# How LLM Hallucinations Actually Work

Large language models hallucinate because they are fundamentally probabilistic prediction engines, not databases of retrieved facts. Their underlying architecture mathematically compels them to generate the most statistically likely next word in a sequence, even when they lack the necessary context or training data to answer accurately. Furthermore, the evaluation benchmarks used to train these models inadvertently reward confident guessing over admitting uncertainty, effectively training the artificial intelligence to bluff rather than confess ignorance.

## The Illusion of Knowledge

When a modern large language model produces a fluent, highly structured, and confident response, it is remarkably easy to assume that the system understands the information it is dispensing. If you ask a chatbot to explain quantum mechanics or summarize a historical event, it often retrieves facts with such precision that it feels like a sentient librarian consulting a vast internal encyclopedia [cite: 1]. However, this anthropomorphic perspective is a cognitive trap. 

The phenomenon known as "hallucination"—where an artificial intelligence confidently generates plausible but entirely fabricated information—shatters this illusion [cite: 2, 3, 4]. Hallucinations are not merely glitches, bugs, or temporary lapses in a model's memory. They are the inevitable result of the mathematical principles that govern how these models are built, trained, and evaluated [cite: 5, 6, 7]. When an AI hallucinates a non-existent legal precedent, misattributes a quote, or invents a fictional chemical property, it is not "lying" in the human sense, because lying requires an awareness of the truth [cite: 1, 8, 9]. Instead, the model is successfully executing the exact task it was programmed to do: predicting the most statistically likely sequence of words.

To truly understand why hallucinations occur, we must move away from the idea that these models search for answers and instead look at the underlying mechanics of language generation. The root cause lies in the architecture of the neural networks, the nature of the training data, and the flawed incentive structures used to measure artificial intelligence performance.

## The Core Engine: Next-Token Prediction

If you strip away the billions of parameters, the sophisticated user interfaces, and the conversational tone, modern generative AI systems are autoregressive engines designed to perform a single, repetitive task: predicting the next token [cite: 10, 11, 12]. This single mathematical objective drives the entire ecosystem of modern language models.

### How Tokenization Obscures Reality

Language models do not process language in the same way human beings read words. Before any text can be analyzed, it must be broken down into smaller units called "tokens" [cite: 9, 11]. A token can be an entire word, but it is often just a fragment of a word or even a single character. For example, the word "playing" might be split into the tokens "play" and "ing," while a rare medical term like "cardiomegaly" might be shattered into meaningless sub-components like "cardio" and "megaly" [cite: 9, 11, 13]. 

Once text is tokenized, these fragments are converted into multidimensional numerical representations called embeddings [cite: 5, 13]. The model learns the statistical relationships between these numbers across billions of documents. This means the model does not understand the real-world concept of a word; it only understands the mathematical distance between tokens in a high-dimensional space. 

This tokenization process is a primary driver of specific, highly frustrating hallucinations, particularly those involving character counting, spelling, or precise numerical outputs [cite: 13, 14]. A well-known example is the difficulty large language models face when asked to count the number of "r"s in the word "strawberry" [cite: 9]. Because the model perceives the word as a sequence of opaque tokens rather than individual letters, its internal architecture is functionally blind to the spelling. It guesses the answer based on statistical likelihood rather than observational counting, leading to confident but absurd errors [cite: 7, 9].

### The Improvisational Actor Analogy

A highly effective way to conceptualize this mechanism is to view the language model not as a researcher retrieving a specific document, but as an improvisational actor performing on stage [cite: 15, 16, 17]. 

When a user provides a prompt, they are handing the actor a script. The actor does not have an internal database of immutable truths to consult. Instead, they rely on their vast experience of observing human dialogue—their training data—to improvise a continuation that sounds natural, plausible, and contextually appropriate [cite: 1, 2]. If you ask the actor a question about a widely documented topic, their improvisation will likely align perfectly with reality because that exact pattern of words has appeared millions of times in their memory [cite: 18, 19]. 

However, if you ask them about an obscure fact, the actor will not stop the performance to check a reference book. They are compelled by their training to keep the scene moving. The model generates a response that sounds authoritative and grammatically fits the context, even if the underlying facts are entirely fictional [cite: 8, 20, 21]. The model is essentially blind to the distinction between a retrieved fact and a statistically probable fabrication; both are simply the output of the same improvisational algorithm.

### The Autoregressive Snowball Effect

The generation process is autoregressive, meaning the model consumes a sequence of text, calculates a probability distribution across its entire vocabulary, and predicts the single most likely token to come next [cite: 2, 11, 13]. Once that new token is generated, it is appended to the previous text. The entire expanded sequence is then fed back into the model to predict the subsequent token. This loop repeats until the model generates a specialized "stop" token. 

This autoregressive loop is breathtakingly powerful at mimicking human reasoning, but it introduces a severe structural vulnerability known as "exposure bias" [cite: 22, 23]. During their initial pre-training phase, models are exposed almost entirely to high-quality, human-written text. They learn to predict the next word by observing perfect sequences. However, during actual deployment (inference), the model must predict the next token based on a sequence that includes its own generated outputs [cite: 23]. 

Because the model has never been trained on how to recover from its own deviations, a single tiny mistake early in a sentence can dramatically skew the probability distribution for the rest of the response [cite: 24]. This creates a compounding mathematical error. When a low-likelihood, factually incorrect token is generated, it becomes part of the permanent context window for the remainder of the generation [cite: 24]. The model's attention mechanism must now attend to this false token, dragging all subsequent logic down an invented path. The model is structurally constrained to maintain internal consistency with its own generated text, even if that text has drifted completely away from reality [cite: 2, 20].

[image delta #1, 0 bytes]





## Architectural Vulnerabilities in Transformers

Beyond the basic mechanics of autoregressive prediction, the specific neural network architecture used by modern models—the Transformer—introduces additional structural vulnerabilities. While Transformers revolutionized artificial intelligence by using a "self-attention" mechanism to track the relationships between words across long distances, they are not immune to critical cognitive bottlenecks [cite: 2, 5, 6].

### Context Limits and Attention Dilution

Transformer models suffer from finite working memory, known as the context window. While recent advancements have expanded these windows to process hundreds of thousands of tokens simultaneously, the fundamental limitation remains: the model must compress all that unstructured text into internal mathematical abstractions [cite: 13, 20]. 

