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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. The practical design and the inherent efficiency of our approach make it well-suited for real-world FL systems. Our plans for future works include extending our approach to asynchronous FL and vertical FL scenarios. REFERENCES T. Aoki. On the stability of the linear transformation in banach spaces. Journal of the Mathematical Society of Japan, 2(1-2):64–66, 1950. E. Bagdasaryan, A. Veit, Y. Hua, D. Estrin, and V. Shmatikov. How to backdoor federated learning. In AISTATS, 2020a. Eugene Bagdasaryan, Andreas Veit, Yiqing Hua, Deborah Estrin, and Vitaly Shmatikov. How to backdoor federated learning. In International Conference on Artificial Intelligence and Statistics, pp. 2938–2948. PMLR, 2020b. Arjun Nitin Bhagoji, Supriyo Chakraborty, Prateek Mittal, and Seraphin Calo. Analyzing federated learning through an adversarial lens. In International Conference on Machine Learning, pp. 634– 643. PMLR, 2019. P. Blanchard, E. M. El Mhamdi, R. Guerraoui, and J. Stainer. 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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. Advances in Neural Information Processing Systems, 34:12613–12624, 2021. Ziteng Sun, Peter Kairouz, Ananda Theertha Suresh, and H Brendan McMahan. Can you really backdoor federated learning? arXiv preprint arXiv:1911.07963, 2019. Circom Contributors. Circom zkSNARK ecosystem, 2022. https://github.com/iden3/circom. Vale Tolpegin, Stacey Truex, Mehmet Emre Gursoy, and Ling Liu. Data poisoning attacks against federated learning systems. In European Symposium on Research in Computer Security, pp. 480– 501. Springer, 2020. Richard Tomsett, Kevin Chan, and Supriyo Chakraborty. Model poisoning attacks against distributed machine learning systems. In Artificial Intelligence and Machine Learning for Multi-Domain Operations Applications, volume 11006, pp. 481–489. SPIE, 2019. H. Wang, K. Sreenivasan, S. Rajput, H. Vishwakarma, S. Agarwal, J. Sohn, K. Lee, and D. Papailiopoulos. Attack of the tails: Yes, you really can backdoor federated learning. In NeurIPS, 2020. Jianhua Wang. Pass: Parameters audit-based secure and fair federated learning scheme against free rider. arXiv preprint arXiv:2207.07292, 2022. S. Weisberg. Yeo-Johnson power transformations. 2001. Available at https://www.stat.umn.edu/arc/yjpower.pdf. Cong Xie, Oluwasanmi Koyejo, and Indranil Gupta. SLSGD: Secure and Efficient Distributed Ondevice Machine Learning. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases, pp. 213–228. Springer, 2020. H. Yang, X. Zhang, M. Fang, and J. Liu. Byzantine-resilient stochastic gradient descent for distributed learning: A Lipschitz-inspired coordinate-wise median approach. In IEEE CDC, 2019. Dong Yin, Yudong Chen, Kannan Ramchandran, and Peter Bartlett. Byzantine-robust distributed learning: Towards optimal statistical rates. In International Conference on Machine Learning, pp. 5650–5659. PMLR, 2018. Zaixi Zhang, Xiaoyu Cao, Jinyuan Jia, and Neil Zhenqiang Gong. 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.

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