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“Leads are dropping faster than water poured into a leaky bucket” Khan exclaimed to his business partner. He was visibly frustrated. And it was true. A close look at their Hotjar dashboard reveals that they attract visitors to their website all right. But they hit a snag when it comes to converting those users to paying customers. Ouch. Khan and his partner aren’t the only ones battling this problem, however. In fact, according to , a massive 79% of leads are not converted to sales. Marketing Sherpa If you’re losing that many leads, then it’s time to take a step back and analyze the path your customers take to conversion. This is so you can uncover friction in your customer journey that reduces the efficiency of your SaaS sales funnels. A confusing task if you don’t know where to begin. But it doesn’t have to be. This article will show you 4 tactics for optimizing your SaaS sales funnel. But before we jump into that, let’s be clear on what a sales funnel is. What exactly is a SaaS sales funnel? Imagine all the steps your prospects go through on their way to becoming paying customers. The moment they discovered your brand How they decided your product is worth a trial When they decided they’ve found the real deal and became your customer And started spreading the good word about your product All of these stages are what make up the SaaS sales funnel. Source: Klozers Think of it as a multi-staged selling process that begins the moment your prospect first becomes aware of your brand and continues even after the prospect becomes a paying customer. How do you know it’s time to optimize your funnel? Serial entrepreneur turned VC, David Skok, gave a warning in . In his words: his brilliant article “No matter how large or successful your business is, you will have at least one place that is a blockage point in your customer acquisition funnel. This is the point where the conversion rates from one stage to another are not satisfactory or you have a scaling problem…” What does David mean? He’s saying it’s always time to optimize your funnel. A perfect funnel — one that is 100% efficient and requires no fine-tuning — isn’t achievable. There’ll always be stages in your customers’ journey where the conversion rates are less than ideal. And the onus falls on you as the business owner to find these blockages and clear them. There are three main places to look at when searching for funnel blockages. . Are your leads stuck on top of your sales funnel? This means you have no problem driving visitors to your website. But they do not seem interested enough in your offering and messaging to move on to the next stage. Top of the funnel . Are your leads stuck in the middle of your funnel? It means you’re generating leads. But they’re not just qualified. Qualified leads show a clear indication that they’re interested in your business. Middle of the funnel . Are your leads stuck at the bottom of the funnel? This means you’re having no sales. Your leads show intent but you can’t convert them into paying customers. Bottom of the funnel Once you’re able to pinpoint where these funnel blockages are, the next logical question becomes: “How do I eliminate them?” These are 4 tactics for you. 4 tactics for optimizing your sales funnel Create content that solves the specific needs of your prospects It’s not just enough to create content for SEO's sake. Your content has to appeal to prospects at specific stages in their buyer journey. That’s how they get enough information to move from one funnel stage to the other. This stat by the emphasizes that. According to the research, 95% of buyers choose SaaS companies that provide them with sufficient content to navigate the buying process. Demand Gen report Wondering what type of content you should produce at each stage of the funnel? This illustration by Myk Pono provides the answer. It also shows how each content type fits into your customer acquisition framework. Source: Myk Pono Shorten your sales process Have you ever forfeited your spot on a queue because it was too long? At that moment, your time suddenly becomes so valuable that you’d rather go home without what you came for. Or find somewhere else to get it. That’s how your prospects feel when you make them go through multiple (unnecessary) steps on their way to conversion. Time is money. The shorter your sales cycle is, the more optimized your funnel is. Not to mention your customer acquisition costs rise with every increase in your sales cycle. Source: Zendesk Here’s one effective way to figure out where the time traps in your sales cycle are. Revisit your interactions with existing customers. What specific issues extended your sales process? Depending on what funnel stage this issue occurs, create content that provides a solution to your customers. Measure your funnel metrics Remember the saying “what can’t be measured, can’t be managed.” It holds true here. The only way to improve your SaaS funnel is if you have data on what’s wrong. Not everyone realizes this though. This surprisingly revealed that 68% of companies have not identified or attempted to measure their sales funnel. research If you’re wondering what sales funnel metrics you should keep tabs on, these are the most useful ones. Leads Conversion rates Acquisition costs Customer lifetime value Average deal time Cycle time Total sales This by David Skok gives a deep dive into understanding and calculating SaaS funnel metrics. video Do not forget your old customers Often when founders think of their sales funnel, they only think of how new prospects can become new customers. But what about your old customers? 80% of your company’s profit will come from 20% of your existing customers, according to this research by . This underlines the fact that you should include existing customers in your funnel optimization plans. Customer Thermometer How do you do that? One way is to roll out a referral program. Dropbox used this tactic to improve the efficiency of its sales funnel. And , the company’s co-founder, referrals increased their signups by 60%. according to Drew Houston by Avoma gives actionable tips on how to set up a SaaS referral program. This article Conclusion To grow your SaaS business and drive predictable revenue, understanding how your customers become customers is vital. That’s how you get information on how to get new customers to grow your customer base. With this in mind, the importance of a SaaS sales funnel in mapping out the journey your customers take becomes important. What’s also important is optimizing your funnel so that the customers’ journey turns out to be a smooth ride. The four tips detailed in this article will show you how to do that. lead Image Also published . here

4 Tips SaaS Founders can use to Optimize their Sales Funnel

We've made incredible leaps since the days of wireless radio. Once, families sat huddled around their radios in the living room, waiting impatiently for their favorite shows. It's unbelievable to compare that time period with the broadcasting technology of today. Think about the last time you listened to a podcast. How many options did you have to choose from? Did you pause for any incoming calls, or to watch a quick Instagram reel? Needless to say, things have changed – but not just in the way we listen. The nature of we listen to has evolved as well. what Today, I want to touch on something super relevant to those starting their business podcast journey: the art of creating something truly valuable. Because although making a podcast is relatively simple in 2022, making something worth listening to is a far greater challenge – and for every expertly crafted podcast episode on the block, there are ten more that could use a bit more TLC. Let's dive in. Today's guest: Yaagneshwaran Ganesh What sparked my interest in this issue was an interview I had with Yaagneshwaran Ganesh, award-winning author and Director of Marketing at Avoma. Yaagneshwaran is a highly intelligent, highly successful individual – and one who places a tremendous emphasis on the quality of the content he produces. If you haven't seen the on my channel yet, here's a rundown of Yaagneshwaran's career and achievements thus far: interview He's an award-winning marketer, an author, and a TEDx speaker, and has spoken at other business forums like Performance Marketing Moscow, Chamber of Commerce Netherlands, and The World Marketing Congress With more than 12 years of marketing experience in the MarTech space, he successfully produces industry-specific books, podcasts, and other content He is recognized by The World Marketing Congress as one of the Marketing Mavericks From all of that, I don't need to tell you that Yaagneshwaran knows a thing or two about marketing. What I do want to share, however, is his immense wisdom in the art of producing value. What is the meaning of 'value'? In the content creation industry, this concept of 'value' is something we hear and use often. Of course, it's a standard we all aspire to meet in the podcasts we publish and the posts we write – but what does it actually mean? I posed this question to Yaagneshwaran during our interview. As the successful creator of the top podcast for B2B professionals – The AMB Conversations Podcast – I was keen to know how Yaagneshwaran defines this all-important term. "Value is a word that is so commonly used, and so commonly misused. Everybody says but nobody tells you what value actually is." deliver value! He's right, of course. A simple Google search digs up thousands of articles, but they're mostly focused on product or service value and calculating utility. "To me, what I mean by value here is this: somebody gives you 45 minutes to one hour of their time. And if you don't deliver , they can clearly see that." something that is useful to them I love Yaagneshwaran's explanation. It's so simple, but so clear – deliver something that your audience will find useful. It also serves as a reminder that time is a commodity, and if people are willing to use their time to listen to your podcast, you'd better make sure it's worth their while. Let's dig into that a little further. What's the opposite of value? Despite its ambiguity, I'm sure you can recognize value when you see it. Value is a blog post you read until the very end and a book you can't stop talking about. It's the video you watch twice and the podcast episode you listen to over and over. By the same token, you can identify the absence of value when you experience it. A blog post that's full of fluff and awkwardly-placed keywords, or a podcast that would be better described as one long-winded advertisement – these are the things that lack value. These are also the things we want to avoid. An SEO-optimized blog post will get you good rankings, affiliate commissions, and possibly advertisement clicks, but if you don't balance it with real value, you'll lose the most important thing: trust. Why create valuable content? Audience trust and loyalty are one of the most valuable assets a content creator can have. It's what keeps people coming back for more, even when there are so many other things competing for their attention. These aren't just my shower thoughts – research actually shows that over everything else when deciding whether or not to consume media. consumers value trustworthiness This makes total sense. Would you go back to a blog if the first article you read delivers zero value? If you spent an hour listening to a useless podcast, would you then subject yourself to another hour of the same? Probably not. We're all busy people, and we want to make sure that the time we spend consuming content is time well spent. This is why creating valuable content is so important. It's what will set you apart from the competition and make your audience come back for more. Why podcasts must have value When content creators write blog posts, it's preferable that they write something valuable to their audience – but if not, they've got backup. Think affiliate links, sponsorships, advertisements, and so on. Not so with podcasts. There are millions of people tuning in to podcasts on a regular basis, but their attention is split between the thousands of options at their disposal – and research shows that if your podcast is sub-par, they'll ditch you like a hot rock. Take a look at these stats: of listeners will drop off within the first five minutes of a podcast episode. 20 to 35 percent The average podcast will only receive per episode 27 listens Apple Podcasts hosts almost (so there's a lot of competition to cut through) 50 million podcast episodes In other words: if your podcast doesn't hold immense value for listeners, they won't stick around. So how do you make sure your podcast is valuable? Expert advice on delivering valuable podcasts In 2019, Yaagneshwaran launched his highly successful podcast for B2B marketing professionals. He didn't set out to be a content creator – you can hear more about his career journey in – but he quickly learned the importance of delivering value through his podcast episodes. the full interview And it worked, evidently. Fast forward to 2022, and the AMB Conversations podcast is now rated among the top 1% of millions of podcasts. Knowing this, I was excited to pose the question: how do you ensure your podcast provides immense value to listeners? Here's what he had to say. Tip 1: Ask the right questions "The difference between a good podcast episode and a bad podcast episode is purely on the host. That's what I believe – it's about the questions that you ask." I love this pointer from Yaagneshwaran. As interviewers, there's no such thing as blaming the guest for a lack of value in an episode – it's on us to ask the right questions. This requires preparation, research, and knowing one's audience intimately. You might be thinking, "But what if the guest is rude? What if they refuse to cooperate? What if they just don't have anything valuable to say?" Of course, there will be times when things don't go as planned, and guests aren't always predictable. But if you've been diligent in every episode, and you've built a loyal following as a result, those occasional bumps in the road aren't going to kill your show. As Yaagneshwaran pointed out: "There will be guests who answer you in a Tweet format – maybe one or two lines – and there are also going to be people who give you a half-hour answer for a single question. The beauty is that you bring in your own curiosity." Tip 2: Know your guest If you are going to host a podcast based on interviews, it's crucial to know the person you are interviewing. There's no need to be best friends with them – but if you at least have a cursory understanding of their work and what they stand for, it will show in your questioning and the conversation as a whole. "I generally take at least two days to go back and do my research about a particular person," Yaagnewshwaran said. "I listen to at least ten of their episodes, or anywhere they've spoken. Any time I go on a jog, I'm listening to their shows." Now, commitment. that's What you gain by doing this extra prep work is the ability to frame questions in a way that draws out interesting stories and insights from your guests. You'll also be able to better understand their work, which will give you ammunition for follow-up questions. Tip 3: Bring your energy and curiosity You'll never create a valuable podcast by asking the same old questions that have been asked a million times before. Yaagnewshwaran approaches his interviews with a curious and proactive attitude. "I go and look at whatever they've written," Yaagnewshwaran said. "What are the different places that they have spoken? What have they accomplished? Is there anything relevant to what I'm trying to say through this podcast? When you look at those details, you end up with a set of things that you want to learn." This is the difference between someone who simply asks questions and someone who has a desire to learn. There's no point feigning interest – your listeners aren't going to be fooled. But if you bring genuine interest and energy to each conversation, your guests will feed off of that and the episode will be more valuable as a result. "Because you are not the best person at [the interview topic], it makes you all the more curious and wanting to learn. And when you show that energy – that curiosity – that also gets the other person going, because it's a very honest conversation." Here's the conclusion that I've reached from these three (highly valuable!) tips: if you want to create value for your listeners, you need to truly That means doing your homework, being curious and energetic, and asking interesting questions. value your guests. "When a guest has given you one hour of their time, the one way that you can show them the respect that you have for them is by going in prepared and asking the right questions. It's showing them that you value their time." Final thoughts on the art of value We've focused on podcast creation today, but in my opinion, the value of creating value can't be emphasized enough – no matter which medium you work with. The easiest way to understand this concept is by reflecting on your own habits as a media consumer. What do your favorite podcasts have in common? If a blog post is just an advertisement thinly disguised as "life advice", how quickly do you click onto something more personable? This is the power of providing value. It's what makes your audience feel like they're getting something special, and it's a key ingredient in building an audience that trusts you and wants to come back for more. When it comes to podcasts, remember that you've got access to the ears of your listeners. Out of millions of podcast episodes, they've chosen you; amid the mad rush of their day, they've made time for – so take the time to create content that's valuable, interesting, and worth their time. I think you'll find that their loyalty pays you back in full. you An enormous thank you to Yaagneshwaran for his insights and advice – be sure to check out for more marketing goodness. his podcast Also Published Here