As the context grows longer, the self-attention mechanism begins to struggle with a phenomenon known as "attention dilution." The model assigns weights to every token, determining how much focus each word should receive relative to the others. However, across massive documents, these weights become spread too thin. The model has difficulty maintaining focus on the most critical, factually grounding pieces of information when they are buried amid thousands of other irrelevant tokens [cite: 13]. 

This dilution often leads to "faithfulness hallucinations," where the model generates a response that sounds highly coherent but directly contradicts or subtly drifts away from the specific constraints provided in the user's prompt [cite: 13, 23]. Rather than synthesizing the complex context provided, the model's attention mechanism fails, and it falls back on its generalized parametric knowledge, ignoring the user's specific instructions.

### The Softmax Bottleneck

Furthermore, the final layer of the neural network utilizes a mathematical function called "softmax" to convert its internal representations into a probability distribution across the entire vocabulary [cite: 13, 25]. This creates a mathematical bottleneck. The model's hidden state often has a significantly smaller dimensional capacity than the total number of possible words in the English language. 

Consequently, the model cannot always represent all valid language patterns perfectly or assign perfectly calibrated probabilities to every potential next token [cite: 13]. The model is forced to compress its vast knowledge into a limited output vector. When forced to choose in a high-uncertainty state, the model relies on the most prominent statistical weights, generating a word that fits grammatically and satisfies the softmax probability curve, but fails entirely on factual grounds.

### Decoding Strategies: Forcing Creativity

The probability distribution generated by the softmax function offers a menu of potential next words, but the system must still choose one. The method used to select that word—the decoding strategy—heavily influences the rate of hallucination [cite: 12, 13, 23].

| Decoding Strategy | Mechanism | Impact on Hallucinations |
| :--- | :--- | :--- |
| **Greedy Decoding** | Always selects the single highest-probability token at every step [cite: 11, 23]. | Generally safer and highly deterministic, but can lead to repetitive, robotic, or overly simplistic text [cite: 12, 23]. |
| **Beam Search** | Explores multiple potential sequences of tokens in parallel, calculating the cumulative probability of entire phrases before selecting the best path [cite: 11, 23]. | Reduces minor errors but can lock the model into a confident, mathematically secure, yet factually incorrect path early in the generation [cite: 23]. |
| **Top-K / Top-P Sampling** | Samples randomly from the top *K* most likely tokens, or the subset of tokens comprising a cumulative probability mass of *P* [cite: 4, 11]. | Introduces necessary human-like variance and creativity, but significantly increases the risk of hallucination by intentionally selecting statistically sub-optimal (and potentially untrue) tokens [cite: 4, 13]. |
| **Temperature Scaling** | A hyperparameter that flattens or sharpens the probability distribution before sampling [cite: 13, 23]. | High temperature flattens the curve, making rare words more likely, heavily boosting creativity but guaranteeing high rates of hallucination and logical drift [cite: 13, 23]. |

## The Data Problem: Imitation Learning and Incompleteness

The computer science adage "garbage in, garbage out" applies exponentially to large language models. These models are voracious consumers of data, trained on petabytes of text scraped from the open internet. This data is notoriously riddled with bias, misinformation, and contradictory statements [cite: 2, 13, 23]. 

However, the hallucination problem extends far beyond simply ingesting false facts. Models learn via imitation. They perfectly mimic the noisy, confident, and often factually loose style of internet text [cite: 23]. If the training corpus contains toxic or erroneous content—as massive datasets like Common Crawl often do—the model will not simply reproduce those errors; it will amplify them, generating new text that mimics the statistical shape of the flawed data [cite: 13, 23].

Furthermore, as the internet becomes increasingly saturated with AI-generated content, models are beginning to train on synthetic data produced by previous generations of AI. This creates a dangerous feedback loop where hallucinations and statistical quirks are absorbed as factual training data for the next model, leading to a phenomenon where the model's grasp on reality slowly degrades over time [cite: 13].

### The Mathematical Floor: Singletons and Undecidability

Recent theoretical research from OpenAI reveals that hallucinations are not merely engineering bugs that can be smoothed out with better data curation; they are a fundamental mathematical limit of statistical learning [cite: 5, 14, 26]. The researchers demonstrated that text generation is a statistically harder problem than text classification [cite: 3, 14]. It is much easier for a model to classify whether a given sentence is true or false than it is to generate a true sentence from scratch out of millions of possible combinations.

The OpenAI researchers quantified this limitation using a concept called the "singleton rate." In any vast training corpus, there is a massive tail of obscure facts, biographical details, and niche knowledge points that appear exactly once. These are called singletons [cite: 3, 14, 27]. Because the model only sees this data point a single time during training, it cannot form the robust, repeated statistical weights necessary to accurately generalize or recall that fact later [cite: 3, 26]. 

The mathematics dictate that the percentage of facts that are singletons in the training data acts as a hard floor for the model's hallucination rate on those topics [cite: 14, 26]. For example, empirical measurements show that roughly 20% to 30% of biographical facts appear exactly once in typical training corpora [cite: 26]. Therefore, the model is mathematically expected to hallucinate on at least 20% to 30% of rare biographical queries, regardless of how large the model is scaled or how much compute power is applied [cite: 3, 26]. When faced with a prompt targeting this sparse data, the model does not have the statistical confidence to provide the exact right answer. But because of its structural constraints, it will still output a highly confident guess.

Other computational theorists go even further, drawing on Gödel's First Incompleteness Theorem to argue that hallucinations are an intrinsic, structural feature of these systems [cite: 5]. Because accurate information retrieval from a finite dataset of ambiguous text requires solving undecidable problems—similar to the Halting Problem in computer science—it is theoretically impossible to build a language model that guarantees zero hallucinations at every stage of generation [cite: 5].

## Post-Training: How We Teach AI to Bluff

If an AI system lacks the parametric knowledge to answer a question, the most logical and safe response would be to output, "I don't know." Yet, large language models rarely do this spontaneously. The reason lies in how these models are evaluated, graded, and fine-tuned after their initial pre-training.

Following the ingestion of raw data, models undergo post-training processes like Reinforcement Learning from Human Feedback (RLHF) and are measured against rigorous academic benchmarks. Unfortunately, the architecture of these evaluations inadvertently incentivizes the model to act as a relentless test-taker that constantly bluffs [cite: 14, 28, 29].

### Benchmarks and the "I Don't Know" Penalty

Most primary AI benchmarks evaluate models using a binary scoring system: a point is awarded for a correct answer, and zero points are awarded for an incorrect answer [cite: 7, 27, 30]. Crucially, abstaining from a question or explicitly expressing uncertainty also yields zero points [cite: 27, 28]. 

