded domain of mental representation. We argue that this is the case for recent claims about the convergence of representational properties across different AI models. In particular, we assess the arguments developed in The Platonic Representation Hypothesis, according to which this convergence is driven by a unified structure of reality. We examine this claim by introducing arguments and ideas from debates about mental representation in the philosophy of mind. We argue that these philosophical resources can clarify what is at stake in such claims, explain why alignment evidence alone is insufficient for strong metaphysical conclusions, and suggest directions for future research.

Conditional generative modeling remains a challenging problem in semi-supervised settings where labeled data is scarce but unlabeled samples are abundant. To effectively leverage structural information embedded within the unlabeled dataset and compensate for sparse conditioning signals, we propose a semi-supervised framework combining conditional stochastic interpolation with low-dimensional latent representations. RepG decomposes generation into two stages: label-dependent latent sampling and high-dimensional reconstruction. This isolates the supervised learning of conditional dependencies to a low-dimensional space, requiring few labels while utilizing the abundant unlabeled data purely for reconstruction. Theoretically, we establish an error decomposition showing that the Kullback-Leibler divergence of RepG comprises stage-wise estimation errors and a structural bias quantified by conditional mutual information. For deep neural network estimators, we derive non-asymptotic convergence rates proving that RepG significantly improves sample complexity. By confining the supervised estimation burden to the low intrinsic dimension of the latent representation, RepG achieves a strictly faster convergence rate. Complemented by a minimax lower bound, our theoretical results demonstrate that this method effectively mitigates the curse of dimensionality inherent in direct ambient-space generative modeling.

End-to-end deep reinforcement learning (DRL) for zero-shot object-goal visual navigation remains challenged by the sim-to-real gap, particularly variations in object appearance and restricted camera field-of-view (FoV). This letter proposes a Temporal Difference-Relational Network (T-DRN) for robust zero-shot sim-to-real transfer. T-DRN combines a Siamese difference-based feature extractor, which computes relational difference between the target and observed objects to produce domain-independent representations, with a dual-frame temporal buffer that preserves short-term object continuity under narrow FoV. Extensive experiments in AI2-THOR demonstrate that T-DRN improves zero-shot generalization in terms of success rates over strong baselines. Furthermore, T-DRN is systematically validated on a physical wheeled robot, demonstrating robust performance under real sensing and actuation constraints and supporting the feasibility of direct sim-to-real transfer.

Rich internal representations of musical structure are essential for music understanding tasks such as machine-assisted music co-writing, yet self-supervised approaches for symbolic music representation remain underexplored, particularly those that encode the hierarchical multiscale nature of musical structures. We present MIDI-RAE-JEPA, combining a pitch- and time-shift equivariance objective with LeJEPA and a Swin Transformer V2 encoder to learn such hierarchical representations of symbolic music encoded as piano roll images. The time-shift equivariance objective encourages the model to internalize temporal musical relationships. The encoder is trained purely on self-supervised objectives -- including a masked embedding predictor (MEP) -- with collapse prevented via SIGReg. A separate decoder trained on the frozen encoder embeddings achieves reconstruction F1 of 0.995, and a flow matching generative model conditioned on those embeddings produces generations that closely match the pitch register and rhythmic density of the conditioning excerpt, while mismatched conditioning yields unrelated but musically plausible output. Learned representations outperform a Haar scattering transform baseline on a downstream emotion classification task, and embedding distances increase monotonically with pitch and time shift magnitude, confirming measurable equivariance. These results suggest that equivariance-based SSL objectives, combined with sufficient fine-level encoder capacity, provide a viable path toward semantically rich, generatively useful representations of symbolic music.

