arXiv subjects

Woojin Kim

Publications and source records attributed to Woojin Kim.

At least 19 recordsLinked to original sources

arXiv2026

TRACE: Learned Proprioceptive Odometry for Legged Robots under Unreliable Contact Conditions

In this paper, we present TRACE (Tokenized Robust Attention for Contact-Aware Estimation), an end-to-end learned proprioceptive odometry estimator for legged robots under unreliable contact conditions. The proposed estimator directly predicts relative displacement, relative rotation, and body-frame velocity from a recent history of onboard inertial and joint measurements. To improve robustness under unreliable contact conditions, we introduce a foot-aware cross-attention module that adaptively weights IMU and leg-wise kinematic tokens without relying on manually defined contact or slip thresholds. The estimator is trained with direct supervision and two physics-inspired auxiliary losses that promote kinematic consistency and reliable use of leg information. To reduce policy-specific overfitting and consequently improve sim-to-real transfer, simulation training incorporates policy randomization, followed by partial real-world fine-tuning of the temporal encoder and prediction head. Experiments across diverse indoor and outdoor terrains demonstrate consistent reductions in position drift compared with classical filtering-based, hybrid, and purely learning-based baselines. Ablation studies further validate the contributions of the proposed training objectives, policy randomization, and real-world fine-tuning, particularly under unreliable contacts and sim-to-real mismatch.

cs.RO↗

arXiv2026

Dynin-Omni: Omnimodal Unified Large Diffusion Language Model

We present Dynin-Omni, the first masked-diffusion-based omnimodal foundation model that unifies text, image, and speech understanding and generation, together with video understanding, within a single architecture. Unlike autoregressive unified models that serialize heterogeneous modalities, or compositional unified models that require orchestration with external modality-specific decoders, Dynin-Omni natively formulates omnimodal modeling as masked diffusion over a shared discrete token space, enabling iterative refinement under bidirectional context. Dynin-Omni adopts a multi-stage training strategy with model-merging-based modality expansion and omnimodal alignment. We evaluate Dynin-Omni across 19 multimodal benchmarks spanning language reasoning, image generation and editing, video understanding, and speech recognition and synthesis. Dynin-Omni achieves 87.6 on GSM8K, 1733.6 on MME-P, 61.4 on VideoMME, 0.87 on GenEval, and 2.1 WER on LibriSpeech test-clean, consistently outperforming existing open-source unified models while remaining competitive with strong modality-specific expert systems. These results demonstrate the potential of masked diffusion as a unified paradigm for any-to-any modeling, providing a flexible foundation for real-time omnimodal systems, unified cross-modal retrieval and generation, and embodied multimodal agents.

cs.CL↗

arXiv2026

VALUEFLOW: Toward Pluralistic and Steerable Value-based Alignment in Large Language Models

Aligning Large Language Models (LLMs) with the diverse spectrum of human values remains a central challenge: preference-based methods often fail to capture deeper motivational principles. Value-based approaches offer a more principled path, yet three gaps persist: extraction often ignores hierarchical structure, evaluation detects presence but not calibrated intensity, and the steerability of LLMs at controlled intensities remains insufficiently understood. To address these limitations, we introduce VALUEFLOW, the first unified framework that spans extraction, evaluation, and steering with calibrated intensity control. The framework integrates three components: (i) HIVES, a hierarchical value embedding space that captures intra- and cross-theory value structure; (ii) the Value Intensity DataBase (VIDB), a large-scale resource of value-labeled texts with intensity estimates derived from ranking-based aggregation; and (iii) an anchor-based evaluator that produces consistent intensity scores for model outputs by ranking them against VIDB panels. Using VALUEFLOW, we conduct a comprehensive large-scale study across ten models and four value theories, identifying asymmetries in steerability and composition laws for multi-value control. This paper establishes a scalable infrastructure for evaluating and controlling value intensity, advancing pluralistic alignment of LLMs.

cs.AI↗

arXiv2026

KTCF: Actionable Recourse in Knowledge Tracing via Counterfactual Explanations for Education