From the perspective of a statistical optimization algorithm, this creates a deeply skewed incentive structure. If admitting ignorance guarantees a score of zero, and guessing provides a fractional probability of randomly hitting the correct answer, the mathematically optimal strategy is to guess every single time [cite: 7, 28]. Models are explicitly optimized by developers to maximize their performance on these standardized tests to climb industry leaderboards. 

Consequently, the systems learn that helpfulness and confident assertion are rewarded, while humility and caution are penalized [cite: 28, 29]. This results in models that are heavily biased toward fabricating answers rather than admitting uncertainty [cite: 21, 29, 30]. The industry has created a vicious cycle: developers want their models at the top of the scoreboards, the scoreboards reward models that guess, and the resulting deployed models confidently dispense misinformation [cite: 29, 30]. 

Researchers argue that until evaluation metrics are fundamentally redesigned to heavily penalize confident falsehoods and actively reward calibrated abstention, hallucinations will remain a persistent, artificially reinforced feature of language model behavior [cite: 28, 29, 31].

## Measuring the Mirage: Semantic Entropy

Because language models present hallucinations with the exact same authoritative tone and syntactical fluency as factual truths, detecting them requires moving beyond simple human intuition. Researchers and engineers have developed sophisticated statistical frameworks to measure when a model is likely confabulating.

### The Limits of Token Uncertainty

Traditionally, engineers tried to measure a model's uncertainty by looking at the standard token probabilities; if the model assigned low probabilities to the next few words, it was assumed to be uncertain and potentially hallucinating. However, this approach fails because natural language is highly flexible [cite: 25, 32]. 

An LLM might assign low probabilities to specific words not because it is factually uncertain, but simply because there are a dozen grammatically correct ways to phrase the exact same true concept. This is known as lexical or syntactic uncertainty [cite: 33]. For example, "The capital of France is Paris" and "Paris is the French capital" mean the same thing, but the model might split its probability perfectly evenly between starting the sentence with "The" or "Paris," leading to low token confidence despite high factual certainty [cite: 25, 32, 33].

### Clustering in Meaning-Space

To solve this, researchers introduced a framework known as Semantic Entropy, which measures uncertainty in "meaning-space" rather than "token-space" [cite: 33, 34]. 

The process involves querying the LLM multiple times with the exact same prompt and forcing it to generate several different answers [cite: 33, 34]. These diverse answers are then algorithmically analyzed—often by a secondary Natural Language Inference (NLI) model—and grouped into clusters based on their underlying semantic meaning [cite: 25, 33]. 

If the model generates five different answers with varied wording, but all five convey the exact same factual meaning, they are grouped into a single cluster. This results in a low Semantic Entropy score, indicating that the model is highly confident in the facts, regardless of its word choice [cite: 33, 35]. 

Conversely, if the model generates five answers that contradict each other or introduce entirely different factual claims, the semantic meaning is highly diverse. The answers will scatter into multiple clusters. This results in a high Semantic Entropy score, serving as a powerful mathematical red flag that the model is operating in a knowledge gap, lacks a factual foundation, and is actively confabulating [cite: 33, 34, 35].

[image delta #2, 0 bytes]





While Semantic Entropy is highly effective at catching "confabulations"—instances where the model makes something up for no apparent reason—it has limitations. It cannot detect hallucinations where the model has been systematically trained on incorrect facts or flawed reasoning, as the model will consistently and confidently output the exact same false claim every time [cite: 33].

### Spotting Hallucinations in the Wild

For end-users who do not have access to a model's underlying logits or sophisticated semantic entropy tooling, spotting a hallucination requires a critical eye and an understanding of the model's blind spots. Common indicators of a confabulation include:

*   **Non-existent citations:** The model generates a perfectly formatted academic citation, complete with a realistic title, real author names, and a DOI, but the paper never actually existed [cite: 36]. This occurs because the model understands the statistical shape and syntax of a citation perfectly, but simply fills the slots with highly probable, adjacent words from its training data.
*   **Suspicious numerical precision:** The model provides exact, highly specific numbers or percentages (e.g., "73.2% of businesses experienced growth") for obscure topics without citing a specific methodology or dataset [cite: 37]. Real-world data is rarely perfectly round or uniformly available, but models often invent highly specific numbers to simulate authority.
*   **Contextual inconsistency:** When probed with follow-up questions, the model immediately contradicts its own previous statement or provides a slightly different factual baseline [cite: 21, 37]. Because it is predicting the next token based on the expanding context window, its logic can drift rapidly.
*   **Software and API fabrications:** When asked for coding assistance, models frequently hallucinate non-existent software packages, libraries, or API endpoints [cite: 21, 38]. The model predicts that a function *should* exist based on naming conventions, leading to frustrating integration failures and potential security vulnerabilities if attackers register those hallucinated package names [cite: 21].

## Mitigation Strategies: Anchoring the AI

While theoretical research proves that hallucinations cannot be entirely eliminated from generative models, their impact can be drastically mitigated through system-level architecture changes and strategic prompt engineering [cite: 5, 38, 39]. The goal is to constrain the model's probabilistic nature and anchor its generations to verified reality.

### Parametric Knowledge vs. External Retrieval

Mitigation begins by understanding when to rely on a model's internal memory and when to seek external facts. An LLM's internal memory—stored in the trillions of numerical weights connecting its neural pathways—is known as parametric knowledge [cite: 18, 19, 40]. 

Relying purely on parametric knowledge is highly effective for synthesizing common concepts, explaining broad scientific principles, or answering straightforward, widely documented factual questions [cite: 18, 19]. Because topics like photosynthesis or the capital of France appear millions of times in the training data, the statistical probability of generating the correct answer approaches certainty [cite: 18, 19]. However, for dynamic information, real-time events, or hyper-niche data, parametric knowledge fails entirely [cite: 41]. 

