As attitude and motion sensing components, inertial sensors are widely used in various portable devices, covering consumer electronics, sports health, aerospace, etc. But the severe intrinsic errors of inertial sensors heavily restrain their function implementation, especially the advanced functionality, including motion trajectory recovery and motion semantic recognition, which attracts considerable attention. As a mainstream signal processing method, wavelet is hailed as the mathematical microscope of signal due to the plentiful and diverse wavelet basis functions. However, complicated noise types and application scenarios of inertial sensors make selecting wavelet basis perplexing. To this end, we propose a wavelet dynamic selection network (WDSNet), which intelligently selects the appropriate wavelet basis for variable inertial signals. In addition, existing deep learning architectures excel at extracting features from input data but neglect to learn the characteristics of target categories, which is essential to enhance the category awareness capability, thereby improving the selection of wavelet basis. Therefore, we propose a category representation mechanism (CRM), which enables the network to extract and represent category features without increasing trainable parameters. Furthermore, CRM transforms the common fully connected network into category representations, which provide closer supervision to the feature extractor than the far and trivial one-hot classification labels. We call this process of imposing interpretability on a network and using it to supervise the feature extractor the feature supervision mechanism, and its effectiveness is demonstrated experimentally and theoretically in this paper. The enhanced inertial signal can perform impracticable tasks with regard to the original signal, such as trajectory reconstruction. Both quantitative and visual results show that WDSNet outperforms the existing methods. Remarkably, WDSNet, as a weakly-supervised method, achieves the state-of-the-art performance of all the compared fully-supervised methods.
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Optimal transport (OT) is an important methodology to measure distribution discrepancy, which has achieved promising performance in artificial intelligence applications, e.g., unsupervised domain adaptation. However, from the view of transportation, there are still limitations: 1) the local discriminative structures for downstream tasks, e.g., cluster structure for classification, cannot be explicitly admitted by the learned OT plan; 2) the entropy regularization induces a dense OT plan with increasing uncertainty. To tackle these issues, we propose a novel Probability-Polarized OT (PPOT) framework, which can characterize the structure of OT plan explicitly. Specifically, the probability polarization mechanism is proposed to guide the optimization direction of OT plan, which generates a clear margin between similar and dissimilar transport pairs and reduces the uncertainty. Further, a dynamic mechanism for margin is developed by incorporating task-related information into the polarization, which directly captures the intra/inter class correspondence for knowledge transportation. A mathematical understanding for PPOT is provided from the view of gradient, which ensures interpretability. Extensive experiments on several datasets validate the effectiveness and empirical efficiency of PPOT.
The Adam optimizer is a popular choice in contemporary deep learning due to its strong empirical performance. However we observe that in privacy sensitive scenarios, the traditional use of Differential Privacy (DP) with the Adam optimizer leads to sub-optimal performance on several tasks. We find that this performance degradation is due to a DP bias in Adam's second moment estimator, introduced by the addition of independent noise in the gradient computation to enforce DP guarantees. This DP bias leads to a different scaling for low variance parameter updates, that is inconsistent with the behavior of non-private Adam, and Adam's sign descent interpretation. We propose the DP-AdamBC optimization algorithm, which corrects for the bias in the second moment estimation and retrieves the expected behaviour of Adam. Empirically, DP-AdamBC significantly improves the optimization performance of DP-Adam by up to 3.5% in final accuracy in image, text, and graph node classification tasks.
This work explores the zero-shot adaptation capability of semantic skills, semantically interpretable experts' behavior patterns, in cross-domain settings, where a user input in interleaved multi-modal snippets can prompt a new long-horizon task for different domains. In these cross-domain settings, we present a semantic skill translator framework SemTra which utilizes a set of multi-modal models to extract skills from the snippets, and leverages the reasoning capabilities of a pretrained language model to adapt these extracted skills to the target domain. The framework employs a two-level hierarchy for adaptation: task adaptation and skill adaptation. During task adaptation, seq-to-seq translation by the language model transforms the extracted skills into a semantic skill sequence, which is tailored to fit the cross-domain contexts. Skill adaptation focuses on optimizing each semantic skill for the target domain context, through parametric instantiations that are facilitated by language prompting and contrastive learning-based context inferences. This hierarchical adaptation empowers the framework to not only infer a complex task specification in one-shot from the interleaved multi-modal snippets, but also adapt it to new domains with zero-shot learning abilities. We evaluate our framework with Meta-World, Franka Kitchen, RLBench, and CARLA environments. The results clarify the framework's superiority in performing long-horizon tasks and adapting to different domains, showing its broad applicability in practical use cases, such as cognitive robots interpreting abstract instructions and autonomous vehicles operating under varied configurations.
