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Deep Learning · Large Language Models

Raeid Saqur, Anastasis Kratsios, Florian Krach, Yannick Limmer, Blanka Horvath, Frank Rudzicz

We propose MoE-F — a formalized mechanism for combining N pre-trained expert Large Language Models (LLMs) in online time-series prediction tasks by adaptively forecasting the best weighting of LLM predictions at every time step. Our mechanism leverages the conditional information in each expert's running performance to forecast the best combination of LLMs for predicting the time series in its next step. Diverging from static (learned) Mixture of Experts (MoE) methods, our approach employs time-adaptive stochastic filtering techniques to combine experts. By framing the expert selection problem as a finite state-space, continuous-time Hidden Markov model (HMM), we can leverage the Wohman-Shiryaev filter. Our approach first constructs N parallel filters corresponding to each of the N individual LLMs. Each filter proposes its best combination of LLMs, given the information that they have access to. Subsequently, the N filter outputs are optimally aggregated to maximize their robust predictive power, and this update is computed efficiently via a closed-form expression, thus generating our ensemble predictor.Our contributions are:- **(I)** the MoE-F algorithm — deployable as a plug-and-play filtering harness,- **(II)** theoretical optimality guarantees of the proposed filtering-based gating algorithm (via optimality guarantees for its parallel Bayesian filtering and its robust aggregation steps), and- **(III)** empirical evaluation and ablative results using state-of-the-art foundational and MoE LLMs on a real-world _Financial Market Movement_ task where MoE-F attains a remarkable 17% absolute and 48.5% relative F1 measure improvement over the next best performing individual LLM expert predicting short-horizon market movement based on streaming news. Further, we provide empirical evidence of substantial performance gains in applying MoE-F over specialized models in the _long-horizon time-series forecasting_ domain. Code available on github: https://github.com/raeidsaqur/moe-f

Toni Liu, Nicolas Boulle, Raphaël Sarfati, Christopher Earls

Large language models (LLMs) demonstrate remarkable emergent abilities to perform in-context learning across various tasks, including time series forecasting. This work investigates LLMs' ability to estimate probability density functions (PDFs) from data observed in-context; such density estimation (DE) is a fundamental task underlying many probabilistic modeling problems. We leverage the Intensive Principal Component Analysis (InPCA) to visualize and analyze the in-context learning dynamics of LLaMA-2 models. Our main finding is that these LLMs all follow similar learning trajectories in a low-dimensional InPCA space, which are distinct from those of traditional density estimation methods like histograms and Gaussian kernel density estimation (KDE). We interpret the LLaMA in-context DE process as a KDE with an adaptive kernel width and shape. This custom kernel model captures a significant portion of LLaMA's behavior despite having only two parameters. We further speculate on why LLaMA's kernel width and shape differs from classical algorithms, providing insights into the mechanism of in-context probabilistic reasoning in LLMs.Our codebase, along with a 3D visualization of an LLM's in-context learning trajectory, is publicly available at https://github.com/AntonioLiu97/LLMICL_inPCA.

Theory · Online Learning and Bandits

Chuan Liu, Ruibing Song, Chunshu Wu, Pouya Haghi, Tong Geng

Time-series modeling is broadly adopted to capture underlying patterns present in historical data, allowing prediction of future values. However, one crucial aspect of such modeling is often overlooked: in highly dynamic environments, data distributions can shift drastically within a second or less. Under these circumstances, traditional predictive models, and even online learning methods, struggle to adapt to the ultra-fast and complex distribution shifts present in highly dynamic scenarios. To address this, we propose InstaTrain, a novel learning approach that enables ultra-fast model updates for real-world prediction tasks, thereby keeping pace with rapidly evolving data distributions. In this work, (1) we transform the slow and expensive training process into an ultra-fast natural annealing process within a dynamical system. (2) Leveraging a recently proposed electronic dynamical system, we augment the system with parameter update modules, extending its capabilities to encompass both rapid training and inference. Experimental results on highly dynamic datasets demonstrate that our method achieves orders-of-magnitude improvements in training speed and energy efficiency while delivering superior accuracy compared to baselines running on GPUs.

