arXiv subjects

Aniruddha Saha

Publications and source records attributed to Aniruddha Saha.

At least 19 recordsLinked to original sources

arXiv2026

Free Resolutions of Symmetric Algebras of Ideals with Deviation Two

For a graded ideal I in a graded ring, the deviation of I is defined as the difference between the minimal number of generators of I and its grade. In this article, we provide bigraded free resolutions of the symmetric algebras for specific classes of ideals of deviation two. Additionally, we study the regularity of powers of deviation two ideals generated by d-sequences. In particular, we examine the powers of Huneke-Ulrich ideals and find bounds on their regularity.

math.AC↗

arXiv2026

Complexity and curvature of (pairs of) Cohen-Macaulay modules, and their applications

The complexity and curvature of a module, introduced by Avramov, measure the growth of Betti and Bass numbers of a module, and distinguish the modules of infinite homological dimension. The notion of complexity was extended by Avramov-Buchweitz to pairs of modules that measure the growth of Ext modules. The related notion of Tor complexity was first studied by Dao. Inspired by these notions, we define Ext and Tor curvature of pairs of modules. The aim of this article is to study (Ext and Tor) complexity and curvature of pairs of certain CM (Cohen-Macaulay) modules, and establish lower bounds of complexity and curvature of pairs of modules in terms of that of a single module. It is known that among all modules, the residue field has maximal complexity and curvature, moreover they characterize complete intersection local rings. As applications of our results, we provide some upper bounds of the curvature of the residue field in terms of curvature and multiplicity of any nonzero CM module. As a final upshot, these allow us to characterize complete intersection local rings (including hypersurfaces and regular rings) in terms of complexity and curvature of pairs of certain CM modules. In particular, under some additional hypotheses, we characterize complete intersection and regular local rings via injective curvature of the ring and that of the module of Kähler differentials respectively. Thus, we make partial progress towards a question of Christensen-Striuli-Veliche, as well as another by Vasconcelos.

math.AC↗

arXiv2026

Test properties of some Cohen-Macaulay modules and criteria for local rings via finite vanishing of Ext or Tor

In this article, we show test properties, in the sense of finitely many vanishing of Ext or Tor, of CM (Cohen-Macaulay) modules whose multiplicity and number of generators (resp., type) are related by certain inequalities. We apply these test behaviour, along with other results, to characterize various kinds of local rings, including hypersurface rings of multiplicity at most two, surprisingly requiring only finitely many vanishing of Ext or Tor involving such CM modules. As further applications, we verify the long-standing (Generalized) Auslander-Reiten Conjecture for every CM module of minimal multiplicity over a Noetherian local ring, thus vastly extending a result of Huneke-Şega-Vraciu.

math.AC↗

arXiv2025

Selection and Stability of Functional Connectivity Features for Classification of Brain Disorders

Brain disorders are an umbrella term for a group of neurological and psychiatric conditions that have a major effect on thinking, feeling, and acting. These conditions encompass a wide range of conditions. The illnesses in question pose significant difficulties not only for individuals, but also for healthcare systems all across the world. In this study, we explore the capability of explainable machine learning for classification of people who suffer from brain disorders. This is accomplished by the utilization of brain connection map, also referred as connectome, derived from functional magnetic resonance imaging (fMRI) data. In order to analyze features that are based on the connectome, we investigated several different feature selection procedures. These strategies included the Least Absolute Shrinkage and Selection Operator (LASSO), Relief, and Analysis of Variance (ANOVA), in addition to a logistic regression (LR) classifier. First and foremost, the purpose was to evaluate and contrast the classification accuracy of different feature selection methods in terms of distinguishing healthy controls from diseased individuals. The evaluation of the stability of the traits that were chosen was the second objective. The identification of the regions of the brain that have an effect on the classification was the third main objective. When applied to the UCLA dataset, the LASSO approach, which is our most effective strategy, produced a classification accuracy of 91.85% and a stability index of 0.74, which is greater than the results obtained by other approaches: Relief and ANOVA. These methods are effective in locating trustworthy biomarkers, which adds to the development of connectome-based classification in the context of issues that impact the brain.

q-bio.NC↗

arXiv2024

From wicking to anti-wicking: A universal framework for capillary dynamics

The dynamics of capillary rise under different geometric and fluid conditions have the common signatures of rapid rise followed by an equilibrium state that describe the underlying competing forces. We present a new interpretation of capillary dynamics using a linear damped system where modulation of damping and forcing characteristics are achieved using axisymmetric channels with sinusoidal variation in radius. The complete axisymmetric design space ranging from hydrophilic channels that enable spontaneous imbibition to hydrophobic channels, that required external pressure mechanisms is modeled and the force dynamics is split into simultaneous damping and forcing characteristics. We introduce the product of damping and forcing terms as the new parameter that effectively characterizes rise dynamics across various geometric and flow conditions, encompassing both flow-enhancing and flow-inhibiting scenarios. The monotonic nature of this parameter enables the development of a stochastic optimization method that can determine optimal channel geometries for controlled capillary rise.