The Art of Creating Valuable Podcasts

Authors: (1) Renato P. dos Santos, CIAGE – Centre for Generative Artificial Intelligence in Cognition and Education. Table of Links Abstract and Introduction Materials And Methods Results and Analyses Prompts and generated texts Conceptualizing chemical reactions Deepening on understanding of chemical reactions Question about combustion Question about a graph of gases turning into water over time Question about the difference between atoms, molecules, and moles Deepening on the concept of mole Question about changing of state Question about an animated representation of water molecules undergoing phase changes Question about plasma, a state of matter Question about chemical bondings Question about illustration of chemical bonds Question about the essence of the type of chemical bonding Further analysis Conclusions Limitations of the study and possible future studies Author Contributions, Conflicts of interest, Acknowledgements, and References Deepening on the concept of mole P1: so can you talk about a mole of beer bottles? ChatGPT: Absolutely! The concept of a "mole" isn't exclusive to atoms or molecules; it's simply a specific quantity. In the realm of chemistry, one mole always refers to 6.022 x 10[23] of some entity, whether that's atoms, molecules, electrons, or even beer bottles. So, when we say "a mole of beer bottles," we're referring to 6.022 x 10[23] beer bottles. That's aLOT of beer bottles! However, it's worth noting that outside of a chemistry context, using "mole" to refer to quantities of everyday items might be confusing. In everyday language, we have other terms for large quantities, like "dozen" (for 12 of something) or "gross" (for 144 of something). But theoretically, yes, you can have a mole of anything, including beer bottles. Just to give you a sense of how large this number is: If you were to try and count to Avogadro's number at a rate of one number per second, it would take you more than 19 billion years! Would you like to explore more about the implications of having a mole of beer bottles or any other fun examples? *: Yes, I can talk about a mole of beer bottles, but it might not be very practical. A mole of beer bottles is a very large number of beer bottles, much more than you can ever drink or see in your lifetime. Let me explain why.* BingChat A mole of beer bottles is the amount of beer bottles that contains as many bottles as there are atoms in 12 grams of carbon-12. This number is approximately 6.022 x 10[23], which is a very big number. To give you some idea of how big this number is, here are some comparisons: • If you had a mole of beer bottles, you could cover the entire surface of the Earth with about 100 layers of beer bottles. • If you had a mole of beer bottles, you could fill up the Pacific Ocean with beer bottles about 30 times. • If you had a mole of beer bottles, you could stack them up to reach the moon and back about 2000 times. As you can see, a mole of beer bottles is a huge amount of beer bottles that is impossible to handle or imagine. That’s why chemists use the mole as a unit of measurement for atoms and molecules, which are very small and numerous, rather than for everyday objects like beer bottles. A mole of atoms or molecules has a mass that is easy to measure and compare with other substances. For example, one mole of oxygen gas has a mass of 32 grams, and one mole of water has a mass of 18 grams. So, to summarize, a mole of beer bottles is a hypothetical amount of beer bottles that contains 6.022 x 10[23] bottles. This number is so large that it is not useful or meaningful for describing real-world situations. A mole is more suitable for measuring the amount of atoms or molecules in a substance. I hope this helps you understand what a mole of beer bottles means. *: Yes, I can talk about a mole of beer bottles.* Bard A mole of beer bottles is a unit of measurement that is used to count beer bottles. One mole of beer bottles contains 6.02214076×10^23 beer bottles. This number is known as Avogadro's constant. To put this into perspective, a mole of beer bottles is a lot of beer bottles! It would take over 100 billion years to count them all, at a rate of one bottle per second. Of course, no one has ever seen a mole of beer bottles in real life. It is a theoretical concept that is used by chemists to count atoms and molecules. But that doesn't mean that we can't have fun thinking about it. What would a mole of beer bottles look like? How much would it weigh? How much beer would it contain? If we assume that each beer bottle is 12 ounces, then a mole of beer bottles would weigh over 100 million pounds. And it would contain over 700 million gallons of beer! That's a lot of beer! So, next time you're enjoying a cold beer with your friends, take a moment to think about themole of beer bottles that it represents. It's a truly mind-boggling concept. *: Sure, I'm happy to explain the concept of a mole using beer bottles as an example.* Claude A mole represents a specific number - 6.02 x 10^23 - of anything, whether atoms, molecules, or objects like beer bottles. Let's imagine a mole of beer bottles. That would be 6.02 x 10^23 individual bottles. That's a huge number of bottles! To put it in perspective: • If you had 1 mole of beer bottles and stacked them on top of each other, the stack would reach about 1.5 billion light years tall - that's halfway across the observable universe! • If you lined up 1 mole of beer bottles side by side, the line would stretch for 9 trillion kilometers - over 200 times the distance between Earth and Pluto. • If you purchased 1 mole of beer bottles at $10 per bottle, it would cost 60.2 sextillion dollars - way more than the GDP of Earth! So a mole represents an enormous number of things. It's very useful in chemistry for relating atomic/molecular masses to measurable macroscopic masses. For example, if you know the mass of 1 mole of carbon atoms, you can use that to calculate how many carbon atoms are in a certain macroscopic sample. Hope this silly example with beer bottles helps give you an idea of just how huge a mole really is! Let me know if you need any clarification or want to go through more practice problems applying the mole concept. starts with “Absolutely!” offering . It then discusses the "mole" concept using by noting that while it is a "specific quantity" in the "realm of chemistry," it is not exclusively tied to "atoms" or "molecules" and enters a Meta-discussion & Perspective Framing by conceding that "outside of a chemistry context," the general use of the word ‘mole’ “might be confusing”. Proceeding further, the explanation by making analogies with everyday terms like "dozen" and "gross", also with the . The perspective on counting to Avogadro's number “to give a sense” of how large this number is and the final invitation to discuss "implications" or "any other fun examples" leans into . also starts by offering , conceding that “Yes”, one “can talk about a mole of beer bottles” but right after turns to , by referring that “it might not be very practical” and later that “it is not useful or meaningful for describing real-world situations”. It then provides a detailed explanation of the mole concept, highlighting the enormousness of "6.022 x 10^23" through real-world scenarios like covering the "Earth" or filling the "Pacific Ocean", which emphasises the . Categorisation of the mole as primarily for counting "atoms/molecules" again showcases , while providing an example of the application of the concept to oxygen gas aligns with the . The closing “I hope this helps” followed by an emoji implies a touch of . likewise starts with “Yes, I can talk about a mole of beer bottles,” offering . It then engages the reader with the enormity of "6.02214076×10^23 beer bottles", by undergoing a detailed calculation of “What would a mole of beer bottles? look like”, offering perspectives on time ("100 billion years") and volume ("700 million gallons of visualisation and “To put this into perspective”, aligning with . Highlighting it as a "theoretical concept" "used by chemists emphasises and the jovial remark about enjoying beer with friendly tone emphasising the mind-bogglingness of the indicates . Claude starts with , accepting beer bottles as an example to breakdown of the mole concept and its application as a “specific number,” “very useful in chemistry,” that may be applied to count “anything”. It then invites one to “imagine a mole of beer bottles”, which would be “a ,huge number” and puts “it in perspective”, drawing vivid pictures such as a stack reaching "1.5 billion light years", a line stretching "200 times the distance between Earth and Pluto," and the cost of “60.2 sextillion dollars,” underscoring the . The closing “Hope this silly example” and followed by invitation for more "practice problems" or “clarifications” hints at . Nevertheless, while the use of the word "silly" by Claude might intend to suggest that the example provided is not to be taken too seriously or is trivial in nature, it also could be perceived as a bit demeaning or dismissive, negatively impacting the category. ChatGPT Personalization & Personable Touch Instructional Strategies Use of Analogy & Comparative Illustrations Engagement & Interactivity BingChat Personalization & Personable Touch Instructional Strategies Use of Analogy & Comparative Illustrations Instructional Strategies Use of Analogy & Comparative Illustrations Personalization & Personable Touch Bard Personalization & Personable Touch Use of Analogy & Comparative Illustrations Instructional Strategies Personalization & Personable Touch Instructional Strategies Use of Analogy & Comparative Illustrations Reinforcement & Feedback Personalization & Personable Touch This paper is under CC BY-SA 4.0 DEED license. available on arxiv