Social Aspects · Accountability, Transparency and Interpretability

Vinitra Swamy, Syrielle Montariol, Julian Blackwell, Jibril Frej, Martin Jaggi, Tanja Käser

In human-centric settings like education or healthcare, model accuracy and model explainability are key factors for user adoption. Towards these two goals, intrinsically interpretable deep learning models have gained popularity, focusing on accurate predictions alongside faithful explanations. However, there exists a gap in the human-centeredness of these approaches, which often produce nuanced and complex explanations that are not easily actionable for downstream users. We present InterpretCC (interpretable conditional computation), a family of intrinsically interpretable neural networks at a unique point in the design space that optimizes for ease of human understanding and explanation faithfulness, while maintaining comparable performance to state-of-the-art models. InterpretCC achieves this through adaptive sparse activation of features before prediction, allowing the model to use a different, minimal set of features for each instance. We extend this idea into an interpretable, global mixture-of-experts (MoE) model that allows users to specify topics of interest, discretely separates the feature space for each data point into topical subnetworks, and adaptively and sparsely activates these topical subnetworks for prediction. We apply InterpretCC for text, time series and tabular data across several real-world datasets, demonstrating comparable performance with non-interpretable baselines and outperforming intrinsically interpretable baselines. Through a user study involving 56 teachers, InterpretCC explanations are found to have higher actionability and usefulness over other intrinsically interpretable approaches.

Miscellaneous Aspects of Machine Learning · Sequential, Network, and Time Series Modeling

Kun Gao, Katsumi Inoue, Yongzhi Cao, Hanpin Wang, Yang Feng

Rule learning-based models are widely used in highly interpretable scenarios due to their transparent structures. Inductive logic programming (ILP), a form of machine learning, induces rules from facts while maintaining interpretability. Differentiable ILP models enhance this process by leveraging neural networks to improve robustness and scalability. However, most differentiable ILP methods rely on symbolic datasets, facing challenges when learning directly from raw data. Specifically, they struggle with explicit label leakage: The inability to map continuous inputs to symbolic variables without explicit supervision of input feature labels. In this work, we address this issue by integrating a self-supervised differentiable clustering model with a novel differentiable ILP model, enabling rule learning from raw data without explicit label leakage. The learned rules effectively describe raw data through its features. We demonstrate that our method intuitively and precisely learns generalized rules from time series and image data.

Eslam Abdelrahman, Liangbing Zhao, Tao Hu, MATTHIEU CORD, Patrick Perez, Mohamed Elhoseiny

Diffusion models break down the challenging task of generating data from high-dimensional distributions into a series of easier denoising steps. Inspired by this paradigm, we propose a novel approach that extends the diffusion framework into modality space, decomposing the complex task of RGB image generation into simpler, interpretable stages. Our method, termed {\papernameAbbrev}, cascades modality-specific models, each responsible for generating an intermediate representation, such as contours, palettes, and detailed textures, ultimately culminating in a high-quality RGB image.Instead of relying on the naive LDM concatenation conditioning mechanism to connect the different stages together, we employ Schr\"odinger Bridge to determine the optimal transport between different modalities.Although employing a cascaded pipeline introduces more stages, which could lead to a more complex architecture, each stage is meticulously formulated for efficiency and accuracy, surpassing Stable-Diffusion (LDM) performance.Modality composition not only enhances overall performance but enables emerging proprieties such as consistent editing, interaction capabilities, high-level interpretability, and faster convergence and sampling rate. Extensive experiments on diverse datasets, including LSUN-Churches, ImageNet, CelebHQ, and LAION-Art, demonstrate the efficacy of our approach, consistently outperforming state-of-the-art methods.For instance, {\papernameAbbrev} achieves notable efficiency, matching LDM performance on LSUN-Churches while operating 2$\times$ faster with a 3$\times$ smaller architecture.The project website is available at:\href{https://toddlerdiffusion.github.io/website/}{$https://toddlerdiffusion.github.io/website/$}

Applications · Time Series

Christian Klötergens, Vijaya Krishna Yalavarthi, Randolf Scholz, Maximilian Stubbemann, Stefan Born, Lars Schmidt-Thieme

State-of-the-art methods for forecasting irregularly sampled time series with missing values predominantly rely on just four datasets and a few small toy examples for evaluation. While ordinary differential equations (ODE) are the prevalent models in science and engineering, a baseline model that forecasts a constant value outperforms ODE-based models from the last five years on three of these existing datasets. This unintuitive finding hampers further research on ODE-based models, a more plausible model family.In this paper, we develop a methodology to generate irregularly sampled multivariate time series (IMTS) datasets from ordinary differentialequations and to select challenging instances via rejection sampling. Using this methodology, we create Physiome-ODE, a large and sophisticated benchmark of IMTS datasets consisting of 50 individual datasets, derived from real-world ordinary differential equations from research in biology. Physiome-ODE is the first benchmark for IMTS forecasting that we are aware of and an order of magnitude larger than the current evaluation setting of four datasets. Using our benchmark Physiome-ODE, we show qualitatively completely different results than those derived from the current four datasets: on Physiome-ODE ODE-based models can play to their strength and our benchmark can differentiate in a meaningful way between different IMTS forecasting models. This way, we expect to give a new impulse to research on ODE-based time series modeling.

Yufan Zhuang, Chandan Singh, Liyuan Liu, Jingbo Shang, Jianfeng Gao

Large language models (LLMs) have shown remarkable in-context learning (ICL) capabilities on textual data. We explore whether these capabilities can be extended to continuous vectors from diverse domains, obtained from black-box pretrained encoders. By aligning input data with an LLM's embedding space through lightweight projectors, we observe that LLMs can effectively process and learn from these projected vectors, which we term Vector-ICL. In particular, we find that pretraining projectors with general language modeling objectives enables Vector-ICL, while task-specific finetuning further enhances performance. In our experiments across various tasks and modalities, including text reconstruction, numerical function regression, text classification, summarization, molecule captioning, time-series classification, graph classification, and fMRI decoding, Vector-ICL often surpasses both few-shot ICL and domain-specific model or tuning. We further conduct analyses and case studies, indicating the potential of LLMs to process vector representations beyond traditional token-based paradigms.

Theory · Deep Learning

Takashi Furuya, Maarten V de Hoop, Gabriel Peyré

Transformers are deep architectures that define ``in-context mappings'' which enable predicting new tokens based on a given set of tokens (such as a prompt in NLP applications or a set of patches for a vision transformer). In this work, we study in particular the ability of these architectures to handle an arbitrarily large number of context tokens. To mathematically, uniformly address their expressivity, we consider the case that the mappings are conditioned on a context represented by a probability distribution of tokens which becomes discrete for a finite number of these. The relevant notion of smoothness then corresponds to continuity in terms of the Wasserstein distance between these contexts. We demonstrate that deep transformers are universal and can approximate continuous in-context mappings to arbitrary precision, uniformly over compact token domains. This result implies, as a special case, that transformers are universal approximators for continuous permutation-invariant mappings over a fixed number of tokens. It also establishes the universal approximation capability of transformers for certain in-context learning tasks, demonstrating in particular their ability to perform regression within context. A key aspect of our results, compared to existing findings, is that for a fixed precision, a single transformer can operate on an arbitrary (even infinite) number of tokens. Additionally, it operates with a fixed embedding dimension of tokens (this dimension does not increase with precision) and a fixed number of heads (proportional to the dimension). The use of MLPs between multi-head attention layers is also explicitly controlled. We consider both unmasked attentions (as used for the vision transformer) and masked causal attentions (as used for NLP and time series applications). We tackle the causal setting leveraging a space-time lifting to analyze causal attention as a mapping over probability distributions of tokens.

Social Aspects · Accountability, Transparency and Interpretability

Xu Zheng, Farhad Shirani, Zhuomin Chen, Chaohao Lin, Wei Cheng, Wenbo Guo, Dongsheng Luo

