We reveal the theoretical foundations of techniques for editing large language models, and present new methods which can do so without requiring retraining. Our theoretical insights show that a single metric (a measure of the intrinsic dimension of the model's features) can be used to assess a model's editability and reveals its previously unrecognised susceptibility to malicious *stealth attacks*. This metric is fundamental to predicting the success of a variety of editing approaches, and reveals new bridges between disparate families of editing methods. We collectively refer to these as *stealth editing* methods, because they directly update a model's weights to specify its response to specific known hallucinating prompts without affecting other model behaviour. By carefully applying our theoretical insights, we are able to introduce a new *jet-pack* network block which is optimised for highly selective model editing, uses only standard network operations, and can be inserted into existing networks. We also reveal the vulnerability of language models to stealth attacks: a small change to a model's weights which fixes its response to a single attacker-chosen prompt. Stealth attacks are computationally simple, do not require access to or knowledge of the model's training data, and therefore represent a potent yet previously unrecognised threat to redistributed foundation models. Extensive experimental results illustrate and support our methods and their theoretical underpinnings. Demos and source code are available at https://github.com/qinghua-zhou/stealth-edits.

Adversarial attacks dramatically change the output of an otherwise accurate learning system using a seemingly inconsequential modification to a piece of input data. Paradoxically, empirical evidence indicates that even systems which are robust to large random perturbations of the input data remain susceptible to small, easily constructed, adversarial perturbations of their inputs. Here, we show that this may be seen as a fundamental feature of classifiers working with high dimensional input data. We introduce a simple generic and generalisable framework for which key behaviours observed in practical systems arise with high probability-notably the simultaneous susceptibility of the (otherwise accurate) model to easily constructed adversarial attacks, and robustness to random perturbations of the input data. We confirm that the same phenomena are directly observed in practical neural networks trained on standard image classification problems, where even large additive random noise fails to trigger the adversarial instability of the network. A surprising takeaway is that even small margins separating a classifier's decision surface from training and testing data can hide adversarial susceptibility from being detected using randomly sampled perturbations. Counter-intuitively, using additive noise during training or testing is therefore inefficient for eradicating or detecting adversarial examples, and more demanding adversarial training is required.

We propose a new kernel that quantifies success for the task of computing a core-periphery partition for an undirected network. Finding the associated optimal partitioning may be expressed in the form of a quadratic unconstrained binary optimization (QUBO) problem, to which a state-of-the-art quantum annealer may be applied. We therefore make use of the new objective function to (a) judge the performance of a quantum annealer, and (b) compare this approach with existing heuristic core-periphery partitioning methods. The quantum annealing is performed on a commercially available D-Wave machine. The QUBO problem involves a full matrix even when the underlying network is sparse. Hence, we develop and test a sparsified version of the original QUBO which increases the available problem dimension for the quantum annealer. Results are provided on both synthetic and real data sets, and we conclude that the QUBO/quantum annealing approach offers benefits in terms of optimizing this new quantity of interest.

In this work we present a formal theoretical framework for assessing and analyzing two classes of malevolent action towards generic Artificial Intelligence (AI) systems. Our results apply to general multi-class classifiers that map from an input space into a decision space, including artificial neural networks used in deep learning applications. Two classes of attacks are considered. The first class involves adversarial examples and concerns the introduction of small perturbations of the input data that cause misclassification. The second class, introduced here for the first time and named stealth attacks, involves small perturbations to the AI system itself. Here the perturbed system produces whatever output is desired by the attacker on a specific small data set, perhaps even a single input, but performs as normal on a validation set (which is unknown to the attacker).We show that in both cases, i.e., in the case of an attack based on adversarial examples and in the case of a stealth attack, the dimensionality of the AI's decision-making space is a major contributor to the AI's susceptibility. For attacks based on adversarial examples, a second crucial parameter is the absence of local concentrations in the data probability distribution, a property known as Smeared Absolute Continuity. According to our findings, robustness to adversarial examples requires either (a) the data distributions in the AI's feature space to have concentrated probability density functions or (b) the dimensionality of the AI's decision variables to be sufficiently small. We also show how to construct stealth attacks on high-dimensional AI systems that are hard to spot unless the validation set is made exponentially large.

Understanding complex networks of protein-protein interactions (PPIs) is one of the foremost challenges of the post-genomic era. Due to the recent advances in experimental bio-technology, including yeast-2-hybrid (Y2H), tandem affinity purification (TAP) and other high-throughput methods for protein-protein interaction (PPI) detection, huge amounts of PPI network data are becoming available. Of major concern, however, are the levels of noise and incompleteness. For example, for Y2H screens, it is thought that the false positive rate could be as high as 64%, and the false negative rate may range from 43% to 71%. TAP experiments are believed to have comparable levels of noise.We present a novel technique to assess the confidence levels of interactions in PPI networks obtained from experimental studies. We use it for predicting new interactions and thus for guiding future biological experiments. This technique is the first to utilize currently the best fitting network model for PPI networks, geometric graphs. Our approach achieves specificity of 85% and sensitivity of 90%. We use it to assign confidence scores to physical protein-protein interactions in the human PPI network downloaded from BioGRID. Using our approach, we predict 251 interactions in the human PPI network, a statistically significant fraction of which correspond to protein pairs sharing common GO terms. Moreover, we validate a statistically significant portion of our predicted interactions in the HPRD database and the newer release of BioGRID. The data and Matlab code implementing the methods are freely available from the web site: http://www.kuchaev.com/Denoising.

Large, sparse networks that describe complex interactions are a common feature across a number of disciplines, giving rise to many challenging matrix computational tasks. Several random graph models have been proposed that capture key properties of real-life networks. These models provide realistic, parametrized matrices for testing linear system and eigenvalue solvers. CONTEST (CONtrollable TEST matrices) is a random network toolbox for MATLAB that implements nine models. The models produce unweighted directed or undirected graphs; that is, symmetric or unsymmetric matrices with elements equal to zero or one. They have one or more parameters that affect features such as sparsity and characteristic pathlength and all can be of arbitrary dimension. Utility functions are supplied for rewiring, adding extra shortcuts and subsampling in order to create further classes of networks. Other utilities convert the adjacency matrices into real-valued coefficient matrices for naturally arising computational tasks that reduce to sparse linear system and eigenvalue problems.

MOTIVATION: Finding a good network null model for protein-protein interaction (PPI) networks is a fundamental issue. Such a model would provide insights into the interplay between network structure and biological function as well as into evolution. Also, network (graph) models are used to guide biological experiments and discover new biological features. It has been proposed that geometric random graphs are a good model for PPI networks. In a geometric random graph, nodes correspond to uniformly randomly distributed points in a metric space and edges (links) exist between pairs of nodes for which the corresponding points in the metric space are close enough according to some distance norm. Computational experiments have revealed close matches between key topological properties of PPI networks and geometric random graph models. In this work, we push the comparison further by exploiting the fact that the geometric property can be tested for directly. To this end, we develop an algorithm that takes PPI interaction data and embeds proteins into a low-dimensional Euclidean space, under the premise that connectivity information corresponds to Euclidean proximity, as in geometric-random graphs. We judge the sensitivity and specificity of the fit by computing the area under the Receiver Operator Characteristic (ROC) curve. The network embedding algorithm is based on multi-dimensional scaling, with the square root of the path length in a network playing the role of the Euclidean distance in the Euclidean space. The algorithm exploits sparsity for computational efficiency, and requires only a few sparse matrix multiplications, giving a complexity of O(N(2)) where N is the number of proteins. RESULTS: The algorithm has been verified in the sense that it successfully rediscovers the geometric structure in artificially constructed geometric networks, even when noise is added by re-wiring some links. Applying the algorithm to 19 publicly available PPI networks of various organisms indicated that: (a) geometric effects are present and (b) two-dimensional Euclidean space is generally as effective as higher dimensional Euclidean space for explaining the connectivity. Testing on a high-confidence yeast data set produced a very strong indication of geometric structure (area under the ROC curve of 0.89), with this network being essentially indistinguishable from a noisy geometric network. Overall, the results add support to the hypothesis that PPI networks have a geometric structure. AVAILABILITY: MATLAB code implementing the algorithm is available upon request.