Industrial time series serve as the foundation for Prognostics and Health Management (PHM) to ensure the reliability and safety of industrial equipment such as aero-engines. However, existing approaches are typically limited to single-modality modeling, which restricts their generalization in complex scenarios. Although recent advances in large language models (LLMs) provide new opportunities for multimodal learning, bridging continuous time-series signals and discrete textual semantics remains an open challenge. To this end, we propose VLT, a multimodal foundation model that jointly models time-series, frequency-spectrum visual representations, and textual knowledge. A key insight is to utilize the frequency spectrum as a visual bridge to connect continuous temporal signals with discrete semantics. Specifically, a Time-aware Mixture-of-Experts (Time-MoE) is designed to capture heterogeneous temporal dynamics, while a Frequency-Text Augmented Learner enables joint modeling of spectral and semantic features within a shared representation space. Furthermore, a time-centric gradient alignment mechanism is introduced to mitigate cross-modal optimization conflicts via gradient normalization and reliability-aware dynamic reweighting. Extensive experiments on multiple industrial datasets demonstrate that VLT outperforms state-of-the-art methods, achieving superior robustness and generalization under few-shot, noisy, and incomplete-modality settings.

Bioacoustic foundation models rely on large-scale citizen science platforms like Xeno-Canto for geographically and ecologically diverse data. Recent work has shown that supervision alone can produce SotA species detection models when trained on this large-scale data -- however, there remains unutilized potential in the form of recording metadata readily available within these community-driven data hubs. In this work, we explore the use of metadata -- such as location and time -- as auxiliary supervision signals, allowing the model to leverage species-metadata correlations in its learned representation. Auxiliary metadata losses provide additional information beyond vocalizations alone that can encourage a richer, more robust representation that generalizes better to species distribution and acoustic domain shifts -- important challenges for deployment in real-world passive acoustic monitoring (PAM) settings. We introduce MetaPerch, a new foundation model that achieves strong species identification performance across multiple challenging domains and present an extensive empirical study of the effects of 9 diverse metadata sources on 17 bioacoustic datasets.

In autonomous driving perception, the fusion of LiDAR and camera modalities has become the dominant paradigm for 3D object detection. However, current multi-modal frameworks heavily rely on massive visual backbones pretrained on 2D semantic tasks. This reliance introduces substantial parameter redundancy and a structural misalignment, as 2D priors are ill-equipped to handle the extreme sparsity of LiDAR projections required for Bird's-Eye-View geometry. To address this, we present DeGuNet, an ultra-compact and plug-and-play image backbone explicitly designed for depth-guided representation learning. By incorporating sparsity-aware feature extraction mechanisms, DeGuNet effectively aligns multi-view images with unstructured LiDAR depth while strictly preventing invalid-region contamination. Extensive experiments on the nuScenes dataset demonstrate DeGuNet's broad plug-and-play applicability and superior efficiency. When integrated into established baselines, it fundamentally eliminates architectural redundancy, reducing GPU memory consumption by up to 66.5% and achieving a 1.16x inference speedup. Concurrently, DeGuNet delivers up to a 6.20 absolute mAP gain, establishing a new paradigm for parameter-efficient multi-modal 3D perception.

Neurological prognostication after cardiac arrest commonly relies on electroencephalography (EEG). However, EEG demands high clinical resources. Bedside electrocardiography (ECG) is standard and low-cost. Yet, its value for predicting neurological outcomes remains underexplored. In this study, we propose NeuroECG, an ECGFounder-based deep representation framework for EEG-free auxiliary prognostication. NeuroECG adapts a pretrained ECG foundation model via task-specific fine-tuning. We implement a gradual unfreezing strategy on single-channel bedside monitoring ECG. Multiple ECG segments per patient are encoded into segment-level deep features. These embeddings are aggregated via quantile pooling (q = 0.24) and compressed using principal component analysis (PCA). Experiments on 412 ECG-available patients from the multicenter I-CARE database show that the adapted ECGFounder backbone achieves the best performance among ECG-only backbone baselines, with a test AUROC of 0.7333. We further combine the learned deep ECG representation with static clinical covariates. The proposed NeuroECG model achieves a test AUROC of 0.8077 and an AUPRC of 0.8970. These results support deep bedside ECG representations as a useful source of auxiliary prognostic information. Their integration with static clinical covariates improves prediction in an EEG-free setting. The source code is available at https://github.com/goddream66/NeuroECG

