ICML 2026 Papers

Building physically grounded protein representations is central to computational biology, yet most existing approaches rely on sequence-pretrained language models or backbone-only graphs that overlook side-chain geometry and chemical detail. We present SLAE, a unified all-atom framework for learning protein representations from each residue’s local atomic neighborhood using only atom types and interatomic geometries. To encourage expressive feature extraction, we introduce a novel multi-task autoencoder objective that combines coordinate reconstruction, sequence recovery, and energy regression. SLAE reconstructs allatom structures with high fidelity from latent residue environments and achieves state-of-the-art performance across diverse downstream tasks via transfer learning. SLAE’s latent space is chemically informative and environmentally sensitive, enabling quantitative assessment of structural qualities and smooth interpolation between conformations at all-atom resolution.

We investigate the relation between end-to-end equivariance and layerwise equivariance in deep neural networks. We prove the following: For a network whose end-to-end function is equivariant with respect to group actions on the input and output spaces, there is a parameter choice yielding the same end-to-end function such that its layers are equivariant with respect to some group actions on the latent spaces. Our result assumes that the parameters of the model are identifiable in an appropriate sense. This identifiability property has been established in the literature for a large class of networks, to which our results apply immediately, while it is conjectural for others. The theory we develop is grounded in an abstract formalism, and is therefore architecture-agnostic. Overall, our results provide a mathematical explanation for the emergence of equivariant structures in the weights of neural networks during training -- a phenomenon that is consistently observed in practice.

Neural acoustic fields often model time-domain impulse responses, which struggle to capture the frequency-selective wave behaviors that dominate confined, resonant environments. To address this, we propose INFER (Implicit Neural Frequency Response fields), a framework that directly learns continuous, complex-valued frequency response fields. Unlike prior time-domain methods, our frequency-first approach enables three key innovations: (1) end-to-end learning of frequency-specific attenuation and phase delay in 3D space; (2) a physics-based Kramers–Kronig consistency constraint that causally regularizes attenuation and phase delay; and (3) perceptual and hardware-aware spectral supervision that prioritizes critical auditory bands. We evaluate INFER across diverse settings, ranging from standard room-scale benchmarks (MeshRIR, RAF) to challenging, highly reverberant environments like real car cabins. Our approach significantly outperforms time- and hybrid-domain baselines, reducing average magnitude and phase reconstruction errors by over 39\% and 51\%, respectively, demonstrating state-of-the-art accuracy in modeling complex acoustic spaces.

A surge of recent advancements has consistently highlighted the superiority of multimodal learning over unimodal approaches across a variety of tasks. However, the theoretical foundations elucidating this advantage remain underexplored: existing theoretical analyses are often constrained by tight assumptions, and lack empirical validation. In this paper, we link this gap by proposing a novel theoretical framework grounded in \textit{convolutional smoothing}, offering a new perspective on how multimodal learning contributes to a smoother loss landscape compared to unimodal learning. Building upon this theoretical foundation, we introduce a simple yet effective distributional training approach based on stochastic modality pairing instead of fixed pairing; thus, further promoting flatter landscape via convolutional smoothing. Our empirical results across various multimodal datasets demonstrate that multimodal models not only achieve better performance but also exhibit smoother loss landscape, which represent better robustness and generalization.

Feature-map knowledge distillation (KD) transfers internal representations well between comparably sized Vision Transformers (ViTs), but it often fails in compression. We revisit this failure and uncover a paradox. Sample-wise SVD shows that each image is highly compressible, which seems to suggest that a narrow student with a linear projector should match the teacher "in principle". However, a dataset-level view contradicts this intuition: PCA shows that the teacher is a union of low-rank subspaces with significant subspace rotation across inputs. We further introduce token-level Spectral Energy Patterns (SEP) and find an architecture-invariant encoding law: tokens spread energy broadly across channel modes even when they live in low-rank subspace, creating a bandwidth mismatch. We refer to this combined phenomenon as an encoding mismatch. We propose two minimal remedies, Lift or WideLast: (i) Lift retains a lightweight lifting projector at inference to provide wider channel, or (ii) WideLast widens only the student’s last block, enabling an input-dependent expansion. On ImageNet-1K, these fixes revive feature KD for ViT compression, improving DeiT-Tiny distilled from CaiT-S24 from 74.86% to 77.53%/78.23% top-1 accuracy, and they also strengthen students trained without distillation. Our analyses clarify when and why feature-map KD fails and then how to fix it. Code and raw data are provided in https://github.com/thy960112/From-Per-Image-Low-Rank-to-Encoding-Mismatch.

Image-to-image relighting requires representations that separate illumination from scene properties while preserving dense geometry, material, and photometric cues. We use this task as a probe of visual priors: unlike recognition tasks that reward invariance, relighting tests whether visual features retain the information needed for light transfer. Through a controlled generative relighting framework, we find that strong semantic encoders can degrade relighting quality, exposing a semantic--photometric trade-off between abstraction and physical fidelity. We introduce \textbf{Augmented Latent Intrinsics (ALI)}, which balances this trade-off by fusing dense, pixel-aligned visual features into a latent-intrinsic relighting model and refining it with self-supervision on unlabeled real image pairs. ALI improves relighting quality, especially on glossy, metallic, and transparent materials, and demonstrates that generative relighting is an effective tool for quantifying what visual encoders encode about the physical world.

Vector quantization is a fundamental tool for compressing high-dimensional embeddings, yet existing multi-codebook methods rely on static codebooks that limit expressiveness under heterogeneous data geometry. While recent dynamic quantizers like QINCo adapt codebooks to individual inputs and improve expressiveness, their strict sequential dependencies create decoding bottlenecks. We propose Residual Quantization via Mixture of Experts (RQ-MoE), a framework combining a two-level MoE with dual-stream quantization to enable input-dependent codebook adaptation for efficient vector quantization. RQ-MoE enables dynamic codebook construction and decouples instruction from quantization, facilitating parallel decoding. Theoretically, we show that standard Residual Quantization and QINCo can be recovered as constrained special cases of RQ-MoE, and derive a guideline for setting expert dimensionality in RQ-MoE. Extensive experiments show that RQ-MoE achieves state-of-the-art or on-par performance in reconstruction and retrieval, while it can provide 6×–14× faster decoding than prior vector quantization methods. The implementation is available at https://github.com/KDEGroup/RQ-MoE.

We present a unified framework for quantifying the similarity between representations through the lens of \textit{usable} information, offering a rigorous theoretical and empirical synthesis across three key dimensions. First, addressing functional similarity, we establish a formal link between stitching performance and conditional mutual information. We further reveal that stitching is inherently asymmetric, demonstrating that robust functional comparison necessitates a bidirectional analysis rather than a unidirectional mapping. Second, concerning representational similarity, we find that reconstruction-based metrics and standard tools (e.g., CKA, RSA) act as estimators of usable information under specific constraints. Crucially, we show that similarity is relative to the capacity of the predictive family: representations that appear distinct to a rigid observer may be identical to a more expressive one. Third, we demonstrate that representational similarity is sufficient but not necessary for functional similarity. We unify these concepts through a task-granularity hierarchy: similarity on a complex task guarantees similarity on any coarser derivative, establishing representational similarity as the limit of maximum granularity: input reconstruction.

Graph Contrastive Learning (GCL) is a powerful self-supervised learning framework that performs data augmentation through graph perturbations, with growing applications in the analysis of biological networks such as Gene Regulatory Networks (GRNs). The artificial perturbations commonly used in GCL, such as node dropping, induce structural changes that can diverge from biological reality. This concern has contributed to a broader trend in graph representation learning toward augmentation-free methods, which view such structural changes as problematic and should be avoided. However, this trend overlooks the fundamental insight that structural changes from biologically meaningful perturbations are not a problem to be avoided, but rather a rich source of information, thereby ignoring the valuable opportunity to leverage data from real biological experiments. Motivated by this insight, we propose SupGCL (Supervised Graph Contrastive Learning), a new GCL method for GRNs that directly incorporates biological perturbations from gene knockdown experiments as supervision. SupGCL is a probabilistic formulation that continuously generalizes conventional GCL, linking artificial augmentations with real perturbations measured in knockdown experiments, and using the latter as explicit supervision. On patient-derived GRNs from three cancer types, we train GRN representations with SupGCL and evaluate it in two regimes: (i) embedding space analysis, where it yields clearer disease-subtype structure and improves clustering, and (ii) task-specific fine-tuning, where it consistently outperforms strong graph representation learning baselines on 13 downstream tasks spanning gene-level functional annotation and patient-level prediction.