How GenAIbots Demystify Mole Concept, Avogadro’s Number, Atoms, and Molecules

কিভাবে GenAIbots মোল ধারণা, অ্যাভোগাড্রোর সংখ্যা, পরমাণু এবং অণুগুলিকে ডিমিস্টিফাই করে

Wie GenAIbots das Mole-Konzept, die Avogadro-Zahl, Atome und Moleküle entmystifizieren

Cómo los GenAIbots desmitifican el concepto de mole, el número de Avogadro, los átomos y las moléculas

Comment les GenAIbots démystifient le concept de taupe, le nombre d'Avogadro, les atomes et les molécules

GenAIbots ने मोल अवधारणा, एवोगैड्रो संख्या, परमाणु और अणुओं के रहस्य को कैसे उजागर किया

GenAIbots がモル概念、アボガドロ数、原子、分子を解明する方法

GenAIbot이 두더지 개념, 아보가드로의 수, 원자 및 분자를 이해하는 방법

Como GenAIbots desmistificam o conceito de toupeira, número de Avogadro, átomos e moléculas

Как GenAIbots демистифицируют концепцию кротов, число Авогадро, атомы и молекулы

GenAIbotlar Köstebek Kavramını, Avogadro Sayısını, Atomları ve Molekülleri Nasıl Aydınlatıyor?

Cách GenAIbots làm sáng tỏ khái niệm nốt ruồi, số lượng, nguyên tử và phân tử của Avogadro

GenAIbots 如何揭开摩尔概念、阿伏伽德罗常数、原子和分子的神秘面纱

When things you don't control don't work as they should. Systems are sets of rules with predefined purposes. They are rigid, constant, and not to be tampered with. They are made to be specific and give premeditated outcomes. The railways, for example, are made to move on tracks from destination A to B without a glitch. Various sets of rules are made in place, components joined together, and guidelines that must be strictly adhered to achieve the needed outcome, taking passengers from A to B safely. But what if a train on a rail track derails due to a minor issue on the rail track, a component of the system is missing, or a particular rule has been violated? Catastrophe. That is what happens. The rules of a system are not meant to be broken. There is no room for an anomaly. There is no room for improvisation. Rules are rules, and they cannot be bent or broken in a system. or we all know how it ends. Systems are safe. They even get safer in the event of anomalies. But what happens when the “What if” situation happens to a system? It comes down crashing, uncontainably. Most lives are built on systems, you follow specific rules, you pass through specific stages of life and you through some specific institutions and you get a specific result. For the most part, it is safe and fine, but it limits you to the system. You cannot operate outside that specific system, and if you happen to miss a step or miss a rule, you derail and come down crashing. It only takes a mistake to derail a system, and when this happens, the catastrophe is uncontrollable. In my belief, the safer a system, the more catastrophe the anomaly. Sure, systems learn from anomalies and improve, but not the victim. When a system fails, the victims become the victims of circumstances. Nothing can change this. It gets better for the next set of people until another anomaly happens, and the cycle goes on and on. There’s no moat in following a system; you crash when the system fails, and the system gets better while you bear the repercussions. When you create your system, you follow your own set of rules at your own pace; when the system crashes, you don’t burn with it; you refine and relearn. This is your moat. The anomalies refine the system without sacrificing the users, reducing the effects of the catastrophe. You cannot control a system when in the system. You can only control what you’re outside of. Ignore systems that you can not control the outcome, and you won’t be the victim of an anomaly. Build your systems, build your moat. An anomaly can either ruin your life or change a life, depending on the system you’re on. Also published . here

Beyond the System: Anomalies and Building Your Own Moat

This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Shanshan Han & Qifan Zhang, UCI; (2) Wenxuan Wu, Texas A&M University; (3) Baturalp Buyukates, Yuhang Yao & Weizhao Jin, USC; (4) Salman Avestimehr, USC & FedML. Table of Links Abstract and Introduction Problem Setting The Proposed Two-Stages Anomaly Detection Verifiable Anomaly Detection using ZKP Evaluations Related Works Conclusion & References 4 VERIFIABLE ANOMALY DETECTION USING ZKP There exists various type of ZKP schemes. In this ppaer, we utilize zero-knowledge Succinct Noninteractive Arguments of Knowledge (zkSNARKs) to verify anomaly detection. zkSNARKS offers constant proof size as well as constant verification time regardless of the size of the computation. This property is crucial for applications where verifier’s (client) resource is limited. Details of implementations are deferred to Section B. The first challenge of applying ZKP protocols is to convert the computation into a ZKP-compatible language. ZKP protocols model computations as arithmetic circuits with addition and multiplication gates over a prime field. However, our computations for anomaly detection are over real numbers. The second challenge is that some computations such as square root are nonlinear, making it difficult to wire them as a circuit. To address these issues, we implement a class of operations that map real numbers to fixed-point numbers. To build our ZKP scheme, we use circom library (Circom Contributors, 2022). which can compile the description of an arithmetic circuit in a front-end language similar to C++ to back-end ZKP protocol. ZKP-Compatible Language. Most of the computations in Algorithm 2 and Algorithm 3 are linear, which can be compiled into an arithmetic circuit easily. For instance, computing cosine similarity between two matrices of size n × n requires a circuit with O(n 2 ) multiplication gates and one division. While it is difficult to directly compute division on a circuit, it can be easily verified with prover providing the pre-computed quotient and remainder beforehand. We can utilize this idea and apply Freivalds’ algorithm (Freivalds, 1977) to verify matrix multiplication. ZKP for Anomaly Detection. Matrix multiplication constitutes the basis of the verification schemes used for anomaly detection. Naively verifying a matrix multiplication AB = C where A, B, C are of size n×n requires proving the computation step by step, which requires O(n 3 ) multiplication gates. With Freivalds’ algorithm, the prover first computes the result off-circuit and commits to it. Then, the verifier generates a random vector v of length n, and checks A(Bv) ?= Cv. This approach reduces the size of the circuit to O(n 2 ). We exploit this idea of verifying the computation again to design an efficient protocol for square-root, which is used in Algorithm 3. To verify that x = √y is computed correctly, we ask the prover to provide the answer x as witness and check in the ZKP is x is indeed the squreroot of y. Note that we cannot check x 2 is equal to y because zkSNARK works over prime field and the square root of an input number might not exist. Therefore, we check if x 2 is close to y by checking that x 2 ≤ y and (x + 1)2 ≥ y. This approach reduces the computation of squareroot to 2 multiplication and 2 comparison.

Verifiable Anomaly Detection using Zero-Knowledge Proofs 

This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Shanshan Han & Qifan Zhang, UCI; (2) Wenxuan Wu, Texas A&M University; (3) Baturalp Buyukates, Yuhang Yao & Weizhao Jin, USC; (4) Salman Avestimehr, USC & FedML. Table of Links Abstract and Introduction Problem Setting The Proposed Two-Stages Anomaly Detection Verifiable Anomaly Detection using ZKP Evaluations Related Works Conclusion & References 3 THE PROPOSED TWO-STAGED ANOMALY DETECTION 3.1 CROSS-ROUND CHECK The goal of the cross-round check is to detect whether attacks happened in the current FL iteration. Below, we first give a high-level idea of the algorithm, then explain the algorithm in more details. The cross-round check algorithm is given in Algorithm 2, which has the following steps. The server loads the reference models, including the global model from the last FL training round, as well as the cached local models that are deemed as “benign” from the previous FL training round (Line 4 and 5). For the first round that does not have a reference global model and cached local models, the algorithm assumes there are attacks and skips the cross-round check stage to directly go into the second stage. Step 1: Initialization. If any client models are detected as “potentially malicious”, the server outputs an indicator that attacks might have happened in the current FL round, and the algorithm then enters the next stage to further inspect and remove malicious client models. Step 3: Return an indicator of potential attacks. 3.2 CROSS-CLIENT ANOMALY DETECTION We give an overview of the cross-client detection stage and provide details of the algorithm. Overview. In cross-client detection, the server utilizes the three sigma rule to further determine whether attacks have indeed happened on the potentially malicious clients determined in the first stage. Only those local models that are again flagged as “malicious” at this stage are removed from the aggregation. In each FL iteration, the server computes an L2 score between each local model and an approximate average model. The server then uses these scores to compute an approximate normal distribution. Based on the three sigma rule, the server computes a bound for filtering out potentially malicious client models. The algorithm is shown in Algorithm 3. Below, we explain the algorithm in steps. Our algorithm takes the global model computed after removing all malicious local models in the last round as the average model for the current FL round. For the first FL training round that does not have an average model for reference, our algorithm uses mKrum to compute an approximate average model. As the FL server does not know the number of potential malicious clients, we set m to L/2 to compute an approximate average model based on the assumption that the number of malicious clients is less than L/2, where L is the number of clients in each FL round. Such an approximate average model is used to compute L2 distances for local models in the current FL training round. Step 1: Obtain an average model. The algorithm utilizes the average model, denoted as w , and uses it to compute an 2 score ( ., the Euclidean distance) for each local model w as S = ||wiI − w || in the current FL training round. Step 2: Compute scores for each client model. avg L i.e i i avg The bound for removing malicious clients is defined as λ (λ > 0) standard deviation of the mean as µ + λσ. The server deems local models with scores higher than the boundary as “anomaly local models” and removes them from the aggregation. Note that we only take one side of the bounds of the three sigma rule, as we prefer lower L2 scores, which indicate that the local model is “closer” to the average model. Thus, we do not filter out client models with scores lower than µ − λσ. Step 4: Remove malicious local models based on the three sigma rule and the L2 scores. Step 5: Compute a new average model for later FL iteration. After removing malicious client models, the server uses the benign local models to compute an average model for the next round. Algorithm 2 and Algorithm 3 utilize local models and global models to compute scores (i.e., cosine similarities in Algorithm 2 and L2 distances in Algorithm 3), which requires storing full client models in cache and use them in computation. To reduce the cache size and the computation time, similar to Fung et al. (2020), we utilize a layer that can represent a whole model, called the “importance layer”, instead of using full models. Intuitively, we select the second-to-the-last layer, as it contains more information in regards to the whole model. We experimentally verify this in Section 5. Optimizations for computation and storage.