Accurately representing atmospheric aerosol populations is essential for simulating aerosol-cloud interactions, radiative forcing, and ice nucleation, yet existing reduced schemes impose structural assumptions that limit their ability to capture composition diversity and mixing state. Machine-learning approaches offer more flexible representations, but standard autoencoders do not preserve the mathematical structure of aerosol populations and therefore cannot support physically meaningful process operators. We introduce AeroMELD (Aerosol Measure Embedding for Latent Dynamics), a mathematically grounded framework for constructing low-dimensional latent variables that retain this structure. We show that any permutation-invariant linear encoder must take a scale-shape decomposition, with total number concentration represented explicitly and latent shape given by a barycentric combination of per-particle embeddings. This aggregated latent state retains the diagnostic expressiveness of a Deep Sets model by moving the nonlinear post-aggregation stage into the learned diagnostic map while preserving latent linearity. Using particle-resolved data as ground truth, we encode weighted particle populations directly rather than binned aerosol states; size-resolved mass and number distributions serve only as diagnostic targets and visual summaries. The latent space accurately reconstructs these distributions, CCN spectra, optical coefficients, and immersion-freezing behavior while preserving the linear population structure needed for hybrid ML-physics models. Although the experiments focus on diagnostic reconstruction, the embedding is designed so that emissions and mixing can be represented exactly and nonlinear microphysical processes learned in a controlled latent space. This work establishes a foundation for learning aerosol-process evolution directly in latent space.

Generative models often represent signals as dense grids of amplitudes, blurring sharp transients that are crucial for the correctness of physical signals. We introduce Singularity Space, a generative framework that represents signals through complex-plane singularities, rooted in the classical pole-residue representation of meromorphic functions. We learn a latent space of physically constrained, per-signal singularity configurations to solve an inverse problem from degraded or partial observations. The framework has three key properties: interpretability, in which each generated singularity configuration corresponds to a set of physical parameters; structural stability, which mitigates Gibbs artifacts at discontinuities; and resolution-free output reconstruction on arbitrary grids without retraining or interpolation. Our framework employs a transformer-based diffusion model that directly predicts samples at complex-plane singularity coordinates, subject to geometric constraints during sampling. As a controlled test case for sharp-feature recovery, we evaluate our framework on 1D Burgers shocks, where each shock is represented by 32 predicted singularities (an $8\times$ reduction versus a 1024-point grid signal). Our framework preserves signal structure ($\text{TV ratio} \approx 1$) under unseen test-time observation noise, achieves a $4.2\times$ lower reconstruction error in zero-shot sub-resolution generalization than a grid-based baseline, and recovers physical parameters to $10^{-4}$ absolute error in-distribution. These results suggest that singularity-based representations may provide a practical foundation for other transient-dominated signals such as speech and biomedical signals, with potential extension to higher-dimensional domains.

Dimensionality reduction has proven powerful for identifying neural manifolds, which are low-dimensional structures underlying high-dimensional neural activity. These low-dimensional representations have improved the interpretability of population-level coding. Yet whether such low-dimensional representations are biologically relevant and confer functional advantages in learning systems, or merely reflect neuron-level activity, remains contested in neuroscience. We show that an explicit information bottleneck forcing a recurrent neural network to learn a low-dimensional representation is necessary for rotational and out-of-distribution generalisation in a time-series prediction task. Using information-theoretic measures of causal emergence, we characterise the dynamics of this representation across the memorisation-to-generalisation transition, finding a non-monotonic trajectory which shows an initial decrease, a minimum, and a subsequent rise to a maximum, even as prediction loss falls monotonically. This trajectory scales with task complexity, and the magnitude of emergent structure reliably predicts generalisation performance. Analysis of CA1 hippocampal activity in mice learning an alternating maze task reveals analogous non-monotonic emergence dynamics that track behavioural performance. Together, these findings indicate that the ability of neural networks to learn compact, distributed and emergent representations confers a functional advantage for generalisation, supporting a causal role for learned representations in cognition.