MOTIVATION: Protein-protein interaction networks are one of the major post-genomic data sources available to molecular biologists. They provide a comprehensive view of the global interaction structure of an organism's proteome, as well as detailed information on specific interactions. Here we suggest a physical model of protein interactions that can be used to extract additional information at an intermediate level: It enables us to identify proteins which share biological interaction motifs, and also to identify potentially missing or spurious interactions. RESULTS: Our new graph model explains observed interactions between proteins by an underlying interaction of complementary binding domains (lock-and-key model). This leads to a novel graph-theoretical algorithm to identify bipartite subgraphs within protein-protein interaction networks where the underlying data are taken from yeast two-hybrid experimental results. By testing on synthetic data, we demonstrate that under certain modelling assumptions, the algorithm will return correct domain information about each protein in the network. Tests on data from various model organisms show that the local and global patterns predicted by the model are indeed found in experimental data. Using functional and protein structure annotations, we show that bipartite subnetworks can be identified that correspond to biologically relevant interaction motifs. Some of these are novel and we discuss an example involving SH3 domains from the Saccharomyces cerevisiae interactome. AVAILABILITY: The algorithm (in Matlab format) is available (see http://www.maths.strath.ac.uk/~aas96106/lock_key.html).

BACKGROUND: Interpretation of simple microarray experiments is usually based on the fold-change of gene expression between a reference and a "treated" sample where the treatment can be of many types from drug exposure to genetic variation. Interpretation of the results usually combines lists of differentially expressed genes with previous knowledge about their biological function. Here we evaluate a method--based on the PageRank algorithm employed by the popular search engine Google--that tries to automate some of this procedure to generate prioritized gene lists by exploiting biological background information. RESULTS: GeneRank is an intuitive modification of PageRank that maintains many of its mathematical properties. It combines gene expression information with a network structure derived from gene annotations (gene ontologies) or expression profile correlations. Using both simulated and real data we find that the algorithm offers an improved ranking of genes compared to pure expression change rankings. CONCLUSION: Our modification of the PageRank algorithm provides an alternative method of evaluating microarray experimental results which combines prior knowledge about the underlying network. GeneRank offers an improvement compared to assessing the importance of a gene based on its experimentally observed fold-change alone and may be used as a basis for further analytical developments.

To augment the discrete Runge-Kutta solutlon to the mitlal value problem, piecewlse Hermite interpolants have been used to provide a continuous approximation with a continuous first derivative We show that it M possible to construct mterpolants with arbltrardy many continuous derivatives which have the same asymptotic accuracy and basic cost as the Hermite interpol ants. We also show that the usual truncation coefficient analysis can be applied to these new interpolants, allowing their accuracy to be examined in more detad As an Illustration, we present some globally C2 interpolants for use with a popular 4th and 5th order Runge-Kutta pair of Dormand and Prince, and we compare them theoretically and numerically with existing interpolants.

article Free Access Share on Remark on algorithm 669 Author: Desmond J. Higham Univ. of Toronto, Toronto, Canada Univ. of Toronto, Toronto, CanadaView Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 17Issue 3Sept. 1991 pp 424–426https://doi.org/10.1145/114697.116814Published:01 September 1991Publication History 0citation233DownloadsMetricsTotal Citations0Total Downloads233Last 12 Months11Last 6 weeks2 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF