Semantic Parsing

Self-supervised learning (SSL) faces a tension between semantic understanding and image reconstruction. High-level semantic SSL methods such as DINO encourage transformation-invariant global representations for augmentation alignment, while reconstruction-oriented methods such as MAE preserve dense feature grids for spatial grounding but often yield weaker semantic abstractions. We introduce STELLAR, a framework that alleviates this tension by factorizing visual features into a low-rank product of semantic concepts and their spatial distributions. This disentanglement allows us to perform augmentation alignment on semantic tokens while maintaining spatial localization through a localization matrix for reconstruction. We demonstrate that as few as 16 sparse tokens under this factorized form can simultaneously support high-quality reconstruction (2.60 FID) and strong semantic transfer (79.10% ImageNet accuracy). Our results highlight STELLAR as a versatile sparse representation that bridges discriminative and generative vision by separating semantic identity from spatial geometry. Code is available at https://github.com/microsoft/STELLAR.

In standard Transformer architectures, semantic importance is often conflated with activation magnitude, obscuring the geometric structure of latent representations. To disentangle these factors, we introduce PRISM, a complex-valued architecture designed to isolate the computational role of phase. By enforcing a strict unit-norm constraint (|z| = 1) and replacing attention with gated harmonic convolutions, the model is encouraged to utilize subtractive interference in the frequency domain to suppress noise, rather than relying on magnitude-based gating. We utilize this constrained regime to study a hybrid architecture—fusing phase-based routing with standard attention—which achieves improved parameter efficiency and representation quality compared to baselines in our evaluated settings. Mechanistically, interventional ablations indicate that the model carries substantial task-relevant information in phase: preserving phase largely maintains performance, whereas disrupting phase causes severe degradation. Together, these results suggest that phase-based spectral interference is a usable computational mechanism for neural sequence modeling at the evaluated scale.

Understanding how the structure of language can be learned from sentences alone is a central question in both cognitive science and machine learning. Studies of the internal representations of Large Language Models (LLMs) support their ability to parse text when predicting the next word, while representing semantic notions independently of surface form. Yet, which data statistics make these feats possible, and how much data is required, remain largely unknown. Probabilistic context-free grammars (PCFGs) provide a tractable testbed for studying these questions. However, prior work has focused either on the post-hoc characterization of the parsing-like algorithms used by trained networks; or on the learnability of PCFGs with fixed syntax, where parsing is unnecessary. Here, we *(i)* introduce a tunable class of PCFGs in which both the degree of ambiguity and the correlation structure across scales can be controlled; *(ii)* provide a learning mechanism---an inference algorithm inspired by the structure of deep convolutional networks---that links learnability and sample complexity to specific language statistics; and *(iii)* validate our predictions empirically across deep convolutional and transformer-based architectures. Overall, we propose a unifying framework where correlations at different scales lift local ambiguities, enabling the emergence of hierarchical representations of the data.

Vector Symbolic Algebras (VSAs) enable robust neurosymbolic reasoning by encoding information into high-dimensional distributed representations. For continuous domains, Spatial Semantic Pointers (SSPs) extend this framework by mapping variables onto precise toroidal manifolds. While generative models offer a promising avenue for cleaning up (denoising) these representations, standard approaches like Flow Matching assume a flat Euclidean geometry. We demonstrate that this assumption fails for SSPs: Euclidean linear interpolants "cut through" the manifold's interior, destroying the phase and magnitude structure required for accurate decoding. To resolve this, we employ Geodesic Flow Matching, adapting Riemannian transport dynamics to strictly restrict the denoising flow to the SSP manifold. We validate this approach in a Spiking Neural SLAM system, showing that manifold-aware cleanup stabilizes path integration against drift. The method achieves a 72\% reduction in tracking error and enables a 40\% increase in neural efficiency compared to classical baselines.

Classical dynamic programming algorithms such as Smith-Waterman, edit distance, and constituency parsing solve structured combinatorial problems using hard constraints. Soft relaxations replace hard $\max$ or $\min$ operators with differentiable probabilistic models whose gradients correspond to alignment or parsing marginals, but existing approaches typically treat the DP algorithm itself as fixed, relying on hand-tuned gap penalties, edit costs, span penalties, and temperatures. We show how to learn these parameters directly from data: the marginals these algorithms produce are themselves first-order derivatives, so learning them is inherently a second-order problem. We derive efficient Hessian-vector products and cross-Jacobians for twelve dynamic programming algorithms spanning alignment, edit distance, and parsing; both derivative families admit closed-form covariance expressions under the induced Gibbs distribution. We implement these operators as fused CUDA kernels in d$^2$p, achieving $100$--$20{,}000\times$ speedups over standard PyTorch and making end-to-end parameter learning practical at modern scales. We then demonstrate that learning these parameters is critical in practice. In protein structure alignment, freezing gap penalties collapses performance from $0.74$ to $0.32$ $F_1$ (and to $0.13$ at lower encoder capacity), while jointly learning them recovers biologically meaningful gap regimes and reaches $0.75$ $F_1$ and $0.445$ lDDT, $91$% of the TM-align lDDT ceiling. The same machinery transfers to constituency parsing, where a structured CKY CRF matches dense per-span supervision to within $0.003$ $F_1$ on English with no direct parse-tree structural supervision.

Learning latent representations that capture both semantic and spatial information is central to efficient spatio-semantic reasoning. However, many existing approaches rely on implicit latent structures combined with dense feature maps or task-specific heads, limiting computational efficiency and flexibility. We propose WorldComp2D, a novel lightweight representation learning framework that explicitly structures latent space geometry according to object identity and spatial proximity using multiscale \textit{local} receptive fields. This framework consists of (i) a proximity-dependent encoder that maps a given observation into a spatio-semantic latent space and (ii) a localizer that infers the coordinates of objects in the input from the resulting spatio-semantic representation. Using facial landmark localization as a proof-of-concept, we show that, compared to SoTA lightweight models, WorldComp2D reduces the numbers of parameters and FLOPs by up to $4.0\times$ and $2.2\times$, respectively, while maintaining real-time performance on CPU. These results demonstrate that explicitly structured latent spaces provide an efficient and general foundation for spatio-semantic reasoning. This framework is open-sourced at https://github.com/JinSeongmin/WorldComp2D.

Dataset distillation aims to synthesize a compact proxy dataset that is unreadable or non-raw from the original dataset for privacy protection and highly efficient learning. However, previous approaches typically adopt a single-stage distillation paradigm, which suffers from learning specific patterns that overfit on a prior architecture, consequently suppressing the expression of semantics and leading to performance degradation across heterogeneous architectures. To address this, we propose a novel dual-stage distillation framework called ${\textbf{DIVER}}$, which leverages the pre-trained diffusion model to dive deeper into $\textbf{DI}$stilled data $\textbf{V}$ia $\textbf{E}$xpressive semantic $\textbf{R}$ecovery, an entire process of semantic inheritance, guidance, and fusion. Semantic inheritance distills high-level semantics of abstract distilled images into the latent space to filter out architecture-specific ``noise" and retain the intrinsic semantics. Furthermore, semantic guidance improves the preservation of the original semantics by directing the reverse procedure. Finally, semantic fusion is designed to provide semantic guidance only during the concrete phase of the reverse process, preventing semantic ambiguity and artifacts while maintaining the guidance information. Extensive experiments validate the effectiveness and efficiency of our method in improving classical distillation techniques and significantly improving cross-architecture generalization, requiring processing time comparable to raw DiT on ImageNet (256$\times$256) with only 4 GB of GPU memory usage.

Generalized Category Discovery (GCD) aims to learn semantically structured representations for discovering novel categories in unlabeled data using supervision from known classes. Most existing methods rely on self-supervised contrastive learning (CL) with consistency and uniformity objectives. We identify an inherent optimization conflict between these objectives: while uniformity enforces global feature dispersion, it can hinder the formation of class-discriminative and semantically coherent structures. To address this issue, we propose a two-stage framework that decouples representation learning from self-contrastive regularization. The first stage learns category-anchored representations aligned with known class prototypes, while the second stage extends the representation space to novel categories via a consistency objective enhanced with unified semantic regularization. We further introduce a Semantic Exploration Energy mechanism to capture shared semantics across categories and mitigate information loss caused by prototype orthogonalization. The resulting framework, termed *Consistency-under-Unified Semantic Regularization*(**CURE**), achieves state-of-the-art performance on multiple benchmarks and substantially reduces the performance gap between known and novel categories.

Soft labels from teacher models are a de facto practice for knowledge transfer and large-scale dataset distillation (e.g., SRe$^2$L, LPLD). However, when we limit the number of crops per image to reduce the substantial cost of storing precomputed soft labels, these methods suffer severely from local semantic drift: visually ambiguous crops can cause soft supervision to deviate from the image-level ground-truth semantics, leading to persistent errors and a train–test distribution mismatch. We revisit the overlooked role of hard labels and show that, when properly integrated, they can act as a content-invariant semantic anchor that calibrates such drift. We theoretically analyze the emergence of drift under sparse soft-label supervision and demonstrate that hybridizing hard and soft labels restores alignment between visual content and semantic supervision. Building on this insight, we propose a new training paradigm, Hard Label for Alleviating Local Semantic Drift (HALD), which uses hard labels as intermediate corrective signals while preserving the fine-grained benefits of soft labels. Extensive experiments on dataset distillation and large-scale classification benchmarks show consistent generalization improvements. On ImageNet-1K, our method achieves 42.7% accuracy with only 285M soft-label storage (reduces by 100$\times$), outperforming prior state-of-the-art LPLD by 9.0%. Code is available at https://github.com/Jiacheng8/HALD.

Each layer of a Transformer refines the hidden state toward a prediction, an iterative process resembling fixed-point iteration. Yet when should this iteration terminate? Existing early exit methods rely on output confidence as a proxy for internal convergence. We take a more direct approach by examining the geometry of the hidden state trajectory. We find that layer-wise updates exhibit a two-phase structure: large, volatile updates in early layers, followed by small, aligned updates as the model propagates an already-formed representation. The transition is remarkably sharp. This yields a simple criterion: exit when step size vanishes and direction stabilizes. We track the normalized update norm and cosine similarity between consecutive updates, exiting when both indicate convergence. The overhead is $O(d)$ per layer, independent of vocabulary size, requiring no learned components or architectural modifications. On LLaMA-2-7B and LLaMA-2-13B across question answering and commonsense reasoning tasks, this geometric criterion reduces FLOPs by 30--35\% while retaining over 98\% of full-depth accuracy.

Learning semantics is essential for deep learning models to be interpretable and better aligned with human reasoning. Concept-based models approach this by representing classes through meaningful semantic abstractions, but typically treat all concepts as a flat, unstructured set learned at a single neural network layer. This overlooks a fundamental property of human semantic understanding: concepts being organized hierarchically, from general to specific. While deep networks do learn a hierarchy of visual features, this structure is rarely aligned with explicit semantic hierarchies. Drawing on Formal Concept Analysis, we demonstrate that formal concept lattices provide principled semantic scaffolds to guide neural network learning. These lattices naturally identify where in the network concepts should be learned based on their level of generality. This allows the model to develop staged, semantically grounded representations throughout its depth. Empirical results on real-world datasets show that our models produce more interpretable embeddings, support more effective interventions, and learn concept representations that are both meaningful and hierarchically structured.

Hypergraph contrastive learning is an effective paradigm for representation learning on higher-order relational data, yet existing methods largely ignore that hyperedges link nodes with multi-level semantics. Standard contrastive objectives emphasize instance discrimination via hyperspherical uniformity and tend to push embeddings apart in an indiscriminate manner. We show that this leads to a *Hierarchy–Uniformity Conflict*, whose geometric manifestation is *Semantic Flattening*, where the semantic depth of hyperedges collapses into a nearly flat cloud of instances. To address this issue, we introduce **HyperDepth**, a hypergraph contrastive learning framework that moves representations towards a hierarchy–uniformity equilibrium by jointly coordinating spectral and geometric signals. HyperDepth employs a decoupled spectral encoding scheme with adaptive gating so that high-frequency components focus on local instance discrimination while low-frequency components capture global hierarchical structure. On top of this, an energy-based hierarchical alignment module attaches a learnable prototype tree to the representation space and minimizes an interpretable energy functional to recover the semantic depth of hyperedges. Theoretically, under a mild frequency-separation assumption, we show that the local contrastive and global hierarchical objectives operate on orthogonal spectral components and admit equilibrium embeddings that preserve semantic depth while still retaining instance-level discrimination. Experiments on 15 hypergraph datasets and 17 supervised and self-supervised baselines, spanning homophilic and heterophilic regimes, show that HyperDepth attains strong performance with the best average rank.