Self-supervised learning for symbolic music has advanced largely through token-level pretraining, but such representations remain tied to tokenizer-specific sequences and often provide time-span-level embeddings only indirectly. In this paper, we propose ARIMA, a reconstruction-grounded latent predictive framework for symbolic music that learns compact window-based representations directly from data. ARIMA encodes each fixed-duration window into a continuous latent representation, trains a causal predictor with contrastive next-latent prediction, and grounds the encoder through structured reconstruction of music elements. This design preserves local musical details while modeling temporal progression across windows. We evaluate ARIMA on downstream tasks spanning various levels of music understanding. Results show that ARIMA is particularly efficient and effective on tasks involving harmonic, timing, and cross-performance retrieval, while remaining competitive with much larger baselines on other tasks. Ablations further show that next-latent prediction is essential for temporally integrated representations, and that structured reconstruction stabilizes latent learning without requiring explicit variance regularization. The code is at https://github.com/AndyWeasley2004/symbolic_music_wm.

How should language interface with a world model's discrete symbol system? The dominant paradigm -- end-to-end injection of LLM/VLM features into robot world models (RT-2, Octo, PaLM-E) -- implicitly assumes that language gradients can directly shape physical symbol representations. We ask whether this assumption is safe, find that it is not, and characterize the minimal architectural constraint that prevents the failure. Any language gradient entering a Gumbel-softmax-based discrete symbol bottleneck forces a structural trade-off: the vanilla estimator collapses to 2.2/64 symbols (4/5 seeds), while five anti-collapse strategies maintain diversity but fail to learn semantic labels (all <= 9.2% accuracy). No tested GumbelBottleneck variant achieves both objectives simultaneously. Within this family of discrete bottlenecks, the failure is structural rather than a matter of optimization. We characterize a sufficient set of three constraints that prevent the failure: (1) cut the gradient chain (z.detach()), preventing language signals from reaching the symbol bottleneck; (2) provide a gradient-free semantic channel -- a non-parametric Memory Table (Dict[symbol -> Counter[label]], zero parameters, zero gradients) where co-occurrence counting replaces gradient-based binding; (3) handle symbol collisions via DP-Means streaming clustering for automatic sub-cluster splitting. All three layers together achieve 97.2% grounding accuracy vs. 22.2% without Layer 3. Across two experiments spanning 74 independent runs, we demonstrate zero symbol collapse in all 32 seeds, with the blackboard achieving 79-100% semantic binding across three encoder architectures (CNN, V-JEPA 300M, CLIP ViT-L), two environments, and three texture conditions. The fix trains fewer than 2M parameters and requires no LLM fine-tuning.

Multimodal learning usually requires a dedicated encoder per modality. When a tabular modality is involved, prior work has been mostly using a plain MLP as the encoder. Yet if it were a strong encoder, the tabular domain would not be ``the last unconquered castle for deep learning''. This study evaluates state-of-the-art tabular models as encoders in the image-tabular setting for the first time. An obstacle stands out. In-Context Learning models, among the best performing methods in the tabular domain, require labels to process instances, making it non-trivial to embed training and test instances the same way. We addressed this problem across multiple models of this family. With this study, we would like to highlight the importance of encoder factor in the multimodal learning.

Prompt-free adaptation of the Segment Anything Model (SAM) has emerged as a promising paradigm for automatic medical image segmentation. Existing methods mainly focus on prompt generation, while overlooking that prompt quality is fundamentally constrained by the expressiveness of anatomical representations. However, deterministic prototypes or semantic tokens are insufficient to jointly capture global anatomical priors, intra-structure diversity, and local structural reliability. To address this limitation, we propose the Hierarchical Probabilistic Representation (HPR) framework, which learns complementary anatomical representations through Distributional Anatomical Representation (DAR), Multi-component Anatomical Representation (MAR), and Local Reliability Representation (LRR), and integrates their predictions via Hierarchical Prediction Fusion (HPF) while remaining compatible with the original SAM decoder. Experiments on the Synapse, LA, and PROMISE12 datasets demonstrate that HPR-SAM achieves state-of-the-art performance on Synapse and the best performance under few-shot settings on LA and PROMISE12, validating the effectiveness of the proposed hierarchical probabilistic representation learning framework for prompt-free medical image segmentation. Code is available at https://anonymous.4open.science/r/HPR-SAM-E4AF.

X-ray fluorescence (XRF) spectroscopy is a key modality for material analysis in cultural heritage. However, automated learning from XRF spectra remains challenging: XRF spectra are complex one-dimensional signals composed of sharp elemental peaks, broader structures, and background variations that are not taken into account by existing learning-based models. This paper introduces XRFormer, a transformer architecture tailored to XRF spectra through a multiscale convolutional tokenizer that injects locality and multi-resolution inductive biases before global self-attention. The tokenizer progressively reduces spectral resolution while increasing embedding dimensionality, and the resulting token sequence is processed by a standard transformer encoder. We further investigate self-supervised pretraining for XRF representation learning using Masked Spectral modeling (MSM) and a physics-informed Peak Presence Prediction (PPP) objective. Experiments on the Pigments Checker STANDARD v.5 dataset for pigment identification and unmixing show that XRFormer consistently outperforms ViT, SpectralFormer (with and without CAF), and a 1D-CNN baseline for pigment identification. For pigment unmixing, XRFormer achieves robust abundance estimation while maintaining significantly higher parameter efficiency than SpectralFormer, operating at a lower token resolution (128 vs. 512 tokens) and with less than half the number of parameters (1.5M vs. 3.37M). MSM yields consistent gains across both tasks, while PPP further enhances performance for both identification and unmixing when tuned with an appropriate peak prominence. These results highlight multiscale, modality-aware tokenization as an effective and parameter efficient foundation for transformer-based XRF modeling under data-limited conditions. A GitHub repository is provided at https://github.com/sofiane1010/XRFormer.

Images tell us what a scene looks like, but rarely what it would feel like to be there. While recent datasets pair visual scenes with electronic-nose measurements, aligning smell signals with images remains challenging because many olfactory cues arise from contextual environmental factors that are not directly visible in pixels. We introduce SCENT, a multimodal framework that uses language guidance as a semantic bridge between vision and olfaction. Our approach leverages Vision-Language Models (VLMs) to generate scene descriptors capturing objects, environmental context, and plausible ambient smell cues suggested by the visual scene. These descriptors provide semantic guidance for learning olfactory representations. We train a smell encoder that maps electronic-nose signals into a shared embedding space aligned with both visual and textual representations, and introduce a languageguided latent decomposition that separates object-specific odors from contextual environmental contributions. Experiments on the New York Smells dataset demonstrate that SCENT significantly improves crossmodal retrieval compared to vision-only baselines, achieving state-of-theart performance on smell-to-image and smell-to-text retrieval tasks. In addition, our framework produces interpretable olfactory representations that enable the disentanglement of complex smell mixtures. Our results reveal the importance of contextual semantic information for grounding olfactory perception in multimodal learning and pave the way for future research in this area.

Audio-language models compress a speech encoder's output through a Querying Transformer (Q-Former) connector before feeding it to a large language model. We identify two failures in this compression. The connector's output vectors collapse to a single direction, and different speakers produce nearly indistinguishable outputs, with paralinguistic cues such as speaker identity, gender, and prosody lost along the way. Our method, ORCA, reverses this collapse by splitting the queries into groups whose outputs are constrained to point in different directions. On SAKURA multi-hop reasoning, ORCA gains 26.4 points over an identically trained 4B baseline, reaching 75.2% (vs. 49.0% for the 8B Audio Flamingo-3). At the connector level, the same change cuts query redundancy by 12x and raises cross-speaker variance by 75x.

