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A primary challenge of physics-informed machine learning (PIML) is its generalization beyond the training domain, especially when dealing with complex physical problems represented by partial differential equations (PDEs). This paper aims to enhance the generalization capabilities of PIML, facilitating practical, real-world applications where accurate predictions in unexplored regions are crucial. We leverage the inherent causality and temporal sequential characteristics of PDE solutions to fuse PIML models with recurrent neural architectures based on systems of ordinary differential equations, referred to as neural oscillators. Through effectively capturing long-time dependencies and mitigating the exploding and vanishing gradient problem, neural oscillators foster improved generalization in PIML tasks. Extensive experimentation involving time-dependent nonlinear PDEs and biharmonic beam equations demonstrates the efficacy of the proposed approach. Incorporating neural oscillators outperforms existing state-of-the-art methods on benchmark problems across various metrics. Consequently, the proposed method improves the generalization capabilities of PIML, providing accurate solutions for extrapolation and prediction beyond the training data.

AAAI 2024

Neural Oscillators for Generalization of Physics-Informed Machine Learning

neural oscillators

piml

generalization

technical paper

We are pleased to announce the Thirty-Eighth AAAI Conference on Artificial Intelligence (AAAI-24), which will be held in Vancouver, British Columbia at the Vancouver Convention Centre – West Building from 20-27 February, 2024.

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-24 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and a range of other activities to be announced.

We expect for AAAI-24 to be an in-person conference – one author of all accepted papers will be expected to present work in person unless there are exceptional circumstances that prevent this.<br><br><br><br>

In order to access the AAAI-24 event page you need to register [here](https://aaai.org/aaai-conference/registration/)

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. 

Machine unlearning, the ability for a machine learning model to forget, is becoming increasingly important to comply with data privacy regulations, as well as to remove harmful, manipulated, or outdated information. The key challenge lies in forgetting specific information while protecting model performance on the remaining data.  While current state-of-the-art methods perform well, they typically require some level of retraining over the retained data, in order to protect or restore model performance. This adds computational overhead and mandates that the training data remain available and accessible, which may not be feasible. In contrast, other methods employ a retrain-free paradigm, however, these approaches are prohibitively computationally expensive and do not perform on par with their retrain-based counterparts. We present Selective Synaptic Dampening (SSD), a novel two-step, post hoc, retrain-free approach to machine unlearning which is fast, performant, and does not require long-term storage of the training data. First, SSD uses the Fisher information matrix of the training and forgetting data to select parameters that are disproportionately important to the forget set. Second, SSD induces forgetting by dampening these parameters proportional to their relative importance to the forget set with respect to the wider training data. We evaluate our method against several existing unlearning methods in a range of experiments using ResNet18 and Vision Transformer. Results show that the performance of SSD is competitive with retrain-based post hoc methods, demonstrating the viability of retrain-free post hoc unlearning approaches.

Fast Machine Unlearning without Retraining through Selective Synaptic Dampening

The audio spectrogram is a time-frequency representation that has been widely used for audio classification. One of the key attributes of the audio spectrogram is the temporal resolution, which depends on the hop size used in the Short-Time Fourier Transform (STFT). Previous works generally assume the hop size should be a constant value (e.g., 10 ms). However, a fixed temporal resolution is not always optimal for different types of sound. The temporal resolution affects not only classification accuracy but also computational cost. This paper proposes a novel method, DiffRes, that enables differentiable temporal resolution modeling for audio classification. Given a spectrogram calculated with a fixed hop size, DiffRes merges non-essential time frames while preserving important frames. DiffRes acts as a "drop-in" module between an audio spectrogram and a classifier and can be jointly optimized with the classification task. We evaluate DiffRes on five audio classification tasks, using mel-spectrograms as the acoustic features, followed by off-the-shelf classifier backbones. Compared with previous methods using the fixed temporal resolution, the DiffRes-based method can achieve the equivalent or better classification accuracy with at least 25% computational cost reduction. We further show that DiffRes can improve classification accuracy by increasing the temporal resolution of input acoustic features, without adding to the computational cost.

Learning Temporal Resolution in Spectrogram for Audio Classification

Large language models (LLMs) have demonstrated remarkable performance in various natural language processing tasks. However, they still face significant challenges in automated reasoning, particularly in scenarios involving multi-step reasoning. In this paper, we focus on the logical reasoning problem. The main task is to answer a question based on a set of available facts and rules. A lot of work has focused on guiding LLMs to think logically by generating reasoning paths, ignoring the structure among available facts. In this paper, we propose a simple approach MindMap by introducing evidence chains for supporting reasoning. An evidence chain refers to a set of facts that involve the same subject. In this way, we can organize related facts together to avoid missing important information. MindMap can be integrated with existing reasoning framework, such as Chain-of-Thought (CoT) and Selection-Inference (SI), by letting the model select relevant evidence chains instead of independent facts. The experimental results on the bAbI and ProofWriterOWA datasets demonstrate the effectiveness of MindMap.It can significantly improve CoT and SI, especially in multi-step reasoning tasks.

MindMap: Constructing Evidence Chains for Multi-Step Reasoning in Large Language Models | VIDEO

Recently, because of the high-quality representations of contrastive learning methods, rehearsal-based contrastive continual learning has been proposed to explore how to continually learn transferable representation embeddings to avoid
the catastrophic forgetting issue in traditional continual settings. Based on this framework, we propose Contrastive Continual Learning via Importance Sampling (CCLIS) to preserve knowledge by recovering previous data distributions with a new strategy for Replay Buffer Selection (RBS), which minimize estimated variance to save hard negative samples for representation learning with high quality. Furthermore, we present the Prototype-instance Relation Distillation
(PRD) loss, a technique designed to maintain the relationship between prototypes and sample representations using a self-distillation process. Experiments on standard continual learning benchmarks reveal that our method notably outperforms existing baselines in terms of knowledge preservation and thereby effectively counteracts catastrophic forgetting in online contexts.

Contrastive Continual Learning with Importance Sampling and Prototype-Instance Relation Distillation | VIDEO

In the machine learning field, the challenge of effectively learning with limited data has grown increasingly crucial. Active Learning (AL) algorithms play a significant role in this by enhancing model performance. We introduce a novel AL algorithm, termed ``Co-learning'' (CoLAL), designed to select the most diverse and representative samples within a training dataset.  This model utilizes noisy labels and predictions made by the primary model on unlabeled data. By leveraging a probabilistic graphical model, we combine two multi-class classifiers into a binary one. This classifier determines if both the main and peer models agree on a prediction. If they do, the unlabeled sample is assumed to be easy to classify and is not beneficial to increase the target model's performance. We prioritize data that represents the unlabeled set without overlapping data decision boundaries. The discrepancies between these boundaries can be estimated by the probability that two models result in the same prediction. Through theoretical analysis and experimental validation, we reveal that these noisy labels' integration into the peer model effectively identifies the target model's potential inaccuracies. Our experiments, conducted on four benchmark datasets - AGNews, DBPedia, PubMed, and SST-2 - used in previous state-of-the-art (SOTA) studies, clearly illustrate that our CoLAL method significantly outperforms existing SOTA AL techniques.

CoLAL: Co-learning Active Learning for Text Classification

Neural networks (NNs) can learn to rely on spurious signals in the training data, leading to poor generalisation. Recent methods tackle this problem by training NNs with additional ground-truth annotations of such signals. These methods may, however, let spurious signals re-emerge in deep convolutional NNs (CNNs). We propose Targeted Activation Penalty (TAP), a new method tackling the same problem by penalising activations to control the re-emergence of spurious signals in deep CNNs, while also lowering training times and memory usage. In addition, ground-truth annotations can be expensive to obtain. We show that TAP still works well with annotations generated by pre-trained models as effective substitutes of ground-truth annotations. We demonstrate the power of TAP against two state-of-the-art baselines on the MNIST benchmark and on two clinical image datasets, using four different CNN architectures.