To illustrate this divergence in utility, it is helpful to contrast the mechanics of an LLM relying on its internal weights against a traditional search engine algorithm.

| Feature | Large Language Models (Parametric Knowledge) | Traditional Search Engines (Retrieval) |
| :--- | :--- | :--- |
| **Core Mechanism** | Probabilistic synthesis and next-token generation based on learned statistical patterns [cite: 42, 43]. | Crawling, indexing, and keyword/semantic matching against a live database [cite: 42, 43, 44]. |
| **Response Format** | Direct, conversational answers and synthesized content [cite: 42, 45]. | Ranked lists of external hyperlinks directing users to source documents [cite: 42, 44]. |
| **Data Freshness** | Static; frozen at the time the model completed its final pre-training phase (the "cutoff date") [cite: 19, 41]. | Real-time; updated constantly as web crawlers index new content [cite: 41, 42]. |
| **Ideal Use Case** | Complex synthesis, language translation, creative writing, and explaining common concepts [cite: 18, 19, 46]. | Fact-checking, locating specific documents, and retrieving highly volatile or hyper-niche data [cite: 18, 46]. |
| **Error Mode** | Hallucinations (fluent, highly confident fabrications) [cite: 2, 26]. | Low relevance (returning links that contain the keywords but miss the user's intent) [cite: 43, 45]. |

### Retrieval-Augmented Generation (RAG)

Because LLMs are static and prone to fabricating rare facts, the most effective architectural defense in production environments is Retrieval-Augmented Generation (RAG) [cite: 22, 38, 42]. 

Rather than asking the language model to rely on its static, parametric memory to answer a question, a RAG system intercepts the user's prompt and executes a traditional search query against a trusted, external database or document repository [cite: 38, 47]. This is often achieved using vector databases (like FAISS or ChromaDB) that find documents semantically similar to the user's query [cite: 38, 40, 47].

The system retrieves the most factually relevant paragraphs from the external database and forcibly inserts them into the language model's context window alongside the original question [cite: 48]. The prompt is then modified under the hood to instruct the LLM: *“Answer the user's question using only the provided context. If the answer is not contained in the context, state that you do not know”* [cite: 38]. 

By offloading the burden of factual accuracy to a traditional retrieval system, the LLM is relegated to doing what it does best: synthesizing, summarizing, and formatting text [cite: 38]. While RAG does not completely immunize a system against hallucinations—the model can still misinterpret the retrieved text or suffer from attention dilution if the context is too long—it drastically reduces the likelihood of the model inventing data out of thin air [cite: 22, 40, 47].

### Prompt Constraints and Chain-of-Thought

For individual users and developers who cannot build full RAG pipelines, altering how a prompt is structured can significantly rein in a model's tendency to guess. 

Providing the model with explicit permission to fail is a crucial first step. Because models are trained to be relentlessly helpful and avoid zero-point penalties on benchmarks, simply adding the phrase, *"If you are uncertain or do not have enough information, reply with 'I don't know' rather than guessing,"* shifts the statistical weights [cite: 39, 49, 50]. This gives the model a safe off-ramp to abstain from confabulation.

Furthermore, employing "Chain-of-Thought" (CoT) prompting forces the model to slow down its autoregressive generation and map out its logic sequentially [cite: 10, 48, 50]. By instructing the model to *"think through this step-by-step before giving your final answer,"* the user forces the model to generate intermediate reasoning tokens [cite: 48, 50]. These intermediate tokens are then fed back into the context window. This effectively grounds the model's final conclusion in its own explicitly stated logic, dramatically reducing the risk of a spontaneous factual deviation [cite: 48, 50]. Research has shown that forcing a model to show its work can cut hallucination rates by more than half in complex reasoning tasks [cite: 50].

### LLM-as-a-Judge and Observability

Finally, as artificial intelligence systems move toward autonomous agentic workflows, treating the first output as a final answer is increasingly recognized as a dangerous anti-pattern. Developers are now utilizing secondary, independent language models to act as a "judge" to verify the claims made by the primary model [cite: 16, 38, 47]. 

Because verifying a response is computationally and statistically easier than generating one, a secondary model can often spot logical inconsistencies or unsupported claims that the first model hallucinated [cite: 47]. Observability platforms are also being deployed to act as "flight data recorders," logging every step of an AI's execution path so engineers can pinpoint the exact moment a model's logic derailed and hallucinated a false tool call or API request [cite: 16, 51].

## Bottom line

Large language models hallucinate not out of an intent to deceive, but because they are autoregressive prediction engines mathematically compelled to generate the most statistically probable next word. This structural reality, combined with finite context windows, the scarcity of rare facts in training data, and evaluation metrics that actively reward guessing, means that generating plausible falsehoods is an inherent feature of the technology. While we cannot entirely eradicate hallucinations, understanding their origin allows us to utilize frameworks like Retrieval-Augmented Generation (RAG) and Semantic Entropy to detect uncertainty, ground the model in verified facts, and safely harness its immense capabilities.