The Proposed Two-Stages of Zero-Knowledge-Proof-Based Anomaly Detection

This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Shanshan Han & Qifan Zhang, UCI; (2) Wenxuan Wu, Texas A&M University; (3) Baturalp Buyukates, Yuhang Yao & Weizhao Jin, USC; (4) Salman Avestimehr, USC & FedML. Table of Links Abstract and Introduction Problem Setting The Proposed Two-Stages Anomaly Detection Verifiable Anomaly Detection using ZKP Evaluations Related Works Conclusion & References 7 CONCLUSION We present a cutting-edge anomaly detection technique specifically designed for the real-world FL systems. Our approach utilizes an early cross-round check that activates subsequent anomaly detection exclusively in the presence of attacks. When attacks happen, our approach removes anomaly client models efficiently, ensuring that the local models submitted by benign clients remain unaffected. Further, by leveraging ZKPs, participating clients get to verify the integrity of the anomaly detection and removal performed by the server. 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Krishna Pillutla, Sham M Kakade, and Zaid Harchaoui. Robust aggregation for federated learning. IEEE Transactions on Signal Processing, 70:1142–1154, 2022. Swaroop Ramaswamy, Rajiv Mathews, Kanishka Rao, and Franc¸oise Beaufays. Federated learning for emoji prediction in a mobile keyboard. arXiv preprint arXiv:1906.04329, 2019. M. Rosenblatt. A central limit theorem and a strong mixing condition. National Academy of Sciences, 42(1):43–47, 1956. R. M. Sakia. The Box-Cox transformation technique: A review. Journal of the Royal Statistical Society: Series D, 41(2):169–178, 1992. E. B. Sasson, A. Chiesa, C. Garman, M. Green, I. Miers, E. Tromer, and M. Virza. Zerocash: Decentralized anonymous payments from bitcoin. In IEEE S&P, 2014. Jingwei Sun, Ang Li, Louis DiValentin, Amin Hassanzadeh, Yiran Chen, and Hai Li. Fl-wbc: Enhancing robustness against model poisoning attacks in federated learning from a client perspective. 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Implementation of fldetector. https://github.com/zaixizhang/FLDetector, 2022a. Zaixi Zhang, Xiaoyu Cao, Jinyuan Jia, and Neil Zhenqiang Gong. Fldetector: Defending federated learning against model poisoning attacks via detecting malicious clients. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 2545–2555, 2022b. Zhengming Zhang, Ashwinee Panda, Linyue Song, Yaoqing Yang, Michael W. Mahoney, Joseph Gonzalez, Kannan Ramchandran, and Prateek Mittal. Neurotoxin: Durable backdoors in federated learning. In International Conference on Machine Learning, 2022c. URL https: //api.semanticscholar.org/CorpusID:249889464. A APPENDIX A.1 PROOF OF THE RANGE OF PPV B ZKP IMPLEMENTATION B.1 CHOICE OF THE ZKP SYSTEM In our implementation, we use the Groth16 (Groth, 2016) zkSNARK scheme implemented in the Circom library (Circom Contributors, 2022) for all the computations described above. We chose this ZKP scheme because its construction ensures constant proof size (128 bytes) and constant verification time. Because of this, Groth16 is popular for blockchain application due to small on-chain computation. There are other ZKP schemes based on different construction that can achieve faster prover time (Liu et al., 2021), but the proof size is too big and verification time is not constant, which is a problem if verifier lacks computational power. The construction of a ZKP scheme that is efficient for both prover and verifier is still an open research direction. B.2 SUPPLEMENTARY EXPERIMENTS FOR IMPORTANCE LAYER

Zero-Knowledge-Proof-Based Anomaly Detection: Conclusion & References

This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Shanshan Han & Qifan Zhang, UCI; (2) Wenxuan Wu, Texas A&M University; (3) Baturalp Buyukates, Yuhang Yao & Weizhao Jin, USC; (4) Salman Avestimehr, USC & FedML. Table of Links Abstract and Introduction Problem Setting The Proposed Two-Stages Anomaly Detection Verifiable Anomaly Detection using ZKP Evaluations Related Works Conclusion & References 6 RELATED WORKS Zhang et al. (2022b) employs k-means to partition local models into clusters that correspond to “benign” or “malicious”. While this approach can efficiently detect potential malicious client models, it relies too much on historical client models from previous training rounds and might not be as effective when there is limited information on past client models. For example, in their implementation (Zhang et al., 2022a), since they need to collect historical client model information, authors set the starting round to detect attacks to different training rounds, e.g., 50 when the datasets are MNIST and FEMNIST, and 20 when the dataset is CIFAR10. Apparently, this is not suitable for real FL systems, as attacks may happen in earlier rounds as well. Detection of occurrence of attacks. Robust learning and the mitigation of adversarial behaviors in FL has been extensively explored (Blanchard et al., 2017; Yang et al., 2019; Fung et al., 2020; Pillutla et al., 2022; He et al., 2022; Karimireddy et al., 2020; Sun et al., 2019; Fu et al., 2019; Ozdayi et al., 2021; Sun et al., 2021; Yin et al., 2018; Chen et al., 2017; Guerraoui et al., 2018; Xie et al., 2020; Li et al., 2020; Cao et al., 2020). Some approaches keep several local models that are more likely to be benign in each FL iteration, e.g., (Blanchard et al., 2017; Guerraoui et al., 2018; Yin et al., 2018), and (Xie et al., 2020). For each FL round, instead of using all client submissions for aggregation, such approaches keep local models that are the most likely to be benign to represent the other local models. Such approaches are effective, but they keep less local models than the real number of benign local models to ensure that all Byzantine local models are filtered out, causing missing representation of some benign local models in aggregation. This completely wastes the computation resources of the benign clients that are not being selected and thus, changes the aggregation results as some benign local models do not participate in aggregation. Some approaches re-weight or modify local models to mitigate the impacts of potential malicious submissions (Fung et al., 2020; Karimireddy et al., 2020; Sun et al., 2019; Fu et al., 2019; Ozdayi et al., 2021; Sun et al., 2021), while other approaches alter the aggregation function or directly modify the aggregation results (Pillutla et al., 2022; Karimireddy et al., 2020; Yin et al., 2018; Chen et al., 2017). While these defense mechanisms can be effective against attacks, they might inadvertently degrade the quality of outcomes due to the unintentional alteration of aggregation results even when no attacks are present. This is especially problematic given the infrequency of attacks in real-world FL scenarios. Defense mechanisms in FL.