Using Artificial Intelligence to improve teaching and learning benefits greater adaptivity and scalability in education. Knowledge Tracing (KT) is recognized for student modeling task due to its superior performance and application potential in education. To this end, we conceptualize and investigate counterfactual explanation as the connection from XAI for KT to education. Counterfactual explanations offer actionable recourse, are inherently causal and local, and easy for educational stakeholders to understand who are often non-experts. We propose KTCF, a counterfactual explanation generation method for KT that accounts for knowledge concept relationships, and a post-processing scheme that converts a counterfactual explanation into a sequence of educational instructions. We experiment on a large-scale educational dataset and show our KTCF method achieves superior and robust performance over existing methods, with improvements ranging from 5.7% to 34% across metrics. Additionally, we provide a qualitative evaluation of our post-processing scheme, demonstrating that the resulting educational instructions help in reducing large study burden. We show that counterfactuals have the potential to advance the responsible and practical use of AI in education. Future works on XAI for KT may benefit from educationally grounded conceptualization and developing stakeholder-centered methods.

cs.LG↗

arXiv2025

Don't Let It Fade: Preserving Edits in Diffusion Language Models via Token Timestep Allocation

While diffusion language models (DLMs) enable fine-grained refinement, their practical controllability remains fragile. We identify and formally characterize a central failure mode called update forgetting, in which uniform and context agnostic updates induce token level fluctuations across timesteps, erasing earlier semantic edits and disrupting the cumulative refinement process, thereby degrading fluency and coherence. As this failure originates in uniform and context agnostic updates, effective control demands explicit token ordering. We propose Token Timestep Allocation (TTA), which realizes soft and semantic token ordering via per token timestep schedules: critical tokens are frozen early, while uncertain tokens receive continued refinement. This timestep based ordering can be instantiated as either a fixed policy or an adaptive policy driven by task signals, thereby supporting a broad spectrum of refinement strategies. Because it operates purely at inference time, it applies uniformly across various DLMs and naturally extends to diverse supervision sources. Empirically, TTA improves controllability and fluency: on sentiment control, it yields more than 20 percent higher accuracy and nearly halves perplexity using less than one fifth the steps; in detoxification, it lowers maximum toxicity (12.2 versus 14.5) and perplexity (26.0 versus 32.0). Together, these results demonstrate that softened ordering via timestep allocation is the critical lever for mitigating update forgetting and achieving stable and controllable diffusion text generation.

cs.CL↗

arXiv2025

On Integer Programming for the Binarized Neural Network Verification Problem

Binarized neural networks (BNNs) are feedforward neural networks with binary weights and activation functions. In the context of using a BNN for classification, the verification problem seeks to determine whether a small perturbation of a given input can lead it to be misclassified by the BNN, and the robustness of the BNN can be measured by solving the verification problem over multiple inputs. The BNN verification problem can be formulated as an integer programming (IP) problem. However, the natural IP formulation is often challenging to solve due to a large integrality gap induced by big-$M$ constraints. We present two techniques to improve the IP formulation. First, we introduce a new method for obtaining a linear objective for the multi-class setting. Second, we introduce a new technique for generating valid inequalities for the IP formulation that exploits the recursive structure of BNNs. We find that our techniques enable verifying BNNs against a higher range of input perturbation than existing IP approaches within a limited time.

cs.LG↗

arXiv2025

Interleaving Distance as a Galois-Edit Distance

The concept of edit distance, which dates back to the 1960s in the context of comparing word strings, has since found numerous applications with various adaptations in computer science, computational biology, and applied topology. By contrast, the interleaving distance, introduced in the 2000s within the study of persistent homology, has become a foundational metric in topological data analysis. In this work, we show that the interleaving distance on finitely presented single- and multi-parameter persistence modules can be formulated as a so-called Galois-edit distance. The key lies in clarifying a connection between the Galois connection and the interleaving distance, via the established relation between the interleaving distance and free presentations of persistence modules. In addition to offering new perspectives on the interleaving distance, we expect that our findings will facilitate the study of stability properties of invariants for multi-parameter persistence modules. As an application of the Galois-edit formulation of the interleaving distance, we present an alternative proof of the well-known bottleneck stability theorem.