Targeted Activation Penalties Help CNNs Ignore Spurious Signals

People want to rely on optimization algorithms for complex decisions but verifying the optimality of the solutions can then become a valid concern, particularly for critical decisions taken by non-experts in optimization. One example is the shortest-path problem on a network, occurring in many contexts from transportation to logistics to telecommunications. While the standard shortest-path problem is both solvable in polynomial time and certifiable by duality, introducing side constraints makes solving and certifying the solutions much harder. We propose a proof system for constrained shortest-path problems, which gives a set of logical rules to derive new facts about feasible solutions. The key trait of the proposed proof system is that it specifically includes high-level graph concepts within its reasoning steps (such as connectivity or path structure), in contrast to, e.g., using linear combinations of model constraints. Thus, using our proof system, we can provide a step-by-step, human-auditable explanation showing that the path given by an external solver cannot be improved. Additionally, to maximize the advantages of this setup, we propose a proof search procedure that specifically aims to find small proofs of this form using a procedure similar to A* search. We evaluate our proof system on constrained shortest path instances generated from real-world road networks and show that it can improve upon the resulting proof width and depth with respect to integer programming proofs in approximately a third of the feasible problem instances despite being more restrictive in available proof steps.

Paths, Proofs, and Perfection: Developing a Human-Interpretable Proof System for Constrained Shortest Paths | VIDEO

3D lookup tables (3D LUTs) are a key component for image enhancement. Modern image signal processors (ISPs) have dedicated support for these as part of the camera rendering pipeline. Cameras typically provide multiple options for picture styles, where each style is usually obtained by applying a unique handcrafted 3D LUT. Current approaches for learning and applying 3D LUTs are notably fast, yet not so memory-efficient, as storing multiple 3D LUTs is required. For this reason and other implementation limitations, their use on mobile devices is less popular. In this work, we propose a Neural Implicit LUT (NILUT), an implicitly defined continuous 3D color transformation parameterized by a neural network. We show that NILUTs are capable of accurately emulating real 3D LUTs. Moreover, a NILUT can be extended to incorporate multiple styles into a single network with the ability to blend styles implicitly. Our novel approach is memory-efficient, controllable and can complement previous methods, including learned ISPs.

NILUT: Conditional Neural Implicit 3D Lookup Tables for Image Enhancement

Bayesian Experimental Design (BED), which aims to find the optimal experimental conditions for Bayesian inference, is usually posed as to optimize the expected information gain (EIG). The gradient information is often needed for efficient EIG optimization, and as a result the ability to estimate the gradient of EIG is essential for BED problems. The primary goal of this work is to develop methods for estimating the gradient of EIG, which, combined with the stochastic gradient descent algorithms,  result in efficient optimization of EIG. Specifically, we first introduce a posterior expected representation of the EIG gradient with respect to the design variables. Based on this, we propose two methods for estimating the EIG gradient, UEEG-MCMC that leverages posterior samples generated through Markov Chain Monte Carlo (MCMC) to estimate the EIG gradient, and BEEG-AP that focuses on achieving high simulation efficiency by repeatedly using parameter samples. Theoretical analysis and numerical studies illustrate that UEEG-MCMC is robust agains the actual EIG value, while BEEG-AP is more efficient when the EIG value to be optimized is small. Moreover, both methods show superior performance compared to several popular benchmarks in our numerical experiments.

On Estimating the Gradient of the Expected Information Gain in Bayesian Experimental Design

Class-agnostic counting (CAC) aims to count objects of interest from a query image given few exemplars. This task is typically addressed by extracting the features of query image and exemplars respectively and then matching their feature similarity, leading to an extract-then-match paradigm. In this work, we show that CAC can be simplified in an extract-and-match manner, particularly using a vision transformer (ViT) where feature extraction and similarity matching are executed simultaneously within the self-attention. We reveal the rationale of such simplification from a decoupled view of the self-attention.The resulting model, termed CACViT, simplifies the CAC pipeline into a single pretrained plain ViT. Further, to compensate the loss of the scale and the order-of-magnitude information due to resizing and normalization in plain ViT, we present two effective strategies for scale and magnitude embedding. Extensive experiments on the FSC147 and the CARPK datasets show that CACViT significantly outperforms state-of-the-art CAC approaches in both effectiveness (23.60% error reduction) and generalization, which suggests CACViT provides a concise and strong baseline for CAC. Code will be available.

Neural Oscillators for Generalization of Physics-Informed Machine Learning

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Neural Oscillators for Generalization of Physics-Informed Machine Learning

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Fast Machine Unlearning without Retraining through Selective Synaptic Dampening

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