Zero-Knowledge-Proof-Based Anomaly Detection: Related Works

This paper is available on arxiv under CC 4.0 license. Authors: (1) Shanshan Han & Qifan Zhang, UCI; (2) Wenxuan Wu, Texas A&M University; (3) Baturalp Buyukates, Yuhang Yao & Weizhao Jin, USC; (4) Salman Avestimehr, USC & FedML. Table of Links Abstract and Introduction Problem Setting The Proposed Two-Stages Anomaly Detection Verifiable Anomaly Detection using ZKP Evaluations Related Works Conclusion & References 5 EVALUATIONS This section presents a comprehensive evaluation of our approach. We focus on the following aspects: (i) effectiveness of cross-round check detection; (ii) effectiveness of the cross-client detection; (iii) performance comparison of our approach against other defenses; (iv) robustness of our approach against a dynamic subset of malicious clients; (v) defense coverage of our approach on different models; (vi) performance of our ZKP-verified anomaly detection protocol. A summary of datasets and models for evaluations can be found in Table 1. By default, we employ CNN and the non-i.i.d. FEMNIST dataset (partition parameter α = 0.5), as the non-i.i.d. setting closely captures real-world scenarios. We utilize FedAVG in our experiments. By default, we use 10 clients for FL training – all clients participate in training in each round. We employ three attack mechanisms, including Byzantine attacks of random mode (Chen et al., 2017; Fang et al., 2020), and model replacement backdoor attack (Bagdasaryan et al., 2020b). We utilize three baseline defense mechanisms: m-Krum (Blanchard et al., 2017), Foolsgold (Fung et al., 2020), and RFA (Pillutla et al., 2022). For m-Krum, we set m to 5, which means 5 out of 10 submitted local models participate in aggregation in each FL training round. By default, the results are evaluated with the accuracy of the global model. Evaluations for anomaly detection are conducted on a server with 8 NVIDIA A100-SXM4-80GB GPUs, and evaluations for ZKP are conducted on Amazon AWS with an m5a.4xlarge instance with 16 CPU cores and 32 GB memory. Our code is implemented using FedMLSecurity benchmark Han et al. (2023). Experimental setting. We utilize the norm of gradients to evaluate the “sensitivity” of each layer. A layer with a high norm indicates high sensitivity and can represent the whole model. We evaluate the sensitivity of layers of CNN, RNN, and ResNet56. The results for RNN is shown in Figure 4, and the results for ResNet56 and CNN are deferred to Figure 14 and Figure 13 in Section B.2, respectively. The results show that we can utilize the second-to-the-last layer of a model as the importance layer, as it includes adequate information on the whole model. Exp1: Selection of importance layer. 5.1 CROSS-ROUND CHECK EVALUATIONS In this subsection, we assess the efficiency of the cross-round check in detecting attacks. We employ the random-Byzantine and the model replacement backdoor attacks, and set the attack probability to 40% for each FL iteration, where 1 out of the clients are malicious when the attack happens. Ideally, the cross-round check should confirm the absence or presence of an attack accurately. The effectiveness of our approach is evaluated by the cross-round check accuracy, which measures the proportion of iterations in which the algorithm correctly detects cases with or without an attack relative to the number of total iterations. A 100% cross-round check accuracy means that all attacks are detected, and none of the benign cases are identified as “attacks”. We evaluate the impact of the cosine similarity threshold γ in the cross-round check by setting γ to 0.5, 0.6, 0.7, 0.8, and 0.9. According to Algorithm 2, a cosine score lower than γ indicates lower similarities between client models of the current round and the last round, which may be an indicator of an attack. As shown in Figure 5, the crossround accuracy is close to 100% in the case of random-Byzantine attacks. Further, when the cosine similarity threshold γ is set to 0.5, the performance is good in all cases, with at least 93% cross-round detection accuracy. Exp2: Impact of the similarity threshold. 5.2 CROSS-CLIENT DETECTION EVALUATIONS This subsection evaluates whether the cross-client detection can successfully detect malicious client submissions given the cases with attacks. We evaluate the quality of anomaly detection using modified Positive Predictive Values (PPV) (Fletcher, 2019), i.e., precision, the proportions of positive results in statistics and diagnostic tests that are true positive results. Let us denote the number of true positive and the false positive results to be NTP and NFP , respectively, then PPV = NTP NTP+NFP . In the context of anomaly detection in FL, client submissions that are detected as “malicious” and are actually malicious are defined as True Positive, corresponding to NTP , while client submissions that are detected as “malicious” even though they are benign are defined as False Positive, corresponding to NFP . Since we would like the PPV to reveal the relation between NTP and the total number of malicious submissions across all FL iterations, denoted as Ntotal , whether they are detected or not, we introduce a modified PPV as PPV = NTP NTP+NFP+Ntotal , where 0 ≤ PPV ≤ 1 2 . In ideal cases, all malicious submissions are detected, where NTP = Ntotal , and PPV is 1 2 . Due to the page limitations we deferred the proof of this statement to Appendix A.1. This experiment utilizes PPV to evaluate the impact of the number of deviations, i.e., the parameter λ in the anomaly bound µ + λσ. To evaluate a challenging case where a large portion of the clients are malicious, we set 4 out of 10 clients to be malicious in each FL training round. Given the number of FL iterations to be 100, the total number of malicious submissions Ntotal is 400. We set the number of deviations λ to be 0.5, 1, 1.5, 2, 2.5, and 3. We select the Byzantine attack of random mode and the model replacement attack, and evaluate our approach on three tasks, as follows: i) CNN+FEMNIST, ii) ResNet-56+Cifar100, and iii) RNN + Shakespeare. The results, as shown in Figure 6, indicate that when λ is 0.5, the results are the best, with the PPV being at least 0.37. In fact, when λ is 0.5, all malicious submissions are detected for the random Byzantine attack for all three tasks, with the PPV being exactly 1/2. In subsequent experiments, unless specified otherwise, we set λ to 0.5 by default. Exp 3: Selection of the number of deviations. This experiment evaluates the effect of our approach compared with various defense mechanisms, including Foolsgold, m-Krum (m = 5), and RFA in the context of ongoing attacks. We include a “benign” baseline scenario with no activated attack or defense, and select random-Byzantine and model replacement backdoor attacks. The results for the random-Byzantine attack and model replacement backdoor attack are shown in Figure 7and Figure 8, respectively. These results demonstrate that our approach effectively mitigates the negative impact of the attacks and significantly outperforms the other defenses, with the test accuracy much closer to the benign case. Exp 4: Comparisons between anomaly detection and various defenses against attacks. This experiment evaluates the impact of varying number of malicious clients on test accuracy. We set the number of malicious clients out of 10 clients in each FL training round to 2 and 4, and include a baseline case where all clients are benign. As shown in Figure 9, the test accuracy remains relatively consistent across different numbers of malicious clients, as in each FL training round, our approach filters out the local models that tend to be malicious to effectively minimize the impact of malicious client models on the aggregation. Exp 5: Varying the number of malicious clients. We evaluate defense mechanisms against the random mode of the Byzantine attack with different models and datasets, including: i) ResNet-20 + Cifar10, ii) ResNet-56 + Cifar100, and iii) RNN + Shakespeare. The results are shown in Figures 10, 11, and 12, respectively. The results show that while the baseline defense mechanisms can mitigate the impact of attacks in most cases, some defenses may fail in some tasks, e.g., m-Krum fails in RNN in Figure 12. This is because those methods either select a fixed number of local models or re-weight the local models in aggregation, which potentially eliminates some local models that are important to the aggregation, leading to an unchanged test accuracy in later FL iterations. In contrast, our approach outperforms those baseline defense methods by effectively filtering out local models that are detected as “outliers”, with a test accuracy close to the benign scenarios. Exp 6: Evaluations on different models. 5.3 ZKP PERFORMANCE We implement the ZKP system in Circom (Circom Contributors, 2022). This system includes a module for cross-round check and cross-client detection. We also implement a prover’s module which contains JavaScript code to generate witness for the ZKP, as well as to perform fixed-point quantization. In our experiments, we include CNN, RNN, and ResNet-56 as our machine learning models. Specifically, we only pull out parameters from the second-to-last layer of each model, i.e., the importance layer, as our weight to reduce complexity. For instance, the second-to-last layer of the CNN model contains only 7, 936 trainable parameters, as opposed to 1, 199, 882 should we use the entire model. We implement both algorithms across 10 clients, and report our results in Table 2. Exp 7: Evaluations of ZKP circuit size, proving time, and verification time.

Zero-Knowledge-Proof-Based Anomaly Detection: Evaluations

This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Shanshan Han & Qifan Zhang, UCI; (2) Wenxuan Wu, Texas A&M University; (3) Baturalp Buyukates, Yuhang Yao & Weizhao Jin, USC; (4) Salman Avestimehr, USC & FedML. Table of Links Abstract and Introduction Problem Setting The Proposed Two-Stages Anomaly Detection Verifiable Anomaly Detection using ZKP Evaluations Related Works Conclusion & References 2 PROBLEM SETTING In this section we present our threat model along with some preliminaries that we leverage in the proposed anomaly detection mechanism. 2.1 ADVERSARY MODEL We consider an FL system where some subset of the clients might be malicious, while most of the clients (i.e., more than 50%) are honest. The clients would like to collaboratively train a model, however, malicious clients may conduct attacks to achieve some adversarial goals, including: i) planting a backdoor to misclassify a specific set of samples while minimally impacting the overall performance of the global model, i.e., backdoor attacks (Bagdasaryan et al., 2020b; Wang et al., 2020); ii) altering the local models to prevent the global model from converging, i.e., Byzantine attacks (Chen et al., 2017; Fang et al., 2020); and iii) randomly submitting contrived models without actual training, i.e., free riders (Wang, 2022). Clients are aware that the FL server may take some defensive measures for their submissions to mitigate potential attacks, and they want to verify the integrity of these defensive measures, to ensure correct operation at the server. 2.2 PRELIMINARIES Krum (Blanchard et al., 2017) is a well-known distance-based anomaly detection method in distributed learning that accepts local models that deviate less from the majority based on their pairwise distances. Given that there are f byzantine clients (i.e., malicious clients) among L clients in the FL system, where the server receives L local models as w1, w2, . . . , wL in each training round, Krum selects one of these models, i.e., the one that is the most likely to be benign, as the global model. An optimization of Krum is m-Krum (Blanchard et al., 2017) that selects m local models, instead of one, with the m smallest scores, to compute an average model when aggregating local models. Algorithms for Krum and m-Krum is shown in Algorithm 1. Krum. The three sigma rule is an empirical rule stating that almost all of the population lies within three standard deviations of the mean in normal distributions. Specifically, in normal distributions N (µ, σ), the percentage of values within one, two, and three standard deviations of the mean are 68%, 95%, and 99.7%, respectively. This rule can be widely applied in real-world applications, since normal distributions are consistent with real-world data distributions (Lyon, 2014), and according to the central limit theorem (Rosenblatt, 1956), when aggregating independent random variables, even if the variables are generated by various distributions, the aggregation tends towards a normal distribution. Further, when the data are not normally distributed, we can transform the distribution to a normal distribution (Aoki, 1950; Osborne, 2010; Sakia, 1992; Weisberg, 2001). The three sigma rule has been used in anomaly detection (Han et al., 2019) since data outside two or three standard deviations of the mean take a very limited proportion; see Figure 2. Three Sigma Rule. Zero-Knowledge Proofs (ZKPs)(Goldwasser et al., 1989) is a proof system that allow a prover to convince a verifier that a function on prover’s secret input (witness) is correctly computed. ZKPs ensures three properties: correctness, soundness, and zero-knowledge. Correctness means that if the prover is honest, then the proof they produce should check out (integrity property). Soundness ensures that a cheating prover will not convince verifier with overwhelming probability. Zero-knowledge guarantees that prover’s winess will be not learned by the verifier (privacy). Due to these properties, ZKP has been widely used in machine learning and blockchain applications (Lee et al., 2020; Feng et al., 2021; Liu et al., 2021; Sasson et al., 2014). Zero-knowledge proofs.