math.AT↗

arXiv2025

MMPB: It's Time for Multi-Modal Personalization

Visual personalization is essential in user-facing AI systems such as smart homes and healthcare, where aligning model behavior with user-centric concepts is critical. However, recent large Vision-Language Models (VLMs), despite their broad applicability, remain underexplored in their ability to adapt to individual users. In this paper, we introduce MMPB, the first extensive benchmark for evaluating VLMs on personalization. MMPB comprises 10k image-query pairs and includes 111 personalizable concepts across four categories: humans, animals, objects, and characters, with the human category enriched with preference-grounded queries. We structure personalization into three main task types, each highlighting a different key property of VLMs. Using 23 widely used VLMs including both open- and closed-source models, we evaluate personalization performance via a three-stage protocol: concept injection, multi-turn dialogue, and personalized querying. Our findings indicate that most VLMs (including some closed-source models) struggle with personalization, particularly in maintaining consistency over dialogue, handling user preferences, and adapting to visual cues. Our analysis reveals that the challenges in VLM personalization (such as refusal behaviors and long-context forgetting) highlight substantial room for improvement. By identifying these limitations and offering a scalable benchmark, MMPB offers valuable insights and a solid foundation for future research toward truly personalized multi-modal AI. Project Page: aidaslab.github.io/MMPB

cs.CV↗

arXiv2025

Limit Theorems for Verbose Persistence Diagrams

The persistence diagram is a central object in the study of persistent homology and has also been investigated in the context of random topology. The more recent notion of the verbose diagram (a.k.a. verbose barcode) is a refinement of the persistence diagram. Whereas the persistence diagram is a complete invariant of persistent homology, the verbose persistence diagram is a complete invariant of the one-level higher object -- a filtered chain complex. It therefore strictly contains the persistence diagram, both in form and in the amount of information it encodes. Concretely, the verbose diagram incorporates ephemeral features that arise in a filtered topological space, representing them as additional points along the diagonal. In this work, we initiate the study of random verbose diagrams. We establish a strong law of large numbers for verbose diagrams as a random point cloud grows in size -- that is, we prove the existence of a limiting verbose diagram, viewed as a measure on the half-plane on and above the diagonal. Also, we characterize its support and compute its total mass. Along the way, we extend the notion of the persistent Betti number, reveal the relation between this extended notion and the verbose diagram (which is an extension of the fundamental lemma of persistent homology), and establish results on the asymptotic behavior of the extended persistent Betti numbers. This work extends the main results of the work by Hiraoka, Shirai, and Trinh and its sequel by Shirai and Suzaki to the setting of verbose diagrams.

math.AT↗

arXiv2025

SECOND: Mitigating Perceptual Hallucination in Vision-Language Models via Selective and Contrastive Decoding

Despite significant advancements in Vision-Language Models (VLMs), the performance of existing VLMs remains hindered by object hallucination, a critical challenge to achieving accurate visual understanding. To address this issue, we propose SECOND: Selective and Contrastive Decoding, a novel approach that enables VLMs to effectively leverage multi-scale visual information with an object-centric manner, closely aligning with human visual perception. SECOND progressively selects and integrates multi-scale visual information, facilitating a more precise interpretation of images. By contrasting these visual information iteratively, SECOND significantly reduces perceptual hallucinations and outperforms a wide range of benchmarks. Our theoretical analysis and experiments highlight the largely unexplored potential of multi-scale application in VLMs, showing that prioritizing and contrasting across scales outperforms existing methods.

cs.CV↗

arXiv2025

Counterfactual Fairness Evaluation of Machine Learning Models on Educational Datasets

As machine learning models are increasingly used in educational settings, from detecting at-risk students to predicting student performance, algorithmic bias and its potential impacts on students raise critical concerns about algorithmic fairness. Although group fairness is widely explored in education, works on individual fairness in a causal context are understudied, especially on counterfactual fairness. This paper explores the notion of counterfactual fairness for educational data by conducting counterfactual fairness analysis of machine learning models on benchmark educational datasets. We demonstrate that counterfactual fairness provides meaningful insight into the causality of sensitive attributes and causal-based individual fairness in education.

cs.CY↗

arXiv2025

Using Multiple Outcomes to Adjust Standard Errors for Spatial Correlation

Empirical research in economics often examines the behavior of agents located in a geographic space. In such cases, statistical inference is complicated by the interdependence of economic outcomes across locations. A common approach to account for this dependence is to cluster standard errors based on a predefined geographic partition. A second strategy is to model dependence in terms of the distance between units. Dependence, however, does not necessarily stop at borders and is typically not determined by distance alone. This paper introduces a method that leverages observations of multiple outcomes to adjust standard errors for cross-sectional dependence. Specifically, a researcher, while interested in a particular outcome variable, often observes dozens of other variables for the same units. We show that these outcomes can be used to estimate dependence under the assumption that the cross-sectional correlation structure is shared across outcomes. We develop a procedure, which we call Thresholding Multiple Outcomes (TMO), that uses this estimate to adjust standard errors in a given regression setting. We show that adjustments of this form can lead to sizable reductions in the bias of standard errors in calibrated U.S. county-level regressions. Re-analyzing nine recent papers, we find that the proposed correction can make a substantial difference in practice.