Cognitive diagnosis assessment is a fundamental and crucial task for student learning. It models the student-exercise interaction, and discovers the students' proficiency levels on each knowledge attribute. In real-world intelligent education systems, generalization and interpretability of cognitive diagnosis methods are of equal importance. However, most existing methods can hardly make the best of both worlds due to the complicated student-exercise interaction. To this end, this paper proposes a symbolic cognitive diagnosis~(SCD) framework to simultaneously enhance generalization and interpretability. The SCD framework incorporates the symbolic tree to explicably represent the complicated student-exercise interaction function, and utilizes gradient-based optimization methods to effectively learn the student and exercise parameters. Meanwhile, the accompanying challenge is that we need to tunnel the discrete symbolic representation and continuous parameter optimization. To address this challenge, we propose to hybridly optimize the representation and parameters in an alternating manner. To fulfill SCD, it alternately learns the symbolic tree by derivative-free genetic programming and learns the student and exercise parameters via gradient-based Adam. The extensive experimental results on various real-world datasets show the superiority of SCD on both generalization and interpretability. The ablation study verifies the efficacy of each ingredient in SCD, and the case study explicitly showcases how the interpretable ability of SCD works.
This paper is a contribution to neural network semantics, a foundational framework for neuro-symbolic AI. The key insight of this theory is that logical operators can be mapped to operators on neural network states. In this paper, we do this for a neural network learning operator. We map a dynamic operator [φ] to iterated Hebbian learning, a simple learning policy that updates a neural network by repeatedly applying Hebb's learning rule until the net reaches a fixed-point. Our main result is that we can "translate away" [φ]-formulas via reduction axioms. This means that completeness for the logic of iterated Hebbian learning follows from completeness of the base logic. These reduction axioms also provide (1) a human-interpretable description of iterated Hebbian learning as a kind of plausibility upgrade, and (2) an approach to building neural networks with guarantees on what they can learn.
GINN-LP: A Growing Interpretable Neural Network for Discovering Multivariate Laurent Polynomial Equations
PDF ↗Traditional machine learning is generally treated as a black-box optimization problem and does not typically produce interpretable functions that connect inputs and outputs. However, the ability to discover such interpretable functions is desirable. In this work, we propose GINN-LP, an interpretable neural network to discover the form and coefficients of the underlying equation of a dataset, when the equation is assumed to take the form of a multivariate Laurent Polynomial. This is facilitated by a new type of interpretable neural network block, named the “power-term approximator block”, consisting of logarithmic and exponential activation functions. GINN-LP is end-to-end differentiable, making it possible to use backpropagation for training. We propose a neural network growth strategy that will enable finding the suitable number of terms in the Laurent polynomial that represents the data, along with sparsity regularization to promote the discovery of concise equations. To the best of our knowledge, this is the first model that can discover arbitrary multivariate Laurent polynomial terms without any prior information on the order. Our approach is first evaluated on a subset of data used in SRBench, a benchmark for symbolic regression. We first show that GINN-LP outperforms the state-of-the-art symbolic regression methods on datasets generated using 48 real-world equations in the form of multivariate Laurent polynomials. Next, we propose an ensemble method that combines our method with a high-performing symbolic regression method, enabling us to discover non-Laurent polynomial equations. We achieve state-of-the-art results in equation discovery, showing an absolute improvement of 7.1% over the best contender, by applying this ensemble method to 113 datasets within SRBench with known ground-truth equations.
Despite the recent progress in deep neural networks (DNNs), it remains challenging to explain the predictions made by DNNs. Existing explanation methods for DNNs mainly focus on post-hoc explanations where another explanatory model is employed to provide explanations. The fact that post-hoc methods can fail to reveal the actual original reasoning process of DNNs raises the need to build DNNs with built-in interpretability. Motivated by this, many self-explaining neural networks have been proposed to generate not only accurate predictions but also clear and intuitive insights into why a particular decision was made. However, existing self-explaining networks are limited in providing distribution-free uncertainty quantification for the two simultaneously generated prediction outcomes (i.e., a sample's final prediction and its corresponding explanations for interpreting that prediction). Importantly, they also fail to establish a connection between the confidence values assigned to the generated explanations in the interpretation layer and those allocated to the final predictions in the ultimate prediction layer. To tackle the aforementioned challenges, in this paper, we design a novel uncertainty modeling framework for self-explaining networks, which not only demonstrates strong distribution-free uncertainty modeling performance for the generated explanations in the interpretation layer but also excels in producing efficient and effective prediction sets for the final predictions based on the informative high-level basis explanations. We perform the theoretical analysis for the proposed framework. Extensive experimental evaluation demonstrates the effectiveness of the proposed uncertainty framework.
While shallow decision trees may be interpretable, larger ensemble models like gradient-boosted trees, which often set the state of the art in machine learning problems involving tabular data, still remain black box models. As a remedy, the Shapley value (SV) is a well-known concept in explainable artificial intelligence (XAI) research for quantifying additive feature attributions of predictions. The model-specific TreeSHAP methodology solves the exponential complexity for retrieving exact SVs from tree-based models. Expanding beyond individual feature attribution, Shapley interactions reveal the impact of intricate feature interactions of any order. In this work, we present TreeSHAP-IQ, an efficient method to compute any-order additive Shapley interactions for predictions of tree-based models. TreeSHAP-IQ is supported by a mathematical framework that exploits polynomial arithmetic to compute the interaction scores in a single recursive traversal of the tree, akin to Linear TreeSHAP. We apply TreeSHAP-IQ on state-of-the-art tree ensembles and explore interactions on well-established benchmark datasets.
Decision Trees (DTs) are commonly used for many machine learning tasks due to their high degree of interpretability. However, learning a DT from data is a difficult optimization problem, as it is non-convex and non-differentiable. Therefore, common approaches learn DTs using a greedy growth algorithm that minimizes the impurity locally at each internal node. Unfortunately, this greedy procedure can lead to inaccurate trees. In this paper, we present a novel approach for learning hard, axis-aligned DTs with gradient descent. The proposed method uses backpropagation with a straight-through operator on a dense DT representation, to jointly optimize all tree parameters. Our approach outperforms existing methods on binary classification benchmarks and achieves competitive results for multi-class tasks. The implementation is available under: https://github.com/s-marton/GradTree
Semi-supervised time-series classification could effectively alleviate the issue of lacking labeled data. However, existing approaches usually ignore model interpretability, making it difficult for humans to understand the principles behind the predictions of a model. Shapelets are a set of discriminative subsequences that show high interpretability in time series classification tasks. Shapelet learning-based methods have demonstrated promising classification performance. Unfortunately, without enough labeled data, the shapelets learned by existing methods are often poorly discriminative, and even dissimilar to any subsequence of the original time series. To address this issue, we propose the Diffusion Language-Shapelets model (DiffShape) for semi-supervised time series classification. In DiffShape, a self-supervised diffusion learning mechanism is designed, which uses real subsequences as a condition. This helps to increase the similarity between the learned shapelets and real subsequences by using a large amount of unlabeled data. Furthermore, we introduce a contrastive language-shapelets learning strategy that improves the discriminability of the learned shapelets by incorporating the natural language descriptions of the time series. Experiments have been conducted on the UCR time series archive, and the results reveal that the proposed DiffShape method achieves state-of-the-art performance and exhibits superior interpretability over baselines.
Recently, neural module networks (NMNs) have yielded ongoing success in answering compositional visual questions, especially those involving multi-hop visual and logical reasoning. NMNs decompose the complex question into several sub-tasks using instance-modules from the reasoning paths of that question and then exploit intermediate supervisions to guide answer prediction, thereby improving inference interpretability. However, their performance may be hindered due to sketchy modeling of intermediate supervisions. For instance, (1) a prior assumption that each instance-module refers to only one grounded object yet overlooks other potentially associated grounded objects, impeding full cross-modal alignment learning; (2) IoU-based intermediate supervisions may introduce noise signals as the bounding box overlap issue might guide the model's focus towards irrelevant objects. To address these issues, a novel method, Detection-based Intermediate Supervision (DIS), is proposed, which adopts a generative detection framework to facilitate multiple grounding supervisions via sequence generation. As such, DIS offers more comprehensive and accurate intermediate supervisions, thereby boosting answer prediction performance. Furthermore, by considering intermediate results, DIS enhances the consistency in answering compositional questions and their sub-questions. Extensive experiments demonstrate the superiority of our proposed DIS, showcasing both improved accuracy and state-of-the-art reasoning consistency compared to prior approaches.
We consider the problem of predictive modeling from irregularly and sparsely sampled longitudinal data with unknown, complex correlation structures and abrupt discontinuities. To address these challenges, we introduce a novel inducing clusters longitudinal deep kernel Gaussian Process (ICDKGP). ICDKGP approximates the data generating process by a zero-mean GP with a longitudinal deep kernel that models the unknown complex correlation structure in the data and a deterministic non-zero mean function to model the abrupt discontinuities. To improve the scalability and interpretability of ICDKGP, we introduce inducing clusters corresponding to centers of clusters in the training data. We formulate the training of ICDKGP as a constrained optimization problem and derive its evidence lower bound. We introduce a novel relaxation of the resulting problem which under rather mild assumptions yields a solution with error bounded relative to the original problem. We describe the results of extensive experiments demonstrating that ICDKGP substantially outperforms the state-of-the-art longitudinal methods on data with both smoothly and non-smoothly varying outcomes.
Time-series generation has crucial practical significance for decision-making under uncertainty. Existing methods have various limitations like accumulating errors over time, significantly impacting downstream tasks. We develop a novel generation method, DT-VAE, that incorporates generalizable domain knowledge, is mathematically justified, and significantly outperforms existing methods by mitigating error accumulation through a cumulative difference learning mechanism. We evaluate the performance of DT-VAE on several downstream tasks using both semi-synthetic and real time-series datasets, including benchmark datasets and our newly curated COVID-19 hospitalization datasets. The COVID-19 datasets enrich existing resources for time-series analysis. Additionally, we introduce Diverse Trend Preserving (DTP), a time-series clustering-based evaluation for direct and interpretable assessments of generated samples, serving as a valuable tool for evaluating time-series generative models.
Graph-based multimedia data clustering has attracted much attention due to the impressive clustering performance for arbitrarily shaped multimedia data. However, existing graph-based clustering methods need post-processing to get labels for multimedia data with high computational complexity. Moreover, it is sub-optimal for label learning due to the fact that they exploit the complementary information embedded in data with different types pixel by pixel. To handle these problems, we present a novel label learning model with good interpretability for clustering. To be specific, our model decomposes anchor graph into the products of two matrices with orthogonal non-negative constraint to directly get soft label without any post-processing, which remarkably reduces the computational complexity. To well exploit the complementary information embedded in multimedia data, we introduce tensor Schatten p-norm regularization on the label tensor which is composed of soft labels of multimedia data. The solution can be obtained by iteratively optimizing four decoupled sub-problems, which can be solved more efficiently with good convergence. Experimental results on various datasets demonstrate the efficiency of our model.
Existing approaches to Implicit Neural Representation (INR) can be interpreted as a global scene representation via a linear combination of Fourier bases of different frequencies. However, such universal basis functions can limit the representation capability in local regions where a specific component is unnecessary, resulting in unpleasant artifacts. To this end, we introduce a learnable spatial mask that effectively dispatches distinct Fourier bases into respective regions. This translates into collaging Fourier patches, thus enabling an accurate representation of complex signals. Comprehensive experiments demonstrate the superior reconstruction quality of the proposed approach over existing baselines across various INR tasks, including image fitting, video representation, and 3D shape representation. Our method outperforms all other baselines, improving the image fitting PSNR by over 3dB and 3D reconstruction to 98.81 IoU and 0.0011 Chamfer Distance.
Prototypical self-explainable classifiers have emerged to meet the growing demand for interpretable AI systems. These classifiers are designed to incorporate high transparency in their decisions by basing inference on similarity with learned prototypical objects. While these models are designed with diversity in mind, the learned prototypes often do not sufficiently represent all aspects of the input distribution, particularly those in low density regions. Such lack of sufficient data representation, known as representation bias, has been associated with various detrimental properties related to machine learning diversity and fairness. In light of this, we introduce pantypes, a new family of prototypical objects designed to capture the full diversity of the input distribution through a sparse set of objects. We show that pantypes can empower prototypical self-explainable models by occupying divergent regions of the latent space and thus fostering high diversity, interpretability and fairness.
Measuring Self-Supervised Representation Quality for Downstream Classification Using Discriminative Features
PDF ↗Self-supervised learning (SSL) has shown impressive results in downstream classification tasks. However, there is limited work in understanding their failure modes and interpreting their learned representations. In this paper, we study the representation space of state-of-the-art self-supervised models including SimCLR, SwaV, MoCo, BYOL, DINO, SimSiam, VICReg and Barlow Twins. Without the use of class label information, we discover discriminative features that correspond to unique physical attributes in images, present mostly in correctly-classified representations. Using these features, we can compress the representation space by up to$40% without significantly affecting linear classification performance. We then propose Self-Supervised Representation Quality Score (or Q-Score), an unsupervised score that can reliably predict if a given sample is likely to be mis-classified during linear evaluation, achieving AUPRC of 91.45 on ImageNet-100 and 78.78 on ImageNet-1K. Q-Score can also be used as a regularization term on pre-trained encoders to remedy low-quality representations. Fine-tuning with Q-Score regularization can boost the linear probing accuracy of SSL models by up to 5.8% on ImageNet-100 and 3.7% on ImageNet-1K compared to their baselines. Finally, using gradient heatmaps and Salient ImageNet masks, we define a metric to quantify the interpretability of each representation. We show that discriminative features are strongly correlated to core attributes and, enhancing these features through Q-score regularization makes SSL representations more interpretable.
Explaining the decisions made by Graph Neural Networks (GNNs) is vital for establishing trust and ensuring fairness in critical applications such as medicine and science. The prevalence of hierarchical structure in real-world graphs/networks raises an important question on GNN interpretability: "On each level of the graph structure, which specific fraction imposes the highest influence over the prediction?" Currently, the prevailing two categories of methods are incapable of achieving multi-level GNN explanation due to their flat or motif-centric nature. In this work, we formulate the problem of learning multi-level explanations out of GNN models and introduce a stratified explainer module, namely STFExplainer, that utilizes the concept of sufficient expansion to generate explanations on each stratum. Specifically, we learn a higher-level subgraph generator by leveraging both hierarchical structure and GNN-encoded input features. Experiment results on both synthetic and real-world datasets demonstrate the superiority of our stratified explainer on standard interpretability tasks and metrics such as fidelity and explanation recall, with an average improvement of 11% and 8% over the best alternative on each data type. The case study on material domains also confirms the value of our approach through detected multi-level graph patterns accurately reconstructing the knowledge-based ground truth.
Generating music with emotion is an important task in automatic music generation, in which emotion is evoked through a variety of musical elements (such as pitch and duration) that change over time and collaborate with each other. However, prior research on deep learning-based emotional music generation has rarely explored the contribution of different musical elements to emotions, let alone the deliberate manipulation of these elements to alter the emotion of music, which is not conducive to fine-grained element-level control over emotions. To address this gap, we present a novel approach employing musical element-based regularization in the latent space to disentangle distinct elements, investigate their roles in distinguishing emotions, and further manipulate elements to alter musical emotions. Specifically, we propose a novel VQ-VAE-based model named MusER. MusER incorporates a regularization loss to enforce the correspondence between the musical element sequences and the specific dimensions of latent variable sequences, providing a new solution for disentangling discrete sequences. Taking advantage of the disentangled latent vectors, a two-level decoding strategy that includes multiple decoders attending to latent vectors with different semantics is devised to better predict the elements. By visualizing latent space, we conclude that MusER yields a disentangled and interpretable latent space and gain insights into the contribution of distinct elements to the emotional dimensions (i.e., arousal and valence). Experimental results demonstrate that MusER outperforms the state-of-the-art models for generating emotional music in both objective and subjective evaluation. Besides, we rearrange music through element transfer and attempt to alter the emotion of music by transferring emotion-distinguishable elements.