Automatic depression detection using audio-visual data faces significant challenges, particularly in disentangling overlapping feature distributions and establishing robust decision boundaries. To address this, we propose a fine-grained multimodal framework featuring a temporal encoder and a mutual transformer to facilitate deep cross-modal fusion. Our core contribution is the Binary Advantage-weighting Ranking Loss, which optimizes the latent space distribution through two complementary mechanisms: Advantage-weighted Separation, which mines hard pairs by computing a pairwise prediction difference matrix and dynamically weighting them based on their difficulty; and Advantage-weighted Compactness, which minimizes intra-class variance to force features to cluster around their respective class centers. Extensive experiments on D-vlog and LMVD demonstrate that our model reconstructs the latent ordinal structure by prioritizing hard pairs, thereby achieving state-of-the-art performance.

Principal Component Analysis or PCA-like properties (orthogonality, variance ranking) are seldom realized in deep autoencoder architectures. In this work, we present ODIN (Orthogonal Dendritic Intrinsic Network), a novel autoencoder architecture that recovers PCA-like latent structure in a fully non-linear regime. By incorporating a set of geometric constraints directly into the training objective, ODIN encourages latent dimensions to be mutually orthogonal and ordered by explained variance, mirroring the interpretable decomposition of PCA while retaining the expressive power of deep networks. We provide theoretical grounding for these constraints and demonstrate their compatibility with standard encoder-decoder frameworks. We also establish empirical results for both synthetic and real world datasets, establishing a principled path toward interpretable, structured feature learning and dimensionality reduction.

We study why diffusion autoencoders can achieve similar image quality while learning substantially different latent structures. We trace this behaviour to optimisation dynamics; we analyse curves of image reconstruction against latent representation quality, revealing trajectories that organise around two distinct regimes early in training. Models in the reconstruction regime prioritise image fidelity early, whereas those in the disentanglement regime improve reconstruction and disentanglement more gradually. We hypothesise that this behaviour can be influenced by targeting shortcut pathways in the diffusion U-Net and controlling early noise-level exposure, thereby shaping the reconstruction-disentanglement trade-off during training. To steer optimisation toward stronger representations, we introduce SteeringDRL, combining gated residual U-Nets with a simple noise-level exposure curriculum for training. Across disentanglement benchmarks, SteeringDRL improves representation quality and reduces seed sensitivity. Our method further extends to spatial disentanglement in object-centric learning, improving segmentation quality on synthetic and real-world datasets.

This paper concerns the problem of unsupervised temporal action segmentation for long, untrimmed videos. Recent successful approaches follow a joint representation learning and clustering paradigm, where optimal transport (OT) is adopted to produce pseudo labels for learning frame representations. These approaches alternate between estimating pseudo labels using OT and optimizing the parameters with gradient descent during training, where OT is used for obtaining the final temporal action segmentation. A major limitation of these works is that they learn a deterministic embedding for frame representations. The iterative procedure between learning deterministic embeddings based on pseudo labels and estimating pseudo labels from the learned embedding can thus get quickly stuck in a local optimum. As an alternative, we thus propose to learn a probabilistic embedding for frame representations. The embeddings are modeled by Gaussian distributions and we sample from the distributions before estimating the pseudo labels. We evaluate our approach on several challenging temporal action segmentation datasets and achieve results comparable to, and in some cases, better than the state of the art. Compared to baselines with deterministic embeddings, our approach improves MoF up to 20.7% and F1-score up to 19.0%. Our code is available at https://github.com/derkbreeze/PEOT.