Zero-Knowledge-Proof-Based Anomaly Detection: Problem Setting

This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Shanshan Han & Qifan Zhang, UCI; (2) Wenxuan Wu, Texas A&M University; (3) Baturalp Buyukates, Yuhang Yao & Weizhao Jin, USC; (4) Salman Avestimehr, USC & FedML. Table of Links Abstract and Introduction Problem Setting The Proposed Two-Stages Anomaly Detection Verifiable Anomaly Detection using ZKP Evaluations Related Works Conclusion & References ABSTRACT Federated learning (FL) systems are vulnerable to malicious clients that submit poisoned local models to achieve their adversarial goals, such as preventing the convergence of the global model or inducing the global model to misclassify some data. Many existing defense mechanisms are impractical in real-world FL systems, as they require prior knowledge of the number of malicious clients or rely on re-weighting or modifying submissions. This is because adversaries typically do not announce their intentions before attacking, and re-weighting might change aggregation results even in the absence of attacks. To address these challenges in real FL systems, this paper introduces a cutting-edge anomaly detection approach with the following features: i) Detecting the occurrence of attacks and performing defense operations only when attacks happen; ii) Upon the occurrence of an attack, further detecting the malicious client models and eliminating them without harming the benign ones; iii) Ensuring honest execution of defense mechanisms at the server by leveraging a zero-knowledge proof mechanism. We validate the superior performance of the proposed approach with extensive experiments. 1 INTRODUCTION Federated Learning (FL) (McMahan et al., 2017a) enables clients to collaboratively train machine learning models without sharing their local data with other parties, maintaining the privacy and security of their local data. Due to its privacy-preserving nature, FL has attracted considerable attention across various domains and has been utilized in numerous areas (Hard et al., 2018; Chen et al., 2019; Ramaswamy et al., 2019; Leroy et al., 2019; Byrd & Polychroniadou, 2020; Chowdhury et al., 2022). However, even though FL does not require sharing raw data with others, its decentralized and collaborative nature inadvertently introduces privacy and security vulnerabilities (Cao & Gong, 2022; Bhagoji et al., 2019; Lam et al., 2021; Jin et al., 2021; Tomsett et al., 2019; Chen et al., 2017; Tolpegin et al., 2020; Kariyappa et al., 2022; Zhang et al., 2022c). Malicious clients in FL systems can harm training by submitting spurious models to disrupt the global model from converging (Fang et al., 2020; Chen et al., 2017), or planting backdoors to induce the global model to perform wrongly for certain samples (Bagdasaryan et al., 2020b;a; Wang et al., 2020). Existing literature on robust learning and mitigation of adversarial behaviors includes Blanchard et al. (2017); Yang et al. (2019); Fung et al. (2020); Pillutla et al. (2022); He et al. (2022); Cao et al. (2022); Karimireddy et al. (2020); Sun et al. (2019); Fu et al. (2019); Ozdayi et al. (2021); Sun et al. (2021), etc. These approaches exhibit shortcomings, making them less suitable for real FL systems. Some of these strategies require prior knowledge about the number of malicious clients within the FL system (Blanchard et al., 2017), even though in practice an adversary would not notify the system before attacking. Also, some of these methods mitigate impacts of potential malicious client submissions by re-weighting the local models (Fung et al., 2020), retaining only several local models that are most likely to be benign while removing others (Blanchard et al., 2017), or modifying the aggregation function (Pillutla et al., 2022). These methods have the potential to unintentionally alter the aggregation results in the absence of deliberate attacks, considering attacks happen infrequently in real-world scenarios. While the defense mechanisms can mitigate the impact of potential attacks, they can inadvertently compromise the result quality when applied to benign cases. Moreover, existing defense mechanisms are deployed at the FL server without any verification procedures to ensure their correct execution. While most of the clients are benign and wish to collaboratively train machine learning models, they can also be skeptic about the server’s reliability due to the execution of the defense mechanisms that modify the original aggregation procedure. Thus, a successful anomaly detection approach should simultaneously satisfy the following: i) It should be able to detect the occurrence of attacks and exclusively handle the cases when attacks happen. ii) If an attack is detected, the strategy must further detect malicious client submissions and accordingly mitigate (or eliminate) their adversarial impacts without harming the benign client models. iii) There should be a robust mechanism to corroborate the honest execution of defense mechanisms. In this work, we propose a novel anomaly detection mechanism that is specifically tailored to address genuine challenges faced by real-world FL systems. Our approach follows a two-stage scheme at the server to filter out malicious client submissions before aggregation. It initiates with a crossround check based on some cache called “reference models” to determine whether any attacks have occurred. In case of attacks, a subsequent cross-client detection is executed to eliminate malicious clients models without harming the benign client models. Meanwhile, the reference models in the cache is renewed. We provide an overview in Figure 1. Our contributions are summarized as follows: Our strategy is equipped with an initial cross-round check to detect the occurrence of potential attacks, ensuring that defensive methods are only activated in response to the presence of attacks, thereby maintaining the sanctity of the process in attack-free scenarios. ) Proactive attack detection. i By coupling the cross-round check with a subsequent crossclient detection, our approach efficiently eliminates malicious client submissions without harming the benign local submissions. ) Enhanced anomaly detection. ii Our method operates effectively without any prerequisites such as data distribution or the number of malicious clients. Such autonomous nature ensures widespread applicability and adaptability of our approach across different FL tasks, regardless of the data distribution and the selection of models. ) Autonomy from prior knowledge. iii Incorporating Zero-Knowledge Proof (ZKP) (Goldwasser et al., 1989) methodologies, our approach guarantees that the elimination of malicious client models is executed correctly, ensuring that clients can place trust in the defense mechanism in the FL system. ) Rigorous verification protocol. iv

A Zero-Knowledge Anomaly Detection Approach for Robust Federated Learning

শক্তিশালী ফেডারেটেড লার্নিংয়ের জন্য একটি শূন্য-জ্ঞান অসঙ্গতি সনাক্তকরণ পদ্ধতি

Ein wissensfreier Anomalieerkennungsansatz für robustes föderiertes Lernen

Un enfoque de detección de anomalías sin conocimiento para un aprendizaje federado sólido

Une approche de détection des anomalies sans connaissance pour un apprentissage fédéré robuste

मजबूत फ़ेडरेटेड लर्निंग के लिए एक शून्य-ज्ञान विसंगति का पता लगाने का दृष्टिकोण

堅牢なフェデレーテッド ラーニングのためのゼロ知識異常検出アプローチ

강력한 연합 학습을 위한 영지식 이상 탐지 접근 방식

Uma abordagem de detecção de anomalias de conhecimento zero para aprendizagem federada robusta

Подход к обнаружению аномалий с нулевым разглашением для надежного федеративного обучения

Güçlü Birleştirilmiş Öğrenme için Sıfır Bilgi Anormallik Tespiti Yaklaşımı

Phương pháp phát hiện bất thường không có kiến thức để học tập liên kết mạnh mẽ

用于鲁棒联邦学习的零知识异常检测方法

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The TechBeat: Anomaly Detection with Privileged Information—Part 1 (12/21/2023)

Before exploring the SVDD+ implementation, let us briefly revisit what SVDD (Support Vector Data Description) and SVDD+ entail. Support Vector Data Description (SVDD) is a method for describing data by encapsulating the target dataset within a hypersphere, suitable for one-class classification or outlier detection. SVDD+, in its turn, is a novel approach that integrates privileged information into the traditional SVDD framework. Unlike classical SVDD, which disregards privileged information often present in human learning, SVDD+ leverages it to optimize the training phase through the construction of a set of corrective functions. Moving forward, we will look in detail at SVDD+ as a quadratic optimization, explore its implementation using the cvxopt library, and conduct a comparative analysis between SVDD+ and OneClassSVM. Optimization problem In the previous , we discussed building an anomaly detection algorithm that could use special information available only during the training phase. post In the process, we show that we have to solve this optimization problem: Alternatively, we could solve a dual problem: Where K(xi, xj) is a dot product in some feature space. Which turns out to be a special case of quadratic optimization problem. We reproduce the solution by running the following: There are techniques designed particularly for this problem. However, during this, we will be using a more generic solver — a free software package for convex optimization based on the Python programming language. cvxopt SVDD+ as Quadratic Optimization Usually, quadratic optimization is written down in the following form: P is a symmetric semi-positive definite matrix, so this doesn’t look like what we previously had. And will require an additional workaround. Change of Variables First of all, let's define a new x, which is a combination of variables α,  δ . We are going to stack them together in the following form. First, let's define a new x, a combination of variables  α,  **δ . We are going to stack them together in the following form: We could always reconstruct original values based on this new vector: Matrix P With this new variable x, we could introduce matrix P as: K is a matrix with pairwise kernel function values on training set data. Kij = K(xi, xj)  The same goes for K* privileged information. Now, we can write down the sum in the optimization problem as matrix multiplication: This is precisely what we have in the dual problem formulation. Equality Constraints Now, we have to deal with equality constraints. We know that the sum of all α is equal to, v let's rewrite it as matrix multiplication: Here, the first l elements are equal to 1, and the second l are equal to 0. This gives us the one off first l elements of x, which are equal to αi. The second equality will be slightly trickier. If we find a product with a vector with the first l elements equal to zero and the second equal to one, we will get: So, the final matrix formula for equal constraints: Inequality Constraints Now, we can describe inequality constraints. Notice that we could isolate α from x by multiplying to block matrix: Here, we have a block matrix of size lx2l combined from the l by l Identity matrix and zeroes matrix. To isolate δ will require slightly more effort. We will combine two identity matrices to get δ: Finally, combining it all together: Using the cvxopt Library Now we are going to use cvxopt library. Having matrices ordinary and privileged features combined with kernel function, we could prepare optimization problem with the following Python function: def prepare_problem(self, X, Z, original_kernel, 
                                        privileged_kernel, nu, gamma)
    gamma = privileged_regularization
    C = 1.0 / len(X) / self.nu
    size = X.shape[0]
    kernel_x = features_kernel(X)
    kernel_z =privileged_kernel(Z)
    zeros_matrix = np.zeros_like(kernel_x)
    P = 2 * np.bmat([[kernel_x, zeros_matrix],
                     [zeros_matrix, 0.5*gamma*kernel_z]])
    P = matrix(P)
    q = matrix(list(np.diag(kernel_x)) + [0] * size)
    A = matrix([[1.]*size + [0.]*size, [1.] * size*2]).T
    b = matrix([1., 1.])
    G = np.bmat([[-np.eye(size), zeros_matrix],
                 [-np.eye(size), np.eye(size)],
                 [np.eye(size), -np.eye(size)]])
    G = matrix(G)
    G = sparse(G)
    h = matrix([0]*size*2 + [C]*size)
    optimization_problem = {'P': P, 'q': q, 'G': G,
                            'h': h, 'A': A, 'b': b}
    return optimization_problem Implementation Example You can find the full implementation in the following repository: . To install the package run: https://github.com/sklef/ISVDD pip install git+https://github.com/sklef/ISVDD.git kdd99 Dataset We will use the kdd99 dataset to show how this approach works. The dataset contains information about TCP connections for the nine weeks of work. The first seven weeks are used as a train set, and the other two are used as a test set. The distribution of the train set and the test set are different. The test set even contains attacks not presented in the train set. To get data, we could use the following code: from sklearn.datasets import fetch_kddcup99
X, y = fetch_kddcup99(return_X_y=True, as_frame=True) Feature Types There are three types of features in kdd99 dataset: The first are generated directly from the TCP dump. It includes the protocol type, number of sent fragments, network service on the destination, etc. The second are features proposed by domain experts and generated from the first ones. The third are features generated from the history of connections in a two-second window. We will consider basic features as ordinary information and content and traffic features as privileged ones. basic_features = ["duration", "src_bytes", "dst_bytes", "land", "wrong_fragment", "urgent"]
content_features = ["hot", "num_failed_logins", "logged_in", "num_compromised", "root_shell",
                    "su_attempted", "num_root", "num_file_creations", "num_shells", "num_access_files",
                    "num_outbound_cmds", "is_host_login", "is_guest_login"]
traffic_features = ["count", "serror_rate", "rerror_rate", "same_srv_rate", "diff_srv_rate",
                    "srv_count", "srv_serror_rate", "srv_rerror_rate", "srv_diff_host_rate"]


ordinary_features = X[basic_features]
privileged_features = X[traffic_features + content_features] Before the experiment, we remove categorical features and normalize the rest by subtracting its mean value and dividing by its standard deviation plus an additional constant equal to 1e-5. This constant was added to prevent dividing by zero. ordinary_features = features[basic_features].astype(float)
ordinary_features = (ordinary_features - ordinary_features.mean()) / (ordinary_features.std() + 1e-5)
privileged_features = features[traffic_features + content_features].astype(float)
privileged_features = (privileged_features - privileged_features.mean()) / (privileged_features.std() + 1e-5) Comparing SVDD+ and OneClassSVM Further on we will compare the work of SVDD+ with OneClassSVM. It’s possible to prove that using rbf_kernel will produce the same result for OneClassSVM and SVDD. So, by comparing with OneClassSVM, we are comparing with the original SVDD. Unfortunately, there are no good enough Python APIs for this algorithm. Let us suppose that we have a train and a test set. We know which records correspond to an attack in the train set and want to determine which ones are malicious on the test set. To do so, we take only normal records from the train set and fit One-Class SVM. After that, we apply this trained model to detect elements from the test set that differed from the normal ones from the train set. As a result, we get an anomaly score, which expresses the algorithm’s confidence in its prediction. Then, we are going to calculate the area under precision-recall. By using cross-validation, we will also get a standard deviation of metric estimation. from sklearn.model_selection import KFold


def evaluate_parameters(model, ordinary_features,
                        labels, privilged_features=None):
    splitter = KFold(n_splits=10)
    all_scores = []
    for test, train in splitter.split(labels):
        train_labels = labels.iloc[train]
        normal_data_indices = train_labels[train_labels == b"normal."].index
        train_oridnary_features = ordinary_features.loc[normal_data_indices]
        if privilged_features is not None:
            train_privileged_features = privilged_features.loc[normal_data_indices]
            model.fit(train_oridnary_features, train_privileged_features)
        else:
            model.fit(train_oridnary_features)
        test_features = ordinary_features.iloc[test]
        predictions = model.decision_function(test_features)
        test_labels = labels.iloc[test] != b"normal."
        all_scores.append(average_precision_score(test_labels, -predictions))
    return np.mean(all_scores), np.std(all_scores) We are going to use RBF kernels with different values of parameter v We will fix parameter v, privileged information kernel, and regularization. all_gammas = np.logspace(-7, 7, 30)
ordinary_average_precision_mean = np.zeros_like(all_gammas)
ordinary_average_precision_std = np.zeros_like(all_gammas)

for index, gamma in enumerate(all_gammas):
    average_precision, average_precision_std = evaluate_parameters(OneClassSVM(gamma=gamma), ordinary_features, labels)
    ordinary_average_precision_mean[index] = average_precision
    ordinary_average_precision_std[index] = average_precision_std


privileged_average_precision_mean = np.zeros_like(all_gammas)
privileged_average_precision_std = np.zeros_like(all_gammas)

for index, gamma in enumerate(all_gammas):
    priv_kernel = partial(rbf_kernel, gamma=1e-4)
    kernel = partial(rbf_kernel, gamma=gamma)
    model = ISVDD(0.1, kernel, priv_kernel, privileged_regularization=0.1, tol=0.0001, max_iter=100, silent=True)
    average_precision, average_precision_std = evaluate_parameters(model, ordinary_features, labels, privileged_features)
    privileged_average_precision_mean[index] = average_precision
    privileged_average_precision_std[index] = average_precision_std Conclusion Though the usage of privileged information leads to better performance on test data with the same feature space, its performance is still worse than using all features for the training and test phase. These results demonstrate that we can see privileged information as a special case of regularization. In addition, we demonstrate performance in test data for different combinations of original features' kernel width and privileged features' kernel width. A wider original kernel width allows us to perform better with a narrower privileged kernel width, which can be explained as the regularization role of the privileged information.

Anomaly Detection with Privileged Information—Part 2

The Noonification: Anomaly Detection with Privileged Information—Part 1 (12/13/2023)

Support Vector Data Description (SVDD) is one of the popular boundary methods used in machine learning for anomaly detection. The goal of SVDD is to create a model that captures the characteristics of normal (non-anomalous) data and then identifies instances that deviate from these characteristics as anomalies. finds extensive use in various applications, such as fraud detection for credit cards, insurance, or health care, intrusion detection for cyber-security, fault detection in safety-critical systems, and military surveillance for enemy activities. Anomaly detection Imagine you have a set of data points, and most of them represent normal behavior. SVDD aims to create a boundary around these normal data points in such a way that the majority of the data falls inside this boundary. Any data point outside this boundary is then considered an anomaly or an outlier. In other words, we are teaching a computer to recognize what "normal" looks like based on a set of examples and then being able to flag something as "unusual" if it doesn't fit the learned pattern. In this article, we deep-dive into the fundamental concepts of SVDD, exploring the utilization of privileged information during the training phase — a technique aimed at enhancing classification accuracy in anomaly detection scenarios. Original SVDD As said above, a classical approach to anomaly detection is to describe expected ("normal") behavior using one-class classification techniques, i.e., to construct a description of a "normal" state using many examples, e.g., by describing a geometrical place of training patterns in a feature space. If a new test pattern does not belong to the "normal" class, we consider it anomalous. To construct a "normal" domain, we can use well-known approaches such as the Support Vector Domain Description. We start with a brief explanation of the original SVDD without using privileged information. We have an i.i.d. samples  (x1, . . . , xl) The main idea of this algorithm is to separate a significant part of samples considered to be "normal" from those considered to be "abnormal" in some sense. We denote by φ(·) mapping the original data point to some more expressive feature space, for example, adding some polynomial features, applying some feature extraction with a deep neural net, or even assuming that mapping is in some infinite dimension space. Let a be some point in the image of the feature map and R be some positive value. A pattern x belongs to a "normal" class if it is inside the sphere  ∥a − φ(x)∥ ≤ R. To find the center and the radius we solve the optimization problem: a R Here ξ  is the distance from the xi, located out of the sphere, to the surface of the sphere. If a point is inside the sphere we consider ξi = 0  The variable R can be considered as a radius only if we require its positivity. However, it can be easily proved that this condition is automatically fulfilled if ν ∈ (0, 1), and for ν ̸ ∈ (0, 1), the solution either contains all points or contains none of them. As you probably guess, since we have support in the name of the algorithm, we will be solving the dual problem: Here we replace the scalar product (φ(xi) · φ(xj )) with the corresponding kernel K(xi, xj). We can calculate a and R using any xi such that αi > 0 Based on this we could define the decision function: If  f(x) > 0, then a pattern x is located outside the sphere and considered anomalous. Also we could notice that f(x) return value and we could tune the threshold to achieve a target level of true positive and true negative values. SVDD and Privileged Information For the original two-class Support Vector Machine, an algorithm creating an optimal boundary between different classes of data points, a modification that allows taking into account privileged information during the training phase to improve classification accuracy. Vapnik proposed Let us provide some examples of privileged information. If we solve an image classification problem, then as privileged information, we can use a textual image description. In the case of malware detection, we can use a source code of malware to get additional features for the classification. Such information is unavailable during the test phase (e.g., it could be computationally prohibitive or too costly to obtain) when we use the trained model for anomaly detection and classification. Still, it can be used during the training phase. Let's assume that training data is coming in pairs (xi, xi*). For example, imagine we are trying to detect anomalies in X-ray images. We have both the image itself and the doctor's description. Generally, a text description is more than enough but requires additional assistance. Can they be used during the model training but only make predictions using images? It is possible to use this additional information to improve detection. In the previous formulation, we have an error in the form of ξi.  let's assume that privileged data is so good it could predict the size of an error: We could think about this as an intelligent teacher who tells during the training that you couldn't get the small error with this value. It's reasonable to concentrate on other, more valuable examples. Now, let's write down this monster-like equation: Here γ is a regularization parameter for the linear approximation of the slack variables. ζi are instrumental variables that prevent those patterns belonging to a "positive" half-plane from being penalized. Note that if γ goes to infinity, then the solution is close to the original solution of SVDD. To avoid complications messing around with the Lagrange function, write down the dual form of this problem: Here we replace the scalar product (φ* (xi* ) · φ*(xj* )) with the corresponding kernel function K* (xi*, xj*). At the end, the decision function has the same form as in the case of the original SVDD: Notice that despite being slightly scarier than the original problem, this task is a specific type of optimization called quadratic optimization and can be easily solved by standard approaches like the logarithmic barrier function. Conclusion The original SVDD approach focuses on constructing a boundary around normal data points in a high-dimensional space. However, the SVDD+ theory introduces the concept of privileged information during the training phase to enhance classification accuracy. Privileged information, not available during testing, can be utilized during training to provide additional insights, improving the model's ability to detect anomalies. Incorporating privileged information involves a modification of the original SVDD algorithm, allowing it to consider supplemental data during training, such as textual descriptions accompanying images in medical anomaly detection. The inclusion of privileged information is framed as a form of intelligent guidance, akin to an informed teacher providing valuable insights to improve the model's learning. The modified SVDD+ formulation involves a quadratic optimization task, solvable through standard approaches like the logarithmic barrier function. Despite the complexity introduced by the inclusion of privileged information, the decision function in the maintains a form similar to the original SVDD, facilitating practical implementation. SVDD+ theory In summary, the SVDD+ theory showcases a promising avenue for improving anomaly detection by leveraging privileged information during the training phase, offering potential applications across various fields, including image classification and malware detection.