## Sources
1. [LLMs vs. Traditional Search Results](https://hawksem.com/blog/llms-vs-traditional-search-results/)
2. [Evaluating User Preferences Across Varied Information Retrieval Scenarios](https://arxiv.org/abs/2401.05761)
3. [Evaluating User Preferences Across Varied Information Retrieval Scenarios (PDF)](https://arxiv.org/pdf/2401.05761)
4. [Large Language Models vs. Search Engines: Evaluating User Preferences](https://www.semanticscholar.org/paper/Large-Language-Models-vs.-Search-Engines%3A-User-Caramancion/e53f09ef1db511aba3b5a79656d712a1fbbb8fd2)
5. [LLMs vs Search Engines: Which Traffic Actually Converts?](https://www.bruceclay.com/eu/blog/llms-vs-search-engines-which-traffic-actually-converts/)
6. [Mathematical Analysis of Hallucination Dynamics in Large Language Models](https://arxiv.org/abs/2511.15005)
7. [The Hallucination Phenomenon in GPT](https://www.mdpi.com/2227-7390/11/10/2320)
8. [Structural Hallucinations in LLMs](https://arxiv.org/html/2409.05746v1)
9. [Theoretical Framework for Studying Auto-regressive Next-Token Predictors](https://arxiv.org/abs/2309.06979)
10. [Early work on LLM factual incorrectness](https://openreview.net/pdf/929359c10c1be0811dd7d4f36408c86df21d77fe.pdf)
11. [Why do Large Language Models Hallucinate (AWS)](https://builder.aws.com/content/2x37YnzachpTBpUDEkM0GX38uD1/why-do-large-language-models-hallucinate)
12. [How Large Language Models are Designed to Hallucinate](https://arxiv.org/abs/2509.16297)
13. [Why do LLMs hallucinate facts? (StackExchange)](https://ai.stackexchange.com/questions/50438/why-do-large-language-models-hallucinate-facts-even-when-trained-on-large-datase)
14. [Why do AI hallucinations happen?](https://aibusiness.com/ml/why-do-ai-hallucinations-happen-)
15. [Why Do LLMs Go Rogue?](https://www.neura.market/directories/chatgpt/blog/why-do-large-language-models-hallucinate-deep-dive-into-causes-types-and-proven-fixes)
16. [Semantic Entropy in LLMs](https://medium.com/@mervenurakkilic/semantic-entropy-in-llms-a-foundation-for-detecting-hallucinations-and-enhancing-reliability-fa61d8b88946)
17. [A New Method to Detect Confabulations](https://towardsdatascience.com/a-new-method-to-detect-confabulations-hallucinated-by-large-language-models-19444475fc7e/)
18. [Semantic Energy Framework (PDF)](https://arxiv.org/pdf/2508.14496)
19. [Semantic Energy Framework (HTML)](https://arxiv.org/html/2508.14496v3)
20. [Detecting Hallucinations Using Semantic Entropy](https://oatml.cs.ox.ac.uk/blog/2024/06/19/detecting_hallucinations_2024.html)
21. [Why Language Models Hallucinate (OpenAI)](https://openai.com/index/why-language-models-hallucinate/)
22. [Why AI Chatbots Hallucinate (Business Insider)](https://www.businessinsider.com/why-ai-chatbots-hallucinate-openai-chatgpt-anthropic-claude-2025-9)
23. [Understanding Hallucinations According to OpenAI](https://medium.com/data-science-collective/understanding-hallucinations-in-llms-according-to-openai-0465ffb10bf6)
24. [Hallucination (artificial intelligence)](https://en.wikipedia.org/wiki/Hallucination_(artificial_intelligence))
25. [OpenAI on LLM Hallucinations (InfoQ)](https://www.infoq.com/news/2025/10/openai-llm-hallucinations/)
26. [How to check if LLM is hallucinating](https://wpseoai.com/blog/how-to-check-if-llm-is-hallucinating/)
27. [Detecting Citation Hallucinations in LLM Outputs](https://ojs.aaai.org/index.php/AAAI/article/view/42257/46218)
28. [Hallucinations in LLMs: Can you even measure the problem?](https://medium.com/google-cloud/hallucinations-in-llms-can-you-even-measure-the-problem-932e23b1873b)
29. [How do you view hallucinations of a Large Language Model](https://www.researchgate.net/post/How_do_you_view_hallucinations_of_a_Large_Language_Model)
30. [Common LLM Misconceptions](https://apxml.com/courses/intro-large-language-models/chapter-1-understanding-large-language-models/common-llm-misconceptions)
31. [Do LLMs always tell the truth?](https://www.enfuse-solutions.com/do-llms-always-tell-the-truth-understanding-hallucinations-and-misinformation/)
32. [LLMs hallucinate constantly (YouTube)](https://www.youtube.com/watch?v=9VNG0h4pLh0)
33. [LLM Hallucinations: Why Models Make Mistakes](https://www.appen.com/blog/ai-hallucinations)
34. [Why LLMs sometimes make stuff up](https://medium.com/@busolasogunle/hallucinating-machines-why-llms-sometimes-make-stuff-up-b5cbe415d44d)
35. [Best Practices for Mitigating Hallucinations (Microsoft)](https://techcommunity.microsoft.com/blog/azure-ai-foundry-blog/best-practices-for-mitigating-hallucinations-in-large-language-models-llms/4403129)
36. [How to reduce AI hallucinations](https://aiblewmymind.substack.com/p/how-to-reduce-ai-hallucinations)
37. [5 Practical Techniques to Detect and Mitigate LLM Hallucinations](https://machinelearningmastery.com/5-practical-techniques-to-detect-and-mitigate-llm-hallucinations-beyond-prompt-engineering/)
38. [Techniques to prevent hallucinations in RAG](https://pub.towardsai.net/5-techniques-to-prevent-hallucinations-in-your-rag-question-answering-25fb501a7e54)
39. [Strategies to Reduce LLM Hallucinations](https://netraneupane.medium.com/strategies-to-reduce-llm-hallucinations-all-in-one-a437ad9ec8ca)
40. [Next Token Prediction Analogy (PDF)](https://arxiv.org/pdf/2408.04666)
41. [From Next Token Prediction to Reasoning Machines](https://kaifkohari10.medium.com/from-next-token-prediction-to-reasoning-machines-how-llms-evolved-beyond-simple-text-generation-to-ac7cd1709ae1)
42. [Next Token Predictor Is An AI's Job](https://www.astralcodexten.com/p/next-token-predictor-is-an-ais-job)
43. [LLM Next Token Prediction](https://www.wwwinsights.com/ai/llm-next-token-prediction/)
44. [How LLMs Master Next-Token Generation](https://python.plainenglish.io/the-art-of-prediction-how-llms-master-next-token-generation-b8f81dc16de2)
45. [Main reasons LLMs hallucinate according to OpenAI](https://openai.com/index/why-language-models-hallucinate/)
46. [How Semantic Entropy Detects Hallucinations](https://oatml.cs.ox.ac.uk/blog/2024/06/19/detecting_hallucinations_2024.html)
47. [Architectural and Data causes of Hallucinations](https://builder.aws.com/content/2x37YnzachpTBpUDEkM0GX38uD1/why-do-large-language-models-hallucinate)
48. [Agentic Testing Tools](https://www.quora.com/What-are-the-best-AI-testing-tools-for-agentic-testing)
49. [Product Mindset 2025-26](https://www.scribd.com/document/928192464/Product-Mindset-2025-26)
50. [AI Storytelling Tools](https://www.quora.com/What-is-the-best-AI-storytelling-tool)
51. [Best AI Testing Tools](https://www.quora.com/Which-is-the-best-AI-tool-for-testing)
52. [OpenAI Singleton Rate Explanation (Medium)](https://medium.com/data-science-collective/understanding-hallucinations-in-llms-according-to-openai-0465ffb10bf6)
53. [Why AI Models Hallucinate (Iain.so)](https://iain.so/why-ai-models-hallucinate)
54. [Why Language Models Hallucinate (Kingy.ai)](https://kingy.ai/blog/why-language-models-hallucinate-openai-paper-summary/)
55. [Why Language Models Hallucinate (OpenAI PDF)](https://cdn.openai.com/pdf/d04913be-3f6f-4d2b-b283-ff432ef4aaa5/why-language-models-hallucinate.pdf)
56. [Understanding Why Language Models Hallucinate (Galileo.ai)](https://galileo.ai/blog/why-language-models-hallucinate)
57. [Parametric Knowledge vs External Source (Milvus)](https://milvus.io/ai-quick-reference/in-what-scenario-might-it-be-better-to-rely-on-the-llms-parametric-knowledge-rather-than-retrieving-from-an-external-source-eg-very-simple-common-knowledge-questions-and-how-to-detect-those)
58. [LLM Training Data vs Web Search](https://www.geekytech.co.uk/llm-training-data-vs-web-search/)
59. [Technical differences between LLMs and Search Algorithms](https://mention.network/learn/the-technical-differences-between-llms-and-search-engine-algorithms-2/)
60. [Parametric Knowledge vs External Source (Zilliz)](https://zilliz.com/ai-faq/in-what-scenario-might-it-be-better-to-rely-on-the-llms-parametric-knowledge-rather-than-retrieving-from-an-external-source-eg-very-simple-common-knowledge-questions-and-how-to-detect-those)
61. [Parametric Knowledge Study (DiVA)](https://www.diva-portal.org/smash/get/diva2:1968861/FULLTEXT01.pdf)