Recent research has developed a number of eXplainable AI (XAI) techniques, such as gradient-based approaches, input perturbation-base methods, and black-box explanation methods. While these XAI techniques can extract meaningful insights from deep learning models, how to properly evaluate them remains an open problem. The most widely used approach is to perturb or even remove what the XAI method considers to be the most important features in an input and observe the changes in the output prediction. This approach, although straightforward, suffers the Out-of-Distribution (OOD) problem as the perturbed samples may no longer follow the original data distribution. A recent method RemOve And Retrain (ROAR) solves the OOD issue by retraining the model with perturbed samples guided by explanations. However, using the model retrained based on XAI methods to evaluate these explainers may cause information leakage and thus lead to unfair comparisons. We propose Fine-tuned Fidelity (F-Fidelity), a robust evaluation framework for XAI, which utilizes i) an explanation-agnostic fine-tuning strategy, thus mitigating the information leakage issue, and ii) a random masking operation that ensures that the removal step does not generate an OOD input. We also design controlled experiments with state-of-the-art (SOTA) explainers and their degraded version to verify the correctness of our framework. We conduct experiments on multiple data modalities, such as images, time series, and natural language. The results demonstrate that F-Fidelity significantly improves upon prior evaluation metrics in recovering the ground-truth ranking of the explainers. Furthermore, we show both theoretically and empirically that, given a faithful explainer, F-Fidelity metric can be used to compute the sparsity of influential input components, i.e., to extract the true explanation size.

Social Aspects · Trustworthy Machine Learning

Buelent Uendes, Shujian Yu, Mark Hoogendoorn

Mask-based explanation methods offer a powerful framework for interpreting deep learning model predictions across diverse data modalities, such as images and time series, in which the central idea is to identify an instance-dependent mask that minimizes the performance drop from the resulting masked input. Different objectives for learning such masks have been proposed, all of which, in our view, can be unified under an information-theoretic framework that balances performance degradation of the masked input with the complexity of the resulting masked representation. Typically, these methods initialize the masks either uniformly or as all-ones.In this paper, we argue that an effective mask initialization strategy is as important as the development of novel learning objectives, particularly in light of the significant computational costs associated with existing mask-based explanation methods. To this end, we introduce a new gradient-based initialization technique called StartGrad, which is the first initialization method specifically designed for mask-based post-hoc explainability methods. Compared to commonly used strategies, StartGrad is provably superior at initialization in striking the aforementioned trade-off. Despite its simplicity, our experiments demonstrate that StartGrad enhances the optimization process of various state-of-the-art mask-explanation methods by reaching target metrics faster and, in some cases, boosting their overall performance.

Applications · Time Series

Phillip Si, Peng Chen

Accurate modeling and prediction of complex physical systems often rely on data assimilation techniques to correct errors inherent in model simulations. Traditional methods like the Ensemble Kalman Filter (EnKF) and its variants as well as the recently developed Ensemble Score Filters (EnSF) face significant challenges when dealing with high-dimensional and nonlinear Bayesian filtering problems with sparse observations, which are ubiquitous in real-world applications. In this paper, we propose a novel data assimilation method, Latent-EnSF, which leverages EnSF with efficient and consistent latent representations of the full states and sparse observations to address the joint challenges of high dimensionlity in states and high sparsity in observations for nonlinear Bayesian filtering. We introduce a coupled Variational Autoencoder (VAE) with two encoders to encode the full states and sparse observations in a consistent way guaranteed by a latent distribution matching and regularization as well as a consistent state reconstruction. With comparison to several methods, we demonstrate the higher accuracy, faster convergence, and higher efficiency of Latent-EnSF for two challenging applications with complex models in shallow water wave propagation and medium-range weather forecasting, for highly sparse observations in both space and time.

Applications · Time Series

Zhaoyang Li, Minghao Han, Xunyuan Yin

The Koopman theory, which enables the transformation of nonlinear systems into linear representations, is a powerful and efficient tool to model and control nonlinear systems. However, the ability of the Koopman operator to model complex systems, particularly time-varying systems, is limited by the fixed linear state-space representation. To address the limitation, the large language model, Mamba, is considered a promising strategy for enhancing modeling capabilities while preserving the linear state-space structure.In this paper, we propose a new framework, the Mamba-based Koopman operator (MamKO), which provides enhanced model prediction capability and adaptability, as compared to Koopman models with constant Koopman operators. Inspired by the Mamba structure, MamKO generates Koopman operators from online data; this enables the model to effectively capture the dynamic behaviors of the nonlinear system over time. A model predictive control system is then developed based on the proposed MamKO model. The modeling and control performance of the proposed method is evaluated through experiments on benchmark time-invariant and time-varying systems. The experimental results demonstrate the superiority of the proposed approach. Additionally, we perform ablation experiments to test the effectiveness of individual components of MamKO. This approach unlocks new possibilities for integrating large language models with control frameworks, and it achieves a good balance between advanced modeling capabilities and real-time control implementation efficiency.

