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Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

Sebastian Damrich, Philipp Berens, Dmitry Kobak

Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much higher dimensionality. We show that in this case traditional persistent homology becomes very sensitive to noise and fails to detect the correct topology. The same holds true for existing refinements of persistent homology. As a remedy, we find that spectral distances on the k-nearest-neighbor graph of the data, such as diffusion distance and effective resistance, allow to detect the correct topology even in the presence of high-dimensional noise. Moreover, we derive a novel closed-form formula for effective resistance, and describe its relation to diffusion distances. Finally, we apply these methods to high-dimensional single-cell RNA-sequencing data and show that spectral distances allow robust detection of cell cycle loops.

Computational Biology

Seul Lee, Karsten Kreis, Srimukh Veccham, Meng Liu, Danny Reidenbach, Saee Paliwal, Arash Vahdat, Weili Nie

Fragment-based drug discovery, in which molecular fragments are assembled into new molecules with desirable biochemical properties, has achieved great success. However, many fragment-based molecule generation methods show limited exploration beyond the existing fragments in the database as they only reassemble or slightly modify the given ones. To tackle this problem, we propose a new fragment-based molecule generation framework with retrieval augmentation, namely *Fragment Retrieval-Augmented Generation* (*f*-RAG). *f*-RAG is based on a pre-trained molecular generative model that proposes additional fragments from input fragments to complete and generate a new molecule. Given a fragment vocabulary, *f*-RAG retrieves two types of fragments: (1) *hard fragments*, which serve as building blocks that will be explicitly included in the newly generated molecule, and (2) *soft fragments*, which serve as reference to guide the generation of new fragments through a trainable *fragment injection module*. To extrapolate beyond the existing fragments, *f*-RAG updates the fragment vocabulary with generated fragments via an iterative refinement process which is further enhanced with post-hoc genetic fragment modification. *f*-RAG can achieve an improved exploration-exploitation trade-off by maintaining a pool of fragments and expanding it with novel and high-quality fragments through a strong generative prior.

Graph Neural Networks

Paolo Pellizzoni, Till Hendrik Schulz, Dexiong Chen, Karsten Borgwardt

Graph neural networks (GNNs) employing message passing for graph classification are inherently limited by the expressive power of the Weisfeiler-Leman (WL) test for graph isomorphism. Node individualization schemes, which assign unique identifiers to nodes (e.g., by adding random noise to features), are a common approach for achieving universal expressiveness. However, the ability of GNNs endowed with individualization schemes to generalize beyond the training data is still an open question. To address this question, this paper presents a theoretical analysis of the sample complexity of such GNNs from a statistical learning perspective, employing Vapnik–Chervonenkis (VC) dimension and covering number bounds. We demonstrate that node individualization schemes that are permutation-equivariant result in lower sample complexity, and design novel individualization schemes that exploit these results. As an application of this analysis, we also develop a novel architecture that can perform substructure identification (i.e., subgraph isomorphism) while having a lower VC dimension compared to competing methods. Finally, our theoretical findings are validated experimentally on both synthetic and real-world datasets.

Learning Theory

Huy Nguyen, Nhat Ho, Alessandro Rinaldo

The softmax gating function is arguably the most popular choice in mixture of experts modeling. Despite its widespread use in practice, the softmax gating may lead to unnecessary competition among experts, potentially causing the undesirable phenomenon of representation collapse due to its inherent structure. In response, the sigmoid gating function has been recently proposed as an alternative and has been demonstrated empirically to achieve superior performance. However, a rigorous examination of the sigmoid gating function is lacking in current literature. In this paper, we verify theoretically that the sigmoid gating, in fact, enjoys a higher sample efficiency than the softmax gating for the statistical task of expert estimation. Towards that goal, we consider a regression framework in which the unknown regression function is modeled as a mixture of experts, and study the rates of convergence of the least squares estimator under the over-specified case in which the number of fitted experts is larger than the true value. We show that two gating regimes naturally arise and, in each of them, we formulate an identifiability condition for the expert functions and derive the corresponding convergence rates. In both cases, we find that experts formulated as feed-forward networks with commonly used activation such as $\mathrm{ReLU}$ and $\mathrm{GELU}$ enjoy faster convergence rates under the sigmoid gating than those under softmax gating. Furthermore, given the same choice of experts, we demonstrate that the sigmoid gating function requires a smaller sample size than its softmax counterpart to attain the same error of expert estimation and, therefore, is more sample efficient.