physics.flu-dyn↗

arXiv2024

Spotting LLMs With Binoculars: Zero-Shot Detection of Machine-Generated Text

Detecting text generated by modern large language models is thought to be hard, as both LLMs and humans can exhibit a wide range of complex behaviors. However, we find that a score based on contrasting two closely related language models is highly accurate at separating human-generated and machine-generated text. Based on this mechanism, we propose a novel LLM detector that only requires simple calculations using a pair of pre-trained LLMs. The method, called Binoculars, achieves state-of-the-art accuracy without any training data. It is capable of spotting machine text from a range of modern LLMs without any model-specific modifications. We comprehensively evaluate Binoculars on a number of text sources and in varied situations. Over a wide range of document types, Binoculars detects over 90% of generated samples from ChatGPT (and other LLMs) at a false positive rate of 0.01%, despite not being trained on any ChatGPT data.

cs.CL↗

arXiv2024

On the Reliability of Watermarks for Large Language Models

As LLMs become commonplace, machine-generated text has the potential to flood the internet with spam, social media bots, and valueless content. Watermarking is a simple and effective strategy for mitigating such harms by enabling the detection and documentation of LLM-generated text. Yet a crucial question remains: How reliable is watermarking in realistic settings in the wild? There, watermarked text may be modified to suit a user's needs, or entirely rewritten to avoid detection. We study the robustness of watermarked text after it is re-written by humans, paraphrased by a non-watermarked LLM, or mixed into a longer hand-written document. We find that watermarks remain detectable even after human and machine paraphrasing. While these attacks dilute the strength of the watermark, paraphrases are statistically likely to leak n-grams or even longer fragments of the original text, resulting in high-confidence detections when enough tokens are observed. For example, after strong human paraphrasing the watermark is detectable after observing 800 tokens on average, when setting a 1e-5 false positive rate. We also consider a range of new detection schemes that are sensitive to short spans of watermarked text embedded inside a large document, and we compare the robustness of watermarking to other kinds of detectors.

cs.LG↗

arXiv2024

Generating Potent Poisons and Backdoors from Scratch with Guided Diffusion

Modern neural networks are often trained on massive datasets that are web scraped with minimal human inspection. As a result of this insecure curation pipeline, an adversary can poison or backdoor the resulting model by uploading malicious data to the internet and waiting for a victim to scrape and train on it. Existing approaches for creating poisons and backdoors start with randomly sampled clean data, called base samples, and then modify those samples to craft poisons. However, some base samples may be significantly more amenable to poisoning than others. As a result, we may be able to craft more potent poisons by carefully choosing the base samples. In this work, we use guided diffusion to synthesize base samples from scratch that lead to significantly more potent poisons and backdoors than previous state-of-the-art attacks. Our Guided Diffusion Poisoning (GDP) base samples can be combined with any downstream poisoning or backdoor attack to boost its effectiveness. Our implementation code is publicly available at: https://github.com/hsouri/GDP .

cs.LG↗

arXiv2024

Homological dimensions of Burch ideals, submodules and quotients

The notion of Burch ideals and Burch submodules were introduced (and studied) by Dao-Kobayashi-Takahashi in 2020 and Dey-Kobayashi in 2022 respectively. The aim of this article is to characterize various local rings in terms of homological invariants of Burch ideals, Burch submodules, or that of the corresponding quotients. Specific applications of our results include the following: Let $(R,\mathfrak{m})$ be a commutative Noetherian local ring. Let $M=I$ be an integrally closed ideal of $R$ such that ${\rm depth}(R/I)=0$, or $M = \mathfrak{m} N \neq 0$ for some submodule $N$ of a finitely generated $R$-module $L$ such that either ${\rm depth}(N)\ge 1$ or $L$ is free. It is shown that: (1) $I$ has maximal projective $($resp., injective$)$ complexity and curvature. (2) $R$ is Gorenstein if and only if ${\rm Ext}_R^n(M,R)=0$ for any three consecutive values of $n \ge \max\{{\rm depth}(R)-1,0\}$. (3) $R$ is CM (Cohen-Macaulay) if and only if CM-$\dim_R(M)$ is finite.