Deep Learning · Generative Models and Autoencoders

Jinyoung Choi, Junoh Kang, Bohyung Han

Diffusion probabilistic models (DPMs), while effective in generating high-quality samples, often suffer from high computational costs due to their iterative sampling process. To address this, we propose an enhanced ODE-based sampling method for DPMs inspired by Richardson extrapolation, which reduces numerical error and improves convergence rates. Our method, RX-DPM, leverages multiple ODE solutions at intermediate time steps to extrapolate the denoised prediction in DPMs. Our method, RX-DPM, leverages multiple ODE solutions at intermediate time steps to extrapolate the denoised prediction in DPMs. This significantly enhances the accuracy of estimations for the final sample while maintaining the number of function evaluations (NFEs). Unlike standard Richardson extrapolation, which assumes uniform discretization of the time grid, we develop a more general formulation tailored to arbitrary time step scheduling, guided by local truncation error derived from a baseline sampling method. The simplicity of our approach facilitates accurate estimation of numerical solutions without significant computational overhead, and allows for seamless and convenient integration into various DPMs and solvers. Additionally, RX-DPM provides explicit error estimates, effectively demonstrating the faster convergence as the leading error term's order increases. Through a series of experiments, we show that the proposed method improves the quality of generated samples without requiring additional sampling iterations.

Miscellaneous Aspects of Machine Learning · Sequential, Network, and Time Series Modeling

Oğuz Kaan Yüksel, Mathieu Even, Nicolas Flammarion

This paper addresses the problem of long-context linear system identification, where the state $x_t$ of the system at time $t$ depends linearly on previous states $x_s$ over a fixed context window of length $p$. We establish a sample complexity bound that matches the _i.i.d._ parametric rate, up to logarithmic factors for a broad class of systems, extending previous work that considered only first-order dependencies. Our findings reveal a ``learning-without-mixing'' phenomenon, indicating that learning long-context linear autoregressive models is not hindered by slow mixing properties potentially associated with extended context windows. Additionally, we extend these results to _(i)_ shared low-rank feature representations, where rank-regularized estimators improve rates with respect to dimensionality, and _(ii)_ misspecified context lengths in strictly stable systems, where shorter contexts offer statistical advantages.

Applications · Genetics, Cell Biology, Health, etc

Dominik Scheuer, Frederic Runge, Jörg Franke, Michael Wolfinger, Christoph Flamm, Frank Hutter

RNA is a dynamic biomolecule crucial for cellular regulation, with its function largely determined by its folding into complex structures, while misfolding can lead to multifaceted biological sequelae. During the folding process, RNA traverses through a series of intermediate structural states, with each transition occurring at variable rates that collectively influence the time required to reach the functional form. Understanding these folding kinetics is vital for predicting RNA behavior and optimizing applications in synthetic biology and drug discovery. While in silico kinetic RNA folding simulators are often computationally intensive and time-consuming, accurate approximations of the folding times can already be very informative to assess the efficiency of the folding process. In this work, we present KinPFN, a novel approach that leverages prior-data fitted networks to directly model the posterior predictive distribution of RNA folding times. By training on synthetic data representing arbitrary prior folding times, KinPFN efficiently approximates the cumulative distribution function of RNA folding times in a single forward pass, given only a few initial folding time examples. Our method offers a modular extension to existing RNA kinetics algorithms, promising significant computational speed-ups orders of magnitude faster, while achieving comparable results. We showcase the effectiveness of KinPFN through extensive evaluations and real-world case studies, demonstrating its potential for RNA folding kinetics analysis, its practical relevance, and generalization to other biological data.