We characterize observability in representation learning through Platonic Projection Structures (PPS), an operator-theoretic framework for analyzing representation accessibility under partial observation. Rather than treating observable outputs as direct reflections of latent representations, PPS models observation through a self-adjoint positive semidefinite operator acting on a latent representation space. A system is represented as a triple $(H, Π, O)$, where $H$ is a latent representation space, $Π\succeq 0$ is an observation operator, and $O(v)=\langle v,Πv\rangle$ defines an induced scalar observable. Observability is characterized by the quotient geometry $H/\ker(Π)$, representing equivalence classes of latent states indistinguishable under observation. We show that quantum measurement and representation inference under linear observation models share this operator-theoretic structure while differing in the algebraic properties of their observation operators; the correspondence is structural rather than physical. Representation transfer and knowledge distillation can likewise be interpreted as approximate preservation of observable geometry through $ΦΠ_T \approx Π_S Φ$. PPS also reveals a structural limitation of output-based interpretability: latent components in $\ker(Π)$ are inaccessible from induced observables, imposing intrinsic constraints on attribution and explanation methods. Controlled empirical validations demonstrate kernel-invariant observability, projection-induced attribution gaps, and rank-controlled observable geometry in latent representation spaces. PPS thus provides an explicit characterization of observability through operator-induced quotient geometry and a unified perspective on representation accessibility, interpretability, and projection-mediated inference.

How does the way information reaches a transformer -- as symbolic tokens, a clean per-factor "oracle" code, or an entangled perceptual vector -- shape whether it binds that information compositionally? We study ~6-10K-parameter transformers on finite factored worlds enumerated exhaustively, so every measurement covers the whole input space (zero sampling variance) and the informative routes are information-matched (exact Bayes ceiling 1.0). We report four findings. (1) Endpoint invariance: on held-out binding queries no informative route reaches converged zero-shot composition -- each ends at or below chance despite a ceiling of 1.0, so within a bounded sweep the failure reflects inductive bias under a lookup-sufficient objective, not missing information. (2) A two-factor account of few-shot binding: sample efficiency is best explained by input-pathway parameter sharing and code readability; a dimension-matched control and a graded readability sweep isolate readability from input dimension, and the clean oracle is not the most sample-efficient readable route. (3) A double dissociation: early in training, distributed -- but not index-like -- codes pass through a transient above-chance phase (tracking code format), while few-shot efficiency tracks pathway sharing. (4) Failure anatomy: symbolic routes lose the answer at the readout; index routes mis-bind (the answer stays decodable, yet an input intervention shows the output tracks the wrong slot); entangled routes inherit their input's readability. The central claim is the two-factor account; the endpoint and anatomy results are diagnostic constraints. All code, manifests, and per-seed logs are released for exact reproduction.

Many real-world games do not admit a fixed, compact rule set: instead, their dynamics are defined by interactions among a large and often evolving collection of game pieces, making general-purpose policy learning impractical. Magic: the Gathering (MTG) exemplifies this setting, where the cards themselves define and alter gameplay rules, strategic constraints, and long-term outcomes, while the pool of available cards is ever-changing. We study Draft, a constrained deck-building format of MTG in which eight players make 39-45 sequential selections from semi-random packs to construct a 40-card deck under partial information. By isolating the card selection process from gameplay, Draft provides a tractable yet non-trivial setting for studying decision-making driven by combinatorial card synergies. We propose an encoder-based model that produces set-contextualized card embeddings to encode the draft decision sequence, with a consistent improvement over linear baselines on large-scale real-world data, establishing a first learned benchmark for outcome prediction in MTG Draft. Our code is available at github.com/akulen/MtGDraftEncoder.

We present FM-ChangeNet, a pathwise-supervised framework for change detection that reformulates bi-temporal reasoning as continuous transport in feature space rather than static endpoint comparison. Given encoded pre and post-temporal representations, we construct intermediate latent states and learn a time-conditioned velocity field $\hat{v}_θ(z_t,t)$ along the transformation trajectory. This pathwise formulation constrains the predictor over a continuum of intermediate states, providing a denser and less ambiguous supervision signal than conventional endpoint-only segmentation and enabling the model to capture temporal evolution explicitly. The learned velocity field is not only a transport mechanism but also an interpretable representation of change: its magnitude serves as a spatially localized change cue that helps distinguish true structural variation from nuisance effects such as illumination shifts and spatial misalignment. We develop a hierarchical multi-scale architecture with cross-temporal alignment, time-conditioned coarse-to-fine flow decoding, and a unified objective that couples flow supervision, trajectory consistency, spatial regularization, and segmentation loss. Experiments on remote sensing benchmarks show that the proposed framework produces more structured and robust change representations while achieving state-of-the-art performance.

Vision-based deep reinforcement learning involves dealing with high-dimensional inputs of image information. It is crucial to abstract effective states from high-dimensional image inputs and limited samples for sample-efficient reinforcement learning. To address this challenge, inspired by fields such as natural language processing and computer vision, we propose a self-supervised task based on mask prediction as an auxiliary task for reinforcement learning. This non-reconstruction method uses the sequence information collected by the agent from the environment and the context information in the sequence to predict the masked information, thereby strengthening the agent's understanding of the task and learning effective representations. Combined with transformers, we find that the model reconstructs the masked input sequence in the latent space. By feeding the compressed representations learned by this method into reinforcement learning models, we observe an improvement in the sample efficiency of reinforcement learning. Moreover, the model outperforms state-of-the-art sample-efficient reinforcement learning methods on multiple continuous and discrete control benchmarks.

Concept erasure aims to remove a target concept from a representation while preserving the other information encoded in it. This is difficult because representations encode many concepts that are often correlated with the erasure target, so removing the target risks damaging them. We propose the Manifold Constraint Hypothesis (MCH): if natural representations concentrate on a structured, lower-dimensional manifold, then interventions should be constrained to that manifold and better preserve other information encoded in the representation during interventions. We instantiate MCH in a new concept erasure method: MANifold aware Concept Erasure (MANCE). MANCE performs iterative updates to the representations using signals from a classifier that predicts a target concept. We estimate the manifold using representations obtained from natural inputs, and then we project the concept removal update to the estimated manifold. We perform extensive evaluation on 119 settings spanning text and vision, including 13 language models, three NLP concepts, and 40 CelebA-CLIP attributes. Employing MANCE on top of previous methods shows consistent improved leakage results. We also introduce MANCE+ and MANCE++, which prepend a closed-form erasure algorithm before employing MANCE, achieving better leakage--surgicality tradeoffs relative to matched full-space updates. MANCE++, our best method, achieves state-of-the-art results on nonlinear concept erasure. These results support MCH in the erasure setting: interventions should be constrained to the natural representation manifold.

Spectral methods are widely used to construct representations from the geometry of data, but they often rely on a fixed kernel, graph Laplacian, or manually selected feature scaling. We propose Physics-Informed Eigenfunction Features with Learnable Scaling (PIEFS), a supervised neural representation-learning framework with a spectral inductive bias, based on a modified Dirichlet energy. In PIEFS, scalar coordinate maps are trained under empirical Gram orthogonality, a supervised linear readout, and a Dirichlet penalty in which the input gradient is transformed by a learnable metric $A(x)=Λ(x)U(x)$. The diagonal factor $Λ(x)$ controls anisotropic scaling, while the orthogonal factor $U(x)$ is parameterized by a structured product of Givens rotations. This construction yields task-adaptive Dirichlet-regularized coordinates rather than eigenfunctions of a fixed supervision-independent operator. Experiments on synthetic, tabular, and image-based benchmarks study the effect of identity, diagonal, and rotation-scaling metrics, and compare the resulting coordinates with classical baselines and NeuralEF. The results support PIEFS as a compact supervised spectral representation method and identify optimization stability, validation on explicit operator eigenproblems, and richer metric parameterizations as the main directions for future work.