Anomaly Detection with Privileged Information—Part 1

বিশেষাধিকারপ্রাপ্ত তথ্যের সাথে অসঙ্গতি সনাক্তকরণ—পার্ট 1

Anomalieerkennung mit vertraulichen Informationen – Teil 1

Detección de anomalías con información privilegiada: Parte 1

Détection d'anomalies avec des informations privilégiées – Partie 1

विशेषाधिकार प्राप्त जानकारी के साथ विसंगति का पता लगाना—भाग 1

特権情報による異常検出 - パート 1

특권 정보를 이용한 이상 탐지 - 1부

Detecção de anomalias com informações privilegiadas – Parte 1

Обнаружение аномалий с использованием конфиденциальной информации. Часть 1.

Ayrıcalıklı Bilgilerle Anormallik Tespiti - Bölüm 1

Phát hiện bất thường bằng thông tin đặc quyền—Phần 1

使用特权信息进行异常检测 - 第 1 部分

Scientific American, Volume XXXVI., No. 8, February 24, 1877 by Various, is part of the HackerNoon Books Series. You can jump to any chapter in this book . Caffeone here Caffeone. Caffeone, the aromatic principle of coffee, may be isolated by distilling 5 or 6 lbs. roasted coffee with water, agitating the aqueous distillate with ether, and afterwards evaporating the ether. It is a brown oil, heavier than water, in which it is only very slightly soluble. An almost imponderable quantity of this essential oil will suffice to aromatize a gallon of water. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Various (2006). Scientific American, Volume XXXVI., No. 8, February 24, 1877. Urbana, Illinois: Project Gutenberg. Retrieved https://www.gutenberg.org/cache/epub/19406/pg19406-images.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at , located at www.gutenberg.org https://www.gutenberg.org/policy/license.html

Caffeone, the aromatic principle of coffee.

Multivariate time series anomaly detection is critical in fields ranging from healthcare and finance to cybersecurity and industrial surveillance. Spotting these anomalies can highlight significant events such as health conditions, fraudulent activity, cyber threats, or equipment malfunctions. As IoT devices and high-frequency data collection become more prevalent, the need for robust anomaly detection models for multivariate time series has become essential. methods have made significant strides in this area. Autoencoders, Generative Adversarial Networks (GANs), and Transformers are just a few of the approaches that have demonstrated effectiveness in identifying anomalies within time series data. A recent piece I shared discussed the innovative application of "inverted transformers" (iTransformers) in time series analysis, which you can read more about . Deep learning here However, a new twist emerged with my latest find—a on the use of diffusion models for time series data analysis. These models are best known for their impressive results in image and audio generation tasks, as evidenced by Stable Diffusion for images and AudioLDM for audio. They've even been applied to help robots adapt to complex environments. new research paper This raises a compelling question: Can be as effective for analyzing time series data? This post will examine the recent paper that has brought this question to the forefront, and we'll assess the viability of diffusion models in this specialized domain. Let's get started. diffusion models The Promise and Limitations of Existing Methods Traditional anomaly detection methods such as One-Class SVMs—a machine learning technique that surrounds normal data points with a decision boundary to identify anomalies—and Isolation Forests—an algorithm that detects outliers by isolating observations—are adept at handling individual data points in isolation. However, they don’t take into account the temporal relationships, the interconnected sequences of data that unfold over time, which are crucial for understanding evolving contexts within the dataset. Deep learning models, by design, are more attuned to these sequential dynamics. Autoencoders, for instance, are neural networks trained to condense normal data into a compact representation during training and then reconstruct it during testing. Anomalies are flagged by measuring the reconstruction error, which is the disparity between the original data and its reconstructed version from the autoencoder; a significant error suggests an anomalous event. Generative Adversarial Networks ( ), composed of two neural networks—the generator and the discriminator—compete in a game-like setting. The generator creates new data instances while the discriminator assesses them, assigning likelihood scores that reflect the probability of a data instance being real. Anomalies are identified when the discriminator assigns low likelihood scores, indicating the data might not be genuine. GANs Transformers, a newer addition to the deep learning arsenal, leverage self-attention mechanisms, allowing the model to consider the entire sequence of data to understand the weight and significance of each part. This approach has led to state-of-the-art results in recognizing complex temporal correlations within time series data. However, these models can sometimes reconstruct anomalies with too much accuracy, which can be a drawback as it makes anomalies less discernible. Additionally, GANs are susceptible to model collapse, where the generator starts producing limited and often repetitive outputs, reducing the model's ability to generalize and detect a wide range of anomalies. Despite their promise, these deep learning techniques still face the challenge of consistently identifying anomalies across various datasets due to the complexity of modeling temporal dependencies and the inherent limitations of each approach. Diffusion Models - A New Approach Diffusion models are a novel class of deep generative models initially recognized for their prowess in generating detailed images. Their approach entails a gradual addition of noise to the data, which the model learns to reverse, effectively enabling it to eliminate noise and reconstruct high-resolution samples. In the context of time series anomaly detection, this paper posits an intriguing hypothesis: If this holds, it would result in a greater disparity between the original anomalous sequences and their reconstructed versions, thereby improving the identification of anomalies. diffusion processes may be particularly effective at smoothing out normal patterns while amplifying the irregularities in anomalies. A diagram in the paper visually explains this theory, depicting how, through iterative rounds of noise addition and subsequent removal, anomalies become more pronounced when compared to their denoised versions. This amplification facilitates the differentiation of anomalous data from the norm post-diffusion. For practical implementation, the model undergoes training on multivariate time series data corrupted with Gaussian noise. In the testing phase, this process is mimicked by adding noise to new input sequences, which the model is then tasked to denoise. The difference between the original sequence and its denoised counterpart is quantified to produce an anomaly score. The paper examines two variants of diffusion models applied to time series data: A straightforward application where the diffusion model processes the raw time series input. An enhanced "DiffusionAE" model, which employs an autoencoder's output as the preliminary input for the diffusion process. The second approach, "DiffusionAE," enhances the diffusion model's robustness to inherent noise in the data by utilizing the autoencoder's capability to pre-filter noise. The comprehensive methodology is depicted in a diagram that outlines the entire pipeline, from the introduction of noise to the generation of the anomaly score. Experimental Setup and Results The models underwent rigorous testing on both synthetic and authentic multivariate time series datasets, which included a variety of anomaly types. These types were classified according to a recognized taxonomy: : Singular data points that are unusual compared to the rest. Point anomalies : Points that are abnormal when considered within their specific context. Contextual anomalies : Irregular patterns that disrupt the expected cyclical trends. Seasonal anomalies : Anomalies within a subsequence or 'shapelet' in the time series. Shapelet anomalies : Points where the trend's direction sharply deviates from the established pattern. Trend anomalies For the synthetic datasets, anomalies were injected at predetermined ratios to maintain control over the experimental conditions. The real-world datasets comprised data recorded from sensors at a water treatment facility, adding a layer of complexity and unpredictability to the analysis. Evaluating Anomaly Detection: Beyond Traditional Metrics Traditional evaluation methods for time series anomaly detection, like the point-adjustment protocol, can misrepresent a system’s performance by producing high F1 scores even if only a single point in an anomalous segment is identified. Recognizing this, researchers in a recent paper have proposed more stringent evaluation protocols. The P A%K protocol emerges as a solution, where 'K' represents the minimum percentage of points that must be detected within an anomalous segment for it to be considered correctly identified. This method ensures that models are recognized not just for detecting anomalies but for the extent of their detection capabilities. Building on this, the researchers introduce the F1K-AUC metric, which calculates the area under the curve of F1-scores at various levels of 'K', offering a comprehensive perspective on a model's precision and recall across different stringencies of detection. To further refine evaluation, the paper suggests using a modified ROC curve that accounts for true and false positive rates across multiple detection thresholds and 'K' values. This gives rise to the ROCK-AUC metric, which facilitates the comparison of anomaly detection models without the influence of threshold bias. This shift in evaluation metrics aims to ensure that high scores in anomaly detection are indicative of genuine, robust model performance across varying degrees of anomaly detection challenges. Key Takeaways and Future Work The paper presents an in-depth analysis of anomaly detection in multivariate time series data, which is increasingly critical in various fields such as healthcare, finance, cybersecurity, and industrial monitoring. Detecting anomalies is key to identifying significant disruptive events, from health issues to fraud, cyber threats, and equipment malfunctions. Given the rise of IoT and high-frequency data collection, the demand for effective anomaly detection models for multivariate time series is more pressing than ever. One of the paper's significant contributions is the exploration of deep learning methods, including autoencoders, GANs, and Transformers, which have already shown promise in identifying anomalies. It builds on this by proposing the use of diffusion models—more commonly associated with image and audio generation—for time series analysis. The central hypothesis is that diffusion processes might uniquely amplify the anomalies against normal patterns, enhancing detectability. To address the inadequacies of traditional evaluation methods, the paper introduces more robust metrics, such as F1K-AUC and ROCK-AUC. These metrics aim to provide a more accurate assessment of an anomaly detection system's capabilities, ensuring that high scores are truly indicative of superior performance. The experimental results, obtained from testing on synthetic and real-world datasets, show that the DiffusionAE model, which combines an autoencoder with diffusion processes, exhibits notable robustness and efficacy. Despite these promising results, the paper does mention the limitations inherent in the approach. For instance, the models, while successful on controlled synthetic data, encounter greater challenges with complex real-world datasets. This points to the need for further refinement to enhance the models' applicability in real-world scenarios. Moreover, while the paper advocates for sophisticated evaluation metrics, these come with their own set of complexities and may require broader validation within the scientific community. Another point of concern is the generalizability of the models across diverse domains and types of anomalies—a common hurdle in machine learning. Lastly, the computational intensity of diffusion models could potentially limit their use in large-scale or real-time applications. In summary, the paper underscores the potential of diffusion-based models in transforming the landscape of time series anomaly detection and calls for continued research to optimize these models for practical, varied applications. It also highlights the necessity for the adoption of advanced evaluation metrics to truly measure and understand the performance of anomaly detection systems. 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Exploring the Potential of Diffusion Models in Time Series Anomaly Detection

টাইম সিরিজ অসঙ্গতি সনাক্তকরণে ডিফিউশন মডেলের সম্ভাব্যতা অন্বেষণ করা

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