econ.EM↗

arXiv2025

Super-Polynomial Growth of the Generalized Persistence Diagram

The Generalized Persistence Diagram (GPD) for multi-parameter persistence naturally extends the classical notion of persistence diagram for one-parameter persistence. However, unlike its classical counterpart, computing the GPD remains a significant challenge. The main hurdle is that, while the GPD is defined as the Möbius inversion of the Generalized Rank Invariant (GRI), computing the GRI is intractable due to the formidable size of its domain, i.e., the set of all connected and convex subsets in a finite grid in $\mathbb{R}^d$ with $d \geq 2$. This computational intractability suggests seeking alternative approaches to computing the GPD. In order to study the complexity associated to computing the GPD, it is useful to consider its classical one-parameter counterpart, where for a filtration of a simplicial complex with $n$ simplices, its persistence diagram contains at most $n$ points. This observation leads to the question: 'Given a $d$-parameter simplicial filtration, could the cardinality of its GPD (specifically, the support of the GPD) also be bounded by a polynomial in the number of simplices in the filtration?' This is the case for $d=1$, where we compute the persistence diagram directly at the simplicial filtration level. If this were also the case for $d\geq2$, it might be possible to compute the GPD directly and much more efficiently without relying on the GRI. We show that the answer to the question above is negative, demonstrating the inherent difficulty of computing the GPD. More specifically, we construct a sequence of $d$-parameter simplicial filtrations where the cardinalities of their GPDs are not bounded by any polynomial in the the number of simplices. Furthermore, we show that several commonly used methods for constructing multi-parameter filtrations can give rise to such "wild" filtrations.

math.AT↗

arXiv2025

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent

The generalized persistence diagram (GPD) is a natural extension of the classical persistence barcode to the setting of multi-parameter persistence and beyond. The GPD is defined as an integer-valued function whose domain is the set of intervals in the indexing poset of a persistence module, and is known to be able to capture richer topological information than its single-parameter counterpart. However, computing the GPD is computationally prohibitive due to the sheer size of the interval set. Restricting the GPD to a subset of intervals provides a way to manage this complexity, compromising discriminating power to some extent. However, identifying and computing an effective restriction of the domain that minimizes the loss of discriminating power remains an open challenge. In this work, we introduce a novel method for optimizing the domain of the GPD through gradient descent optimization. To achieve this, we introduce a loss function tailored to optimize the selection of intervals, balancing computational efficiency and discriminative accuracy. The design of the loss function is based on the known erosion stability property of the GPD. We showcase the efficiency of our sparsification method for dataset classification in supervised machine learning. Experimental results demonstrate that our sparsification method significantly reduces the time required for computing the GPDs associated to several datasets, while maintaining classification accuracies comparable to those achieved using full GPDs. Our method thus opens the way for the use of GPD-based methods to applications at an unprecedented scale.

math.AT↗

arXiv2024

Barcoding Invariants and Their Comparison

The persistence barcode, which can be obtained from the interval decomposition of a persistence module, plays a pivotal role in applications of persistent homology. For multi-parameter persistent homology, which lacks a complete discrete invariant, and where persistence modules are no longer always interval decomposable, many alternative invariants have been proposed. Many of these invariants are akin to persistence barcodes, in that they assign (signed) multisets of intervals. Furthermore, to any interval decomposable module, those invariants assign the multiset of intervals that correspond to its summands. Naturally, identifying the relationships among invariants of this type, or ordering them by their discriminating power, is a fundamental question. To address this, we formalize the notion of barcoding invariants and compare them by comparing their kernels, which are taken as a measure of their (in-)discriminating power. We show that any two different barcoding invariants $f$ and $g$ with the same basis are incomparable; i.e. one cannot be strictly finer than the other. Furthermore, we identify what we call a transfer isomorphism between the kernels of $f$ and $g$, implying that, given any pair of persistence modules that are not distinguishable via $f$ but are via $g$, one can generate another pair of persistence modules that are so via $f$, but not via $g$. One implication of the existence of the transfer isomorphism is that introducing a new barcoding invariant does not add any value in terms of its generic discriminating power, even if it is distinct from the existing barcoding invariants. Another implication is a novel characterization of the generalized persistence diagram without involving M\"obius inversion. Along the way, we generalize several recent results on the discriminative power of invariants for poset representations within our unified framework.