math.AC↗

arXiv2023

NEFTune: Noisy Embeddings Improve Instruction Finetuning

We show that language model finetuning can be improved, sometimes dramatically, with a simple augmentation. NEFTune adds noise to the embedding vectors during training. Standard finetuning of LLaMA-2-7B using Alpaca achieves 29.79% on AlpacaEval, which rises to 64.69% using noisy embeddings. NEFTune also improves over strong baselines on modern instruction datasets. Models trained with Evol-Instruct see a 10% improvement, with ShareGPT an 8% improvement, and with OpenPlatypus an 8% improvement. Even powerful models further refined with RLHF such as LLaMA-2-Chat benefit from additional training with NEFTune.

cs.CL↗

arXiv2023

Baseline Defenses for Adversarial Attacks Against Aligned Language Models

As Large Language Models quickly become ubiquitous, it becomes critical to understand their security vulnerabilities. Recent work shows that text optimizers can produce jailbreaking prompts that bypass moderation and alignment. Drawing from the rich body of work on adversarial machine learning, we approach these attacks with three questions: What threat models are practically useful in this domain? How do baseline defense techniques perform in this new domain? How does LLM security differ from computer vision? We evaluate several baseline defense strategies against leading adversarial attacks on LLMs, discussing the various settings in which each is feasible and effective. Particularly, we look at three types of defenses: detection (perplexity based), input preprocessing (paraphrase and retokenization), and adversarial training. We discuss white-box and gray-box settings and discuss the robustness-performance trade-off for each of the defenses considered. We find that the weakness of existing discrete optimizers for text, combined with the relatively high costs of optimization, makes standard adaptive attacks more challenging for LLMs. Future research will be needed to uncover whether more powerful optimizers can be developed, or whether the strength of filtering and preprocessing defenses is greater in the LLMs domain than it has been in computer vision.

cs.LG↗

arXiv2023

Bring Your Own Data! Self-Supervised Evaluation for Large Language Models

With the rise of Large Language Models (LLMs) and their ubiquitous deployment in diverse domains, measuring language model behavior on realistic data is imperative. For example, a company deploying a client-facing chatbot must ensure that the model will not respond to client requests with profanity. Current evaluations approach this problem using small, domain-specific datasets with human-curated labels. These evaluation sets are often sampled from a narrow and simplified distribution, and data sources can unknowingly be leaked into the training set which can lead to misleading evaluations. To bypass these drawbacks, we propose a framework for self-supervised evaluation of LLMs by analyzing their sensitivity or invariance to transformations on the input text. Self-supervised evaluation can directly monitor LLM behavior on datasets collected in the wild or streamed during live model deployment. We demonstrate self-supervised evaluation strategies for measuring closed-book knowledge, toxicity, and long-range context dependence, in addition to sensitivity to grammatical structure and tokenization errors. When comparisons to similar human-labeled benchmarks are available, we find strong correlations between self-supervised and human-supervised evaluations. The self-supervised paradigm complements current evaluation strategies that rely on labeled data.

cs.CL↗

arXiv2023

Revisiting Image Classifier Training for Improved Certified Robust Defense against Adversarial Patches

Certifiably robust defenses against adversarial patches for image classifiers ensure correct prediction against any changes to a constrained neighborhood of pixels. PatchCleanser arXiv:2108.09135 [cs.CV], the state-of-the-art certified defense, uses a double-masking strategy for robust classification. The success of this strategy relies heavily on the model's invariance to image pixel masking. In this paper, we take a closer look at model training schemes to improve this invariance. Instead of using Random Cutout arXiv:1708.04552v2 [cs.CV] augmentations like PatchCleanser, we introduce the notion of worst-case masking, i.e., selecting masked images which maximize classification loss. However, finding worst-case masks requires an exhaustive search, which might be prohibitively expensive to do on-the-fly during training. To solve this problem, we propose a two-round greedy masking strategy (Greedy Cutout) which finds an approximate worst-case mask location with much less compute. We show that the models trained with our Greedy Cutout improves certified robust accuracy over Random Cutout in PatchCleanser across a range of datasets and architectures. Certified robust accuracy on ImageNet with a ViT-B16-224 model increases from 58.1\% to 62.3\% against a 3\% square patch applied anywhere on the image.