Molecular representation learning has achieved remarkable progress in molecular property prediction, yet out-of-distribution (OOD) generalization remains challenging. In practice, training data typically cover only a limited portion of the chemical space, causing models to rely on environment-dependent factors that fail to transfer when scaffold structures or functional compositions shift. To address this issue, we propose MoSIR, a framework for learning molecular semantic invariant representation with prototype constraint, which projects entangled molecular embeddings into a learnable semantic prototype space to extract semantic invariant representation while isolating environment-sensitive variations. Building upon this decomposition, we optimize a bi-level min-max objective that introduces representation perturbations to simulate plausible environment shifts and enforce semantic stability. We further provide theoretical guarantees for MoSIR by deriving an OOD generalization bound under distribution shifts. Extensive experiments on multiple molecular OOD benchmarks demonstrate that MoSIR consistently outperforms strong baselines across diverse shift settings, and qualitative analyses confirm that the learned prototypes capture meaningful chemical semantics.

Maximum inner product search (MIPS) is a crucial subroutine in machine learning, requiring identification of database vectors that align most strongly with a given query. We propose amortized MIPS: a learning-based approach that trains neural networks to directly predict MIPS solutions, amortizing the computational cost of search across queries drawn from a known distribution. Our key insight is that the MIPS value function - the maximum inner product as a function of the query - is convex (as the pointwise maximum of linear functions), and its gradient at each query equals the optimal database vector. We explore two complementary architectures: (1) Input Convex Neural Networks (ICNNs) that learn the convex value function and recover the optimal match via gradient computation, and (2) VectorICNNs that directly regress the argmax, bypassing gradient computation entirely at inference time. For ICNNs, we combine score regression with gradient matching losses; for VectorICNNs, we introduce a score consistency loss derived from Euler's theorem for homogeneous functions. We further propose homogenization wrappers that enforce positive 1-homogeneity, theoretically linking function values to gradients. Our experiments on retrieval benchmarks demonstrate that convexity provides an effective inductive bias, with learned potentials achieving high match rates while requiring only a single forward pass at inference. Our code is available at: https://github.com/apple/ml-amips.

Visuo-tactile sensors have been widely adopted in robotic manipulation. However, inherent heterogeneity in sensor designs hinders the learning of unified tactile representations in cross-sensor scenarios. Existing methods that focus on reconstruction or task-specific supervision often fail to capture the common information between different tactile sensors, particularly in the presence of substantial sensor variations, resulting in limited generalization to unseen sensors. To address this, we propose Cross-Tactile Sensor Representation Learning (CTSRL), a unified framework for sensor-agnostic tactile representation learning. CTSRL introduces a Cross-Sensor Modulator (CSM) to eliminate sensor-specific biases and adopts a two-stage learning paradigm: (1) leveraging aligned synthetic data for cross-sensor self-supervised learning to extract shared latent representations across sensor domains; and (2) integrating real-world multimodal tactile data to bridge the sim-to-real semantic gap through cross-modal alignment, thereby enriching representations with fine-grained semantic attributes. Experimental results show that our method demonstrates strong multi-sensor generalization, significantly improving sensor-agnostic representation learning.

We introduce physics-as-representation, a learning paradigm that encodes physical structure and geometric laws into visual representations, enabling models to see the unseen—the underlying 3D geometry and motion dynamics not apparent in raw pixels. We instantiate this paradigm in gaze perception by proposing SG-Gaze, a framework that learns a Structurally and Geometrically Consistent Representation (SGR) through dual-branch adversarial learning. An analytical branch embeds appearance features onto a spherical manifold aligned with gaze geodesics, while a model-guided branch reconstructs the 3D eyeball with weak 2D edge supervision. We further introduce View-Consistent Regularization, which augments SGR learning with synthetic view perturbations and enforces rotation-equivariant consistency across gaze vectors and structural projections, eliminating the need for multi-view calibration or explicit 3D labels. Extensive experiments across 12 challenging cross-domain transfers demonstrate that SG-Gaze achieves state-of-the-art accuracy and strong generalization. Our work highlights that enforcing structural and geometric consistency with equivariant regularization serves as effective inductive biases for interpretable and generalizable representation learning—a step toward machines that perceive the world not only from pixels, but from physics.