math.AT↗

arXiv2024

The Generalized Rank Invariant: Möbius invertibility, Discriminating Power, and Connection to Other Invariants

In addition to inherent computational challenges, the absence of a canonical method for quantifying `persistence' in multi-parameter persistent homology remains a hurdle in its application. One of the best known quantifications of persistence for multi-parameter persistent homology is the rank invariant, which has recently evolved into the generalized rank invariant (GRI) by naturally extending its domain. This extension enables us to quantify persistence across a broader range of regions in the indexing poset compared to the rank invariant. However, the size of the domain of the GRI is generally formidable, making it desirable to restrict its domain to a more manageable subset for computational purposes. The foremost questions regarding such a restriction of the domain are: (1) How to restrict, if possible, the domain of the GRI without any loss of information? (2) When can we more compactly encode the GRI as a `persistence diagram'? (3) What is the trade-off between computational efficiency and the discriminating power of the GRI as the amount of the restriction on the domain varies? (4) What proxies exist for persistence diagrams in the multi-parameter setting that can be derived from the GRI? To address the first three questions, we generalize and axiomatize the classic fundamental lemma of persistent homology via the notion of Möbius invertibility of the GRI which we propose. This extension also contextualizes known results regarding the (generalized) rank invariant within the classical theory of Möbius inversion. We conduct a comprehensive comparison between Möbius invertibility and other existing concepts related to the structural simplicity of persistence modules. We address the fourth question through the notion of motivic invariants. We demonstrate that many invariants from the literature can be both derived from the GRI and recast as motivic invariants.

math.AT↗

arXiv2024

Bigraded Betti numbers and Generalized Persistence Diagrams

Commutative diagrams of vector spaces and linear maps over $\mathbb{Z}^2$ are objects of interest in topological data analysis (TDA) where this type of diagrams are called 2-parameter persistence modules. Given that quiver representation theory tells us that such diagrams are of wild type, studying informative invariants of a 2-parameter persistence module $M$ is of central importance in TDA. One of such invariants is the generalized rank invariant, recently introduced by Kim and Mémoli. Via the Möbius inversion of the generalized rank invariant of $M$, we obtain a collection of connected subsets $I\subset\mathbb{Z}^2$ with signed multiplicities. This collection generalizes the well known notion of persistence barcode of a persistence module over $\mathbb{R}$ from TDA. In this paper we show that the bigraded Betti numbers of $M$, a classical algebraic invariant of $M$, are obtained by counting the corner points of these subsets $I$s. Along the way, we verify that an invariant of 2-parameter persistence modules called the interval decomposable approximation (introduced by Asashiba et al.) also encodes the bigraded Betti numbers in a similar fashion. We also show that the aforementioned results are optimal in the sense that they cannot be extended to $d$-parameter persistence modules for $d \geq 3$.

math.AT↗

arXiv2023

MKConv: Multidimensional Feature Representation for Point Cloud Analysis

Despite the remarkable success of deep learning, an optimal convolution operation on point clouds remains elusive owing to their irregular data structure. Existing methods mainly focus on designing an effective continuous kernel function that can handle an arbitrary point in continuous space. Various approaches exhibiting high performance have been proposed, but we observe that the standard pointwise feature is represented by 1D channels and can become more informative when its representation involves additional spatial feature dimensions. In this paper, we present Multidimensional Kernel Convolution (MKConv), a novel convolution operator that learns to transform the point feature representation from a vector to a multidimensional matrix. Unlike standard point convolution, MKConv proceeds via two steps. (i) It first activates the spatial dimensions of local feature representation by exploiting multidimensional kernel weights. These spatially expanded features can represent their embedded information through spatial correlation as well as channel correlation in feature space, carrying more detailed local structure information. (ii) Then, discrete convolutions are applied to the multidimensional features which can be regarded as a grid-structured matrix. In this way, we can utilize the discrete convolutions for point cloud data without voxelization that suffers from information loss. Furthermore, we propose a spatial attention module, Multidimensional Local Attention (MLA), to provide comprehensive structure awareness within the local point set by reweighting the spatial feature dimensions. We demonstrate that MKConv has excellent applicability to point cloud processing tasks including object classification, object part segmentation, and scene semantic segmentation with superior results.

cs.CV↗