Generative Models · New Approaches

Peter Sorrenson, Felix Draxler, Armand Rousselot, Sander Hummerich, Ullrich Köthe

We propose Manifold Free-Form Flows (M-FFF), a simple new generative model for data on manifolds. The existing approaches to learning a distribution on arbitrary manifolds are expensive at inference time, since sampling requires solving a differential equation. Our method overcomes this limitation by sampling in a single function evaluation. The key innovation is to optimize a neural network via maximum likelihood on the manifold, possible by adapting the free-form flow framework to Riemannian manifolds. M-FFF is straightforwardly adapted to any manifold with a known projection. It consistently matches or outperforms previous single-step methods specialized to specific manifolds. It is typically two orders of magnitude faster than multi-step methods based on diffusion or flow matching, achieving better likelihoods in several experiments. We provide our code at https://github.com/vislearn/FFF.

Learning Theory

Weihang Xu, Maryam Fazel, Simon Du

We study the gradient Expectation-Maximization (EM) algorithm for Gaussian Mixture Models (GMM) in the over-parameterized setting, where a general GMM with $n>1$ components learns from data that are generated by a single ground truth Gaussian distribution. While results for the special case of 2-Gaussian mixtures are well-known, a general global convergence analysis for arbitrary $n$ remains unresolved and faces several new technical barriers since the convergence becomes sub-linear and non-monotonic. To address these challenges, we construct a novel likelihood-based convergence analysis framework and rigorously prove that gradient EM converges globally with a sublinear rate $O(1/\sqrt{t})$. This is the first global convergence result for Gaussian mixtures with more than $2$ components. The sublinear convergence rate is due to the algorithmic nature of learning over-parameterized GMM with gradient EM. We also identify a new emerging technical challenge for learning general over-parameterized GMM: the existence of bad local regions that can trap gradient EM for an exponential number of steps.

Probabilistic Methods · Monte Carlo and Sampling Methods

Ye He, Alireza Mousavi-Hosseini, Krishnakumar Balasubramanian, Murat Erdogdu

We study the complexity of heavy-tailed sampling and present a separation result in terms of obtaining high-accuracy versus low-accuracy guarantees i.e., samplers that require only $\mathcal{O}(\log(1/\varepsilon))$ versus $\Omega(\text{poly}(1/\varepsilon))$ iterations to output a sample which is $\varepsilon$-close to the target in $\chi^2$-divergence. Our results are presented for proximal samplers that are based on Gaussian versus stable oracles. We show that proximal samplers based on the Gaussian oracle have a fundamental barrier in that they necessarily achieve only low-accuracy guarantees when sampling from a class of heavy-tailed targets. In contrast, proximal samplers based on the stable oracle exhibit high-accuracy guarantees, thereby overcoming the aforementioned limitation. We also prove lower bounds for samplers under the stable oracle and show that our upper bounds cannot be fundamentally improved.

Fairness

Eoin Delaney, Zihao Fu, Sandra Wachter, Brent Mittelstadt, Chris Russell

We present OxonFair, a new open source toolkit for enforcing fairness in binary classification. Compared to existing toolkits: (i) We support NLP and Computer Vision classification as well as standard tabular problems. (ii) We support enforcing fairness on validation data, making us robust to a wide range of overfitting challenges. (iii) Our approach can optimize any measure based on True Positives, False Positive, False Negatives, and True Negatives. This makes it easily extensible and much more expressive than existing toolkits. It supports all 9 and all 10 of the decision-based group metrics of two popular review articles. (iv) We jointly optimize a performance objective alongside fairness constraints. This minimizes degradation while enforcing fairness, and even improves the performance of inadequately tuned unfair baselines. OxonFair is compatible with standard ML toolkits, including sklearn, Autogluon, and PyTorch and is available at https://github.com/oxfordinternetinstitute/oxonfair.

Graph Neural Networks

Shijin Duan, Ruyi Ding, Jiaxing He, Aidong Ding, Yunsi Fei, Xiaolin Xu

Graph-structured data is integral to many applications, prompting the development of various graph representation methods. Graph autoencoders (GAEs), in particular, reconstruct graph structures from node embeddings. Current GAE models primarily utilize self-correlation to represent graph structures and focus on node-level tasks, often overlooking multi-graph scenarios. Our theoretical analysis indicates that self-correlation generally falls short in accurately representing specific graph features such as islands, symmetrical structures, and directional edges, particularly in smaller or multiple graph contexts.To address these limitations, we introduce a cross-correlation mechanism that significantly enhances the GAE representational capabilities. Additionally, we propose the GraphCroc, a new GAE that supports flexible encoder architectures tailored for various downstream tasks and ensures robust structural reconstruction, through a mirrored encoding-decoding process. This model also tackles the challenge of representation bias during optimization by implementing a loss-balancing strategy. Both theoretical analysis and numerical evaluations demonstrate that our methodology significantly outperforms existing self-correlation-based GAEs in graph structure reconstruction.

Deep Learning · Everything Else

Jay Bear, Adam Prugel-Bennett, Jonathon Hare

Iterative algorithms solve problems by taking steps until a solution is reached. Models in the form of Deep Thinking (DT) networks have been demonstrated to learn iterative algorithms in a way that can scale to different sized problems at inference time using recurrent computation and convolutions. However, they are often unstable during training, and have no guarantees of convergence/termination at the solution. This paper addresses the problem of instability by analyzing the growth in intermediate representations, allowing us to build models (referred to as Deep Thinking with Lipschitz Constraints (DT-L)) with many fewer parameters and providing more reliable solutions. Additionally our DT-L formulation provides guarantees of convergence of the learned iterative procedure to a unique solution at inference time. We demonstrate DT-L is capable of robustly learning algorithms which extrapolate to harder problems than in the training set. We benchmark on the traveling salesperson problem to evaluate the capabilities of the modified system in an NP-hard problem where DT fails to learn.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Hui Chen, Yanbin Liu, Yongqiang Ma, Nanning Zheng, Xin Yu

Pre-trained vision-language models (VLMs) such as CLIP have shown excellent performance for zero-shot classification. Based on CLIP, recent methods design various learnable prompts to evaluate the zero-shot generalization capability on a base-to-novel setting. This setting assumes test samples are already divided into either base or novel classes, limiting its application to realistic scenarios. In this paper, we focus on a more challenging and practical setting: generalized zero-shot learning (GZSL), i.e., testing with no information about the base/novel division. To address this challenging zero-shot problem, we introduce two unique designs that enable us to classify an image without the need of knowing whether it comes from seen or unseen classes. Firstly, most existing methods only adopt a single latent space to align visual and linguistic features, which has a limited ability to represent complex visual-linguistic patterns, especially for fine-grained tasks. Instead, we propose a dual-space feature alignment module that effectively augments the latent space with a novel attribute space induced by a well-devised attribute reservoir. In particular, the attribute reservoir consists of a static vocabulary and learnable tokens complementing each other for flexible control over feature granularity. Secondly, finetuning CLIP models (e.g., prompt learning) on seen base classes usually sacrifices the model's original generalization capability on unseen novel classes. To mitigate this issue, we present a new topology-preserving objective that can enforce feature topology structures of the combined base and novel classes to resemble the topology of CLIP. In this manner, our model will inherit the generalization ability of CLIP through maintaining the pairwise class angles in the attribute space. Extensive experiments on twelve object recognition datasets demonstrate that our model, termed Topology-Preserving Reservoir (TPR), outperforms strong baselines including both prompt learning and conventional generative-based zero-shot methods.

Graph Neural Networks

Yuefei Lyu, Chaozhuo Li, Sihong Xie, Xi Zhang

Adversarial attacks against graph neural networks (GNNs) through perturbations of the graph structure are increasingly common in social network tasks like rumor detection. Social media platforms capture diverse attack sequence samples through both machine and manual screening processes. Investigating effective ways to leverage these adversarial samples to enhance robustness is imperative. We improve the maximum entropy inverse reinforcement learning (IRL) method with the mixture-of-experts approach to address multi-source graph adversarial attacks. This method reconstructs the attack policy, integrating various attack models and providing feature-level explanations, subsequently generating additional adversarial samples to fortify the robustness of detection models. We develop precise sample guidance and a bidirectional update mechanism to reduce the deviation caused by imprecise feature representation and negative sampling within the large action space of social graphs, while also accelerating policy learning. We take rumor detector as an example targeted GNN model on real-world rumor datasets. By utilizing a small subset of samples generated by various graph adversarial attack methods, we reconstruct the attack policy, closely approximating the performance of the original attack method. We validate that samples generated by the learned policy enhance model robustness through adversarial training and data augmentation.