Applications · Time Series

Ke-Yuan Shen

In multivariate time series anomaly detection (MTSAD), reconstruction-based models reconstruct testing series with learned knowledge of only normal series and identify anomalies with higher reconstruction errors. In practice, over-generalization often occurs with unexpectedly well reconstruction of anomalies. Although memory banks are employed by reconstruction-based models to fight against over-generalization, these models are only efficient to detect point anomalies since they learn normal prototypes from time points, leaving interval anomalies and periodical anomalies to be discovered. To settle this problem, this paper propose a hybrid prototypes learning model for MTSAD based on reconstruction, named as H-PAD. First, normal prototypes are learned from different sizes of the patches for time series to discover interval anomalies. These prototypes in different sizes are integrated together to reconstruct query series so that any anomalies would be smoothed off and high reconstruction errors are produced. Furthermore, period prototypes are learned to discover periodical anomalies. One period prototype is memorized for one variable of the query series. Finally, extensive experiments on five benchmark datasets show the effectiveness of H-PAD.

Applications · Time Series

Yizi Zhang, Jingyan Shen, Xiaoxue Xiong, Yongchan Kwon

Evaluating the contribution of individual data points to a model's prediction is critical for interpreting model predictions and improving model performance. Existing data contribution methods have been applied to various data types, including tabular data, images, and text; however, their primary focus has been on i.i.d. settings. Despite the pressing need for principled approaches tailored to time series datasets, the problem of estimating data contribution in such settings remains under-explored, possibly due to challenges associated with handling inherent temporal dependencies. This paper introduces TimeInf, a model-agnostic data contribution estimation method for time-series datasets. By leveraging influence scores, TimeInf attributes model predictions to individual time points while preserving temporal structures between the time points. Our empirical results show that TimeInf effectively detects time series anomalies and outperforms existing data attribution techniques as well as state-of-the-art anomaly detection methods. Moreover, TimeInf offers interpretable attributions of data values, allowing us to distinguish diverse anomalous patterns through visualizations. We also showcase a potential application of TimeInf in identifying mislabeled anomalies in the ground truth annotations.

Applications · Neuroscience, Cognitive Science

Geeling Chau, Christopher Wang, Sabera Talukder, Vighnesh Subramaniam, Saraswati Soedarmadji, Yisong Yue, Boris Katz, Andrei Barbu

We present a self-supervised framework that learns population-level codes for arbitrary ensembles of neural recordings at scale. We address key challenges in scaling models with neural time-series data, namely, sparse and variable electrode distribution across subjects and datasets. The Population Transformer (PopT) stacks on top of pretrained temporal embeddings and enhances downstream decoding by enabling learned aggregation of multiple spatially-sparse data channels. The pretrained PopT lowers the amount of data required for downstream decoding experiments, while increasing accuracy, even on held-out subjects and tasks. Compared to end-to-end methods, this approach is computationally lightweight, while achieving similar or better decoding performance. We further show how our framework is generalizable to multiple time-series embeddings and neural data modalities. Beyond decoding, we interpret the pretrained and fine-tuned PopT models to show how they can be used to extract neuroscience insights from large amounts of data. We release our code as well as a pretrained PopT to enable off-the-shelf improvements in multi-channel intracranial data decoding and interpretability. Code is available at https://github.com/czlwang/PopulationTransformer.

Applications · Neuroscience, Cognitive Science

Geeling Chau, Christopher Wang, Sabera Talukder, Vighnesh Subramaniam, Saraswati Soedarmadji, Yisong Yue, Boris Katz, Andrei Barbu

We present a self-supervised framework that learns population-level codes for arbitrary ensembles of neural recordings at scale. We address key challenges in scaling models with neural time-series data, namely, sparse and variable electrode distribution across subjects and datasets. The Population Transformer (PopT) stacks on top of pretrained temporal embeddings and enhances downstream decoding by enabling learned aggregation of multiple spatially-sparse data channels. The pretrained PopT lowers the amount of data required for downstream decoding experiments, while increasing accuracy, even on held-out subjects and tasks. Compared to end-to-end methods, this approach is computationally lightweight, while achieving similar or better decoding performance. We further show how our framework is generalizable to multiple time-series embeddings and neural data modalities. Beyond decoding, we interpret the pretrained and fine-tuned PopT models to show how they can be used to extract neuroscience insights from large amounts of data. We release our code as well as a pretrained PopT to enable off-the-shelf improvements in multi-channel intracranial data decoding and interpretability. Code is available at https://github.com/czlwang/PopulationTransformer.