cs.CV↗

arXiv2022

Backdoor Attacks on Vision Transformers

Vision Transformers (ViT) have recently demonstrated exemplary performance on a variety of vision tasks and are being used as an alternative to CNNs. Their design is based on a self-attention mechanism that processes images as a sequence of patches, which is quite different compared to CNNs. Hence it is interesting to study if ViTs are vulnerable to backdoor attacks. Backdoor attacks happen when an attacker poisons a small part of the training data for malicious purposes. The model performance is good on clean test images, but the attacker can manipulate the decision of the model by showing the trigger at test time. To the best of our knowledge, we are the first to show that ViTs are vulnerable to backdoor attacks. We also find an intriguing difference between ViTs and CNNs - interpretation algorithms effectively highlight the trigger on test images for ViTs but not for CNNs. Based on this observation, we propose a test-time image blocking defense for ViTs which reduces the attack success rate by a large margin. Code is available here: https://github.com/UCDvision/backdoor_transformer.git

cs.CV↗

arXiv2022

Backdoor Attacks on Self-Supervised Learning

Large-scale unlabeled data has spurred recent progress in self-supervised learning methods that learn rich visual representations. State-of-the-art self-supervised methods for learning representations from images (e.g., MoCo, BYOL, MSF) use an inductive bias that random augmentations (e.g., random crops) of an image should produce similar embeddings. We show that such methods are vulnerable to backdoor attacks - where an attacker poisons a small part of the unlabeled data by adding a trigger (image patch chosen by the attacker) to the images. The model performance is good on clean test images, but the attacker can manipulate the decision of the model by showing the trigger at test time. Backdoor attacks have been studied extensively in supervised learning and to the best of our knowledge, we are the first to study them for self-supervised learning. Backdoor attacks are more practical in self-supervised learning, since the use of large unlabeled data makes data inspection to remove poisons prohibitive. We show that in our targeted attack, the attacker can produce many false positives for the target category by using the trigger at test time. We also propose a defense method based on knowledge distillation that succeeds in neutralizing the attack. Our code is available here: https://github.com/UMBCvision/SSL-Backdoor .

cs.CV↗

arXiv2021

Coalescence of polymeric sessile drops on a partially wettable substrate

Coalescence of sessile polymeric fluid drops on a partially wettable substrate exhibits a transition from inertial to viscoelastic regime at concentration ratio $c/c^* \sim 1$. Our findings unveil that the temporal evolution of the growing bridge height follows a power-law behaviour $t^b$, such that the coefficient $b$ continuously decreases from 2/3 in the inertial regime ($c/c^*<1$) to an asymptotic value of 1/2 in the visco-elastic regime ($c/c^*>1$). To account for fluid elasticity and characteristic time-scale in the viscoelastic regime, a modified thin film equation under lubrication approximation has been proposed using the linear Phan-Thien- Tanner constitutive equation. The temporal evolution of the droplet has been evaluated by solving the modified one-dimensional thin-film equation using a marching explicit scheme. The initial droplet shapes are obtained by re-sorting to energy minimization. A good agreement between numerical and experimental results is obtained.

physics.flu-dyn↗

arXiv2021

Contact line pinning and de-pinning can modulate the rod-climbing effect

Our experiments on the rod-climbing effect with an oil-coated rod revealed two key differences in the rod-climbing phenomena compared to a bare rod. On one hand, an enhancement in magnitude of climbing height for any particular value of rod rotation speed and second, a decrease in threshold rod rotation speed required for the appearance of the rod-climbing effect were observed. Observed phenomena is explained by considering the contact line behavior at the rod-fluid interface. Transient evolution of meniscus at the rod-fluid interface revealed that the three-phase contact line was pinned for a bare rod and de-pinned for an oil-coated rod. We modelled the subject fluid as a Giesekus fluid to predict the climbing height. The differences in the contact line behaviour were incorporated via the contact angle at the rod-fluid interface as a boundary condition. An agreement was found between the observed and predicted climbing height establishing that contact line behaviour may modulate rod-climbing effect.

physics.flu-dyn↗

arXiv2020

Universal Litmus Patterns: Revealing Backdoor Attacks in CNNs

The unprecedented success of deep neural networks in many applications has made these networks a prime target for adversarial exploitation. In this paper, we introduce a benchmark technique for detecting backdoor attacks (aka Trojan attacks) on deep convolutional neural networks (CNNs). We introduce the concept of Universal Litmus Patterns (ULPs), which enable one to reveal backdoor attacks by feeding these universal patterns to the network and analyzing the output (i.e., classifying the network as `clean' or `corrupted'). This detection is fast because it requires only a few forward passes through a CNN. We demonstrate the effectiveness of ULPs for detecting backdoor attacks on thousands of networks with different architectures trained on four benchmark datasets, namely the German Traffic Sign Recognition Benchmark (GTSRB), MNIST, CIFAR10, and Tiny-ImageNet. The codes and train/test models for this paper can be found here https://umbcvision.github.io/Universal-Litmus-Patterns/.

cs.CV↗