Computer Vision

Qi Tang, Yao Zhao, Meiqin Liu, Chao Yao

Diffusion-based Video Super-Resolution (VSR) is renowned for generating perceptually realistic videos, yet it grapples with maintaining detail consistency across frames due to stochastic fluctuations. The traditional approach of pixel-level alignment is ineffective for diffusion-processed frames because of iterative disruptions. To overcome this, we introduce SeeClear--a novel VSR framework leveraging conditional video generation, orchestrated by instance-centric and channel-wise semantic controls. This framework integrates a Semantic Distiller and a Pixel Condenser, which synergize to extract and upscale semantic details from low-resolution frames. The Instance-Centric Alignment Module (InCAM) utilizes video-clip-wise tokens to dynamically relate pixels within and across frames, enhancing coherency. Additionally, the Channel-wise Texture Aggregation Memory (CaTeGory) infuses extrinsic knowledge, capitalizing on long-standing semantic textures. Our method also innovates the blurring diffusion process with the ResShift mechanism, finely balancing between sharpness and diffusion effects. Comprehensive experiments confirm our framework's advantage over state-of-the-art diffusion-based VSR techniques.

Deep Learning · Attention Mechanisms

Zican Dong, Junyi Li, Xin Men, Xin Zhao, Bingning Wang, Zhen Tian, weipeng chen, Ji-Rong Wen

Transformer-based large language models (LLMs) typically have a limited context window, resulting in significant performance degradation when processing text beyond the length of the context window. Extensive studies have been proposed to extend the context window and achieve length extrapolation of LLMs, but there is still a lack of in-depth interpretation of these approaches. In this study, we explore the positional information within and beyond the context window for deciphering the underlying mechanism of LLMs. By using a mean-based decomposition method, we disentangle positional vectors from hidden states of LLMs and analyze their formation and effect on attention. Furthermore, when texts exceed the context window, we analyze the change of positional vectors in two settings, i.e., direct extrapolation and context window extension. Based on our findings, we design two training-free context window extension methods, positional vector replacement and attention window extension. Experimental results show that our methods can effectively extend the context window length.

Neuroscience, Cognitive Science

Yongxu Zhang, Shreya Saxena

Neural population activity often exhibits distinct dynamical features across time, which may correspond to distinct internal processes or behavior. Linear methods and variations thereof, such as Hidden Markov Model (HMM) and Switching Linear Dynamical System (SLDS), are often employed to identify discrete states with evolving neural dynamics. However, these techniques may not be able to capture the underlying nonlinear dynamics associated with neural propagation. Recurrent Neural Networks (RNNs) are commonly used to model neural dynamics thanks to their nonlinear characteristics. In our work, we develop Switching Recurrent Neural Networks (SRNN), RNNs with weights that switch across time, to reconstruct switching dynamics of neural time-series data. We apply these models to simulated data as well as cortical neural activity across mice and monkeys, which allows us to automatically detect discrete states that lead to the identification of varying neural dynamics. In a monkey reaching dataset with electrophysiology recordings, a mouse self-initiated lever pull dataset with widefield calcium recordings, and a mouse self-initiated decision making dataset with widefield calcium recording, SRNNs are able to automatically identify discrete states with distinct nonlinear neural dynamics. The inferred switches are aligned with the behavior, and the reconstructions show that the recovered neural dynamics are distinct across different stages of the behavior. We show that the neural dynamics have behaviorally-relevant switches across time and we are able to use SRNNs to successfully capture these switches and the corresponding dynamical features.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Lixu Wang, Xinyu Du, Qi Zhu

Cross-domain retrieval (CDR) is finding increasingly broad applications across various domains. However, existing efforts have several major limitations, with the most critical being their reliance on accurate supervision. Recent studies thus focus on achieving unsupervised CDR, but they typically assume that the category spaces across domains are identical, an assumption that is often unrealistic in real-world scenarios. This is because only through dedicated and comprehensive analysis can the category composition of a data domain be obtained, which contradicts the premise of unsupervised scenarios. Therefore, in this work, we introduce the problem of **U**niversal **U**nsupervised **C**ross-**D**omain **R**etrieval (U^2CDR) for the first time and design a two-stage semantic feature learning framework to address it. In the first stage, a cross-domain unified prototypical structure is established under the guidance of an instance-prototype-mixed contrastive loss and a semantic-enhanced loss, to counteract category space differences. In the second stage, through a modified adversarial training mechanism, we ensure minimal changes for the established prototypical structure during domain alignment, enabling more accurate nearest-neighbor searching. Extensive experiments across multiple datasets and scenarios, including close-set, partial, and open-set CDR, demonstrate that our approach significantly outperforms existing state-of-the-art CDR methods and other related methods in solving U^2CDR challenges.

Multimodal Models

lianyu hu, Tongkai Shi, Wei Feng, Fanhua Shang, Liang Wan

Large-scale multimodal models have shown excellent performance over a series of tasks powered by the large corpus of paired multimodal training data. Generally, they are always assumed to receive modality-complete inputs. However, this simple assumption may not always hold in the real world due to privacy constraints or collection difficulty, where models pretrained on modality-complete data easily demonstrate degraded performance on missing-modality cases. To handle this issue, we refer to prompt learning to adapt large pretrained multimodal models to handle missing-modality scenarios by regarding different missing cases as different types of input. Instead of only prepending independent prompts to the intermediate layers, we present to leverage the correlations between prompts and input features and excavate the relationships between different layers of prompts to carefully design the instructions. We also incorporate the complementary semantics of different modalities to guide the prompting design for each modality. Extensive experiments on three commonly-used datasets consistently demonstrate the superiority of our method compared to the previous approaches upon different missing scenarios. Plentiful ablations are further given to show the generalizability and reliability of our method upon different modality-missing ratios and types.

Deep Learning · Representation Learning

Feiqing Huang, Shenghan Zhang, Sara Sweet, Tianxi Cai

In recent years, there has been a proliferation of ready-to-use large language models (LLMs) designed for various applications, both general-purpose and domain-specific. Instead of advocating for the development of a new model or continuous pretraining of an existing one, this paper introduces a pragmatic teacher-teacher framework to facilitate mutual learning between two pre-existing models.By leveraging two teacher models possessing complementary knowledge, we introduce a LIghtweight kNowledge alignmEnt (LINE) module aimed at harmonizing their knowledge within a unified representation space. This framework is particularly valuable in clinical settings, where stringent regulations and privacy considerations dictate the handling of detailed clinical notes. Our trained LINE module excels in capturing critical information from clinical notes, leveraging highly de-identified data. Validation and downstream tasks further demonstrate the effectiveness of the proposed framework.

Probabilistic Methods · Bayesian Models and Methods

Daolang Huang, Yujia Guo, Luigi Acerbi, Samuel Kaski

Many critical decisions, such as personalized medical diagnoses and product pricing, are made based on insights gained from designing, observing, and analyzing a series of experiments. This highlights the crucial role of experimental design, which goes beyond merely collecting information on system parameters as in traditional Bayesian experimental design (BED), but also plays a key part in facilitating downstream decision-making. Most recent BED methods use an amortized policy network to rapidly design experiments. However, the information gathered through these methods is suboptimal for down-the-line decision-making, as the experiments are not inherently designed with downstream objectives in mind. In this paper, we present an amortized decision-aware BED framework that prioritizes maximizing downstream decision utility. We introduce a novel architecture, the Transformer Neural Decision Process (TNDP), capable of instantly proposing the next experimental design, whilst inferring the downstream decision, thus effectively amortizing both tasks within a unified workflow. We demonstrate the performance of our method across several tasks, showing that it can deliver informative designs and facilitate accurate decision-making.

Deep Learning · Representation Learning

David McSharry, Christos Kaplanis, Fernando Rosas, Pedro A.M Mediano

Cognitive processes usually take place at a macroscopic scale in systems characterised by emergent properties, which make the whole ‘more than the sum of its parts.’ While recent proposals have provided quantitative, information-theoretic metrics to detect emergence in time series data, it is often highly non-trivial to identify the relevant macroscopic variables a priori. In this paper we leverage recent advances in representation learning and differentiable information estimators to put forward a data-driven method to find emergent variables. The proposed method successfully detects emergent variables and recovers the ground-truth emergence values in a synthetic dataset. Furthermore, we show the method can be extended to learn multiple independent features, extracting a diverse set of emergent quantities. We finally show that a modified method scales to real experimental data from primate brain activity, paving the ground for future analyses uncovering the emergent structure of cognitive representations in biological and artificial intelligence systems.