**Sources:**
1. [apxml.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHUvtbtJVRYQzR5yqoMtnPlDpkJwDXTt6KSnWJv5HOdBhHJ8cG8EFKE-RjEGa9EoF5uFzoS9CC0xN2Z2BR_e-Zdx6RH5mE6bz1udE1eV9xIFvLNEgvYHUIcZPZCyvPdCzJPwT_1QqnNeZm8Lp2Mr7KUQGEnUfd-hAs8PtVCSGEWCqM70ybkolycmjYSlTb8xMR04o75AOLeXqtGdN38QjMgymMg727h2VG_lA7fOUXEpgcW0A==)
2. [aibusiness.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQENZXJJHr7muEJ6YY-89r8pecoMO95-jxBhcPj7SyyDuVYHeCdeGs4aV2wSrCDRRauEziIwHkVkBYZxAq14D5wq4cP4ex_1k4UoYI1VBNvpFhyKYwTbfs8queH92DAMirX5EtKKLSZvTYVdFN4Apbhd)
3. [medium.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHmFpxtglfSrROKnSPGutYChuKe09j8kSSpmEAlLHIkuBJx_KEx51nw7LKxIaGW6ek-zZdyHV799IUvZ_rtDbEitPgViq6-MTVF9noOQR8P4hjdhPvMTMs2finN7QFdyPUBA3Y_qrB5nsiyVqnzm--2eYWuKotA_VDedggfOKiJ6qV__6UqBUPPtlIbt1ref-yGoaG1K2SiAYr4y-d6icn-sxKPexPO)
4. [wikipedia.org](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEgvbzVdKLZUm2CrkJUHgDeuapQEGSxomzCNBuJzokHuVDIJLtK9Og2sb746msArsgb7n7sGkH9_ZjZBszew4amwoTjLG2Jq_3uEeBd8-PQr4KG7Lle0TavY55Q2huKeQBbjbM4_nj4XpGdRP2H5a0xNI-j9yqLCSljS4U=)
5. [arxiv.org](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFBl02cCtB-h6RbZAymrhs-Y0rutM4p3sB_arFb6CvjG46mfZy5sKkwBgYmjDGOb7aCFJzJChL9ZGaF3Jm0LnD2PQiieCuXK-JVuZMHobW6Z6X3Fc3SezBp7w==)
6. [arxiv.org](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQF_6boR9nYOoRb5hw_wKXoPq9OPR4yIuZ9N1lSGfrJ3ql_GkBU_TSv98TLWrcEwXApxj1ykgIhIrKMWcqtwrDFZnCZI_aXxE5W8STk3FA5QAq7f-zgGfA==)
7. [appen.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFew-zYz6bRvr1PTpDgv9TY0zjs0tPy-gTZgPJTGDmBCHzkl_lxY4de7CMciP5xmYGgnz_aSykasGiEQ9lfFNjKEdZjpRE311-6BYxMSngtnV9uzP81l_iY1cOY6WP7XL66DA==)
8. [enfuse-solutions.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFE7nhudqmAaP7NneSmSDlbFiOy5Ri1kjkyGRmVHJsiUVIIjgL3Dt_lN-g8_IvyizYfLZMQeYmEHFN54eZwotS87PlyLIhzAHe8vcOhvMyS2aLErT8nJYujl930rmPrZuL9HdD_3a6ZzTt97h4ZL1ZmYAipc_0mB0-0wn-ylJdT6yFDZsG8hDkV1zMMeDd0CkYKFEcODI9YdVft4oya6SiE38WRtV0=)
9. [medium.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQG5kjCQBXxhkwaUMV9X3u1-acgDCVanFj-J8QbHyhvj7podizwgFeddDvOHcvshaqEtWfyvqaKO7kFZ56o0BlyvNfdh0XUTpILtxcBOdbwnCfNmQNWD26i47zB9S9hnQQq_FfUwPY0mENv0A5WZwzNb6RQ2xecRHGCRMKVKzWwwF2X7iy8c1xWahYDydQsk3gSktesrd39ddVDJ9rA=)
10. [arxiv.org](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFqNrtYHWX9u_Pz5MbHrCwjSvdONmN94Mq8pqsNHJ0ziTKrXWr7_KqwAk0meBeRjdPXt72LEjJaw95spiuSiQUaeK_jU1NeoxVJ3JCO83ppO1GZB3nF6g==)
11. [wwwinsights.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQE5RJV9WkDmkXFR9bPTPbkknHYyY_P8xreNMhxhBDjs-TZUnqGWYWFhivejNl4G9Ti9_5LI0XQK6aKQXxaKRVr0UM0VWI-okjXJqeFvy77thK4e8KbpS7vLwmMtVYAJzNT3oUcwKPDYLCXJtVcg8WQ=)
12. [plainenglish.io](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFJMjZuH5gYxsi1fEhvjCI_USspHw5oyfhClB1gF8QAiz6QwGZBdxSqAAgiqmj5RUecOANof6EihQ28Gu4rWWsHi4xOApUZYIY8So96hs-EcsgxHAAiQidb3LVw6q2QuWYxmjgk_9nAFV3ZXpWfWiZu2x2pJZ7VQWISPGRcKRfrxRHqa1koMWQ8mJV4gitLc8hlftigZU2zTyVC_rXC)
13. [aws.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEXlF2ingytT4f-BZ3bt_umIBDHVD2ugeYyBfRxhjZvf_yZRVx9crf_5rYG6bx8wmbPuNrNrERod7yQzxhUOG_YtXLV0lAF7A_pvdW7kqO6aVn3_t_lWjWYriWAQCt6ilB5UFAU7J31LuGOeH3Z0-s6MJcKgSK0r_DEqNq-eJqn6QC2Ba0mEUTg9fNVVoxtDjJ9YTkrhzTagDh2)
14. [kingy.ai](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHxgrBM_4-p7eF2RdnXN6cAhmuMEsJ5ae9dwVnrFDd3UDKFUNhe1R_rHEHOBNRPzt0Jxby7MDFQuZUeiahaNKgBzTjOadfia6UHoF36e0GO8TLFKXw19NnV_8QH1sGBgLCmXTO46w8fOk383gY08ZOTolBbZKGsydbzqXyyKH7zi64=)
15. [arxiv.org](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEml8uzN9ZxWKWCwX2Qpz4fxY4FHNo5bRYUEcIKCgA0Lx_khjn2OCOj-TrM_tdyJozamHwGuN8imw5BrKhScr2Y386SEz1HvW40GjPgftki0Cr7U7J2NA==)
16. [quora.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGuKblZvhS8f-bQq6xyM7HO6ujTuocdVJ_K0HtcUXIKQOVKIJfK14OblRIBV6Qv3oQmWFn5-9VV_4I6iMPlyF4RuSqDn4-IBYovmKutMITMsz-B1zmEA_wTCRF-Bd2h35KtEBMBxrjoTb02QA3ZgUnFJunjP9L0cZXUvHYykBmSeb4m)
17. [quora.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQETzs4m1V9rnPyGoZAuqEGyORaSjN1ffJiN2qQ2uxsnyoiizqSy38tdoxPiiUgA28hZNXQDRyS3AzlPtkmyocmL0vv4Z3B2hvdHiumlveLsfz1tpupWZl8KxemEVULouDxNj9FytL8F58a6pfyUPpgyoA==)
18. [milvus.io](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFVweRjeudzIMoSrGhkFxy43h_PNHFFovSbQ4lCn0gfQoOYzGn5-_Vf4a0XY8bRXAD_CRyoerb2eW_qbUXaHcco6Gl_v2MCTryS2mAlZkTs3dFv8DH-oTBthxa0dO9bX7AW0glhkTMNseULEXy_BBVTRVeL_CWm19Lh0u6RBWSBCKwmeRgT4Hm_NkRlr5GEeMQz7gc1A83lO2mfQ9nwvzDhAcQSMGBA7eEJrwNgsg5qbkb6x4hVw5kW19VmmAqdrnTLWOxxalT8LnwqZ986vdgSbBpkZtd_96ybuXz4JZwlO17VDPLs7gQyYuFQOU_05UpSG1GqQDuLyjgyZM_cjD9xkH3lXciaN95h7sZxnFK-an4nEpokL_dt-w==)
19. [zilliz.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHAN3pdG8L9S0Mct7rxbdUfWvJjj4Au2ELme-1A7vhjVvsb4s42MN9RWQsaBxVzKzgZMxdaluJImCpelFSQU06rZYjdXDHEHDvZvbxT7fTw2c5SKb8jkBGJW95o5ZnSInfdCdXLT9fZmFS0M-nNfjRj5-eW03WSR_BAXvMdF3PzAp4D_wGg9y8k-8Jj_93_qrSTfxGk7yB8ygJyTPdo5Zab5SKU1ZsOxhynl9YRgIcVyUA3Qq4JT1gxFWiMT7cq6Xz5H7Xjd9ymYgUcgU0Mk3SreIq3XMoEJYpzjGoYgM9tVc9JkyRu-H7JAnbNUJGeirx0Y2sEo1P0S5lCXx48wE4pkypWiqVhETgDrNRwmPI=)
20. [stackexchange.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEJqmDGPakXSjYNZexjsH43bLntM07prFA37voH-NPEBBnLieeLnTCRkSkGJ_T-FrB67SJAhRqYhgzq4rrfC-b6zk2V7xEy2M0eHASD2YJlafpwF9K9AYTan_A9GMJZfH6rlBqmMWSPztHxZhHP8uLn_o1AL3blWMUQoKJww4t9gy-VlbUKfBC7a7WK2aZ0wTZ77NFaIu2KIhposYJRwap3PFvxXli0c4H6FZmr2PG4J_1fbg==)
21. [youtube.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEL7f-ZBGEXZ6NsA1-G9w5H2c9hw6-WOB67EkjtUFvA-iRRbOPPinzRW6s9qcuitzkiis84ZuqZ9Euey3odcGyb1sCe2GIxRI6fnUHJGh_Tg-hQfXVN4S0c5ZzvDvLTOOzv)
22. [openreview.net](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHoGGqoAUIKkHinhFtMIb-08PazjFpRznujccWgnI0K3IkCNKCn5a_5OXk6UWkVsqSz5Nc-qqLZoPhoGtCWrrrSZQQx1Qwai0xufIwBQd-zCO9KsFAMkp95tudYOTWIf3GYuYTgagYfvyaR-3Kzj7hEtV_Ke-92_lznisJCEQ==)
23. [neura.market](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGwoOH3RDGj2q4RGlojhFi9LB7o53sIIH-iQdRjmXjfd2mozPrbJvUvTESbQtNsqmL5MuUBdNhuZu0f2NhvG8UOd03Gis5TURHT78RzO9e0BjQRhuBdK6-Ac5Me4UnG5MBTD9Q3la4WmtqpjT9bc4hLWGfGUZBnObo_CEPR9sE7JeTG5zU2aR9tBJd0Qv5X0ggxVxq-y-ecnhpGQBCKAwnYLcHZJ9fktzqtLLvGRqlclRiTrgCneYHt68fhNG93)
24. [mdpi.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGe1Tbw2TLYdMjLlssQn1PqadfKOZ2Z4HSCLQMXOzF9I2RWD7iA89gvEFeT-l7Lx6ye5KR1DfApVTnlQM04Fk9RaS05wtH-AjPlOd8a2QKtUVH-rQzFIqeaob9WN3VliQ==)
25. [arxiv.org](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHzIG9gYXJQ_OShmR_p8c1GxG54B-_RgXU18BbgNq8Nd2GcagRNjSkmgX2os51P2x0iLbUjRcxXczAUFkN-BxygxAEiYlFgp0zuM5YoSZt5Ozf2fi7SiA==)
26. [galileo.ai](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFNrZBrk38QyI4J-dFILZd8CrApCBY4bo8a2gAdkT9e7ZoaReLLAh50vdKfDqO8zUvYu7MAjW-NvjV5NVtuuaSJiZDrsFr_F2NVeBl_rp9walQOEEEOeZzNZdeX4NJlaqYISpPegx9yy8OwDnwl)
27. [openai.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEZLMRAMx8MwJ6KYXZSEkhlfsvFbfoZANrTOka5MUo_9gSypd6FhLCm1lMRjdKaXv_qAww1R3u1AcHyivRk8cZEvGLrmX_5ybNhsiLYrd7_isel6C6mDiq_C-u1C7WzZcRKgzCL0KwSXiEMfyu3GBUiPbWpFF2IOPuJXoGB8869FPUPCYm7Ox2Jt1wH_ttHlImoBEEUQONX0PA=)
28. [businessinsider.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGydsVXwHkNvq1Mcz9Coam7Q1iKSH0FNon8Nzeio6GuGHAqn4LRPeZ9YKogR9VJYWpGwrgK4Bhchnh5YOrQ5mt_1Z3w-zSE-j9l0F_NacnbO9gNp5R-vw-KhhdCBdGHkH63W0zJ_SPOMGjPpmqMzWl17OgkRiGyL6syioISAXlk_4MHuAoBPIEYsEDXffrZDD1NYleWB5Zr2Q==)
29. [iain.so](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFHD-q-wPtaPrj776RJeX2PePOlZ79DRc8bHD3V1ih5wZ2RaOfPdF_12moLByom0Iim5KYkefagyJQHzGoIy1tQHGuFBnQyau6OT6SreDqAXMr7JNQ7KQ3_14f2zoIbtQ==)
30. [infoq.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEyk0JKwxHrjYlR96LD2lNsrX1ot33NbAF05SNfPco9OuMzf4m7fdoftDyCZgwbaaX466uU6pbibrcDwVDcHOMFscyrPsDCVy5zJRjZSeXd-wUVyIvXDzqPE01DtQY4h2MndCen2uRIxMBOyXbAAjVnE7Na)
31. [openai.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQECLeoIqLlWiDsbiV2w0K-8nIJsdkTNRF1Qc_7w_E6U6ytlkcG5MN68HELb7nbIdWPYCWsr2YMCaCUhejmoV7sp18ivUdEOPQi-_DZ2r6zdyaWrZfprDTynE1lXJn5fpylGbCoxu04ChseMkiJFbX8=)
32. [arxiv.org](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHHBm7eK4xnEvbAOIxZ_CScn_hZbVzEh7F7NO37tGRCse3lebHJXlyPl9PXXOEJjHHRfsurbp--fXbwGY7aIk073oWwh_fSKz-IpOt8AO17jplnmaypzymyiw==)
33. [ox.ac.uk](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQF1Kr0HCBxfXmvtmDqZfPNwu1MSYk_Q1DcEiIEQ5cJwoUXwN7GSsKHeYg4fyOgw0rUDoHWK1mUTc5uF6iQ6KcrpAXLvR0oUCkA8_PWnKpX_25ikCwAe6BBhLUt-TIy6ksxFQ3lxCAPK7ALs8bZMtpX9q1rQVYuYRzrAKiQquN9GHALg)
34. [towardsdatascience.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGrxuWBBpXZcII8HMzusJq3l66a5f0Mgvn3xZSLo1YrjgFeA1u-DZw5SOc9crQOmh_p-dk_sWfkg4ezrxQ8Y3Pb0mVErUP_oiERRWcJDiGoMmpaduWt22mKEBNC6_83kIvZHMlDuUXc30W5OeleMweC7JPeug3lsQsjF8ind2KCPDNCkxFHlAPJ6DR7MVItqSB-PlUH4d9ynqdi3qkb7E26jPhwzvXsND79k7qcPX4=)
35. [medium.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEg8qo-H7QqwktyquxHtmNFZd3GF1Cp3wV6HsRYojOQmlOnmZQg-NnkSGz7xYroGO4I4o_9kW65es9u2127TfeuqA45u09xhnHYwZUNd32-gPxeCwU6jqwgYP2oRj6TD9Iie9-rRwBdmPcFfQD5uj1Cj2fkFhdqyPWfhGyvYhDz-CRljGNO7Imp1SpN0OZzPXPFun0JlM36PJ1mSesKTMrP5PtTBibSGa-2IbVxN1Qm_k7jcSHvQbEOTjjFriKegc3vBCpF)
36. [aaai.org](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHkbYvLTi2RdKIOf9Szs7YPMwLfvmDJ8iXUT5FYpsqMS2DAmLKztauiLpajEMyK_Xb33Bk_3-Mp7vDFy6vsOXBXS9yjPkSXFSZ-AlF6QFrL3FiBmh1xRWvBIyOHTQ-9bEhfxNz44Z7gmVGJBPrxrZwdMbk=)
37. [wpseoai.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFhXcQuIrH2tG0B14s7Ul2-dMULQyn5UyfUz5wUGcwXNsDCjT61fIwNoVbJK6WC7YjCjjzJOXkp89War-p4gjb4tL6ydpCtj1ns1NPjOswFpSpB43PVNy_80D6Ks8Wg_dwt-5oj6LVUuBYA6PtHuaS6pcsO2Q==)
38. [machinelearningmastery.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQF7YCG53s2XM_ogWbeStgVCYPD7nj9-jaDWM-xrydWxLC6ZQOkYXs2LW3CXMwlVRl5ECLB3tKtCa1mE1RcN2_ixS_YuCeGbX2Qazq_7fy-WjPStVxVMA_g7NasZcfKT9WYgmgR9Bb2kE2s5itDulVjiF3iCd5YNWuhBq7RhElA4Jyg1M0EeW_RLDMkPny9hyjcBEByhE2IxbU-XHCl_FNGFS5QrIHmUGG4daLk72crn3meKmzo=)
39. [medium.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFLf-dBo9vyCOoWp6zqJZNJ_oGvVM5P5tNZoznpT4QXf_V84okmy6aMQVwtifMUMAXVexWlBPBB_iBOc8XBt1y8QNRUGsY5asNvSYNJMYyXgMjd19WDRHqYYD8sMgJCrK4jzef-XEivWuAfPsmZ-jpsjwujH0tSOsWeklwlB1nbgdN4gE0dlTbexwasJEDQej52vcoR9g==)
40. [diva-portal.org](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQH5HdyiCVgl9-Osmx9V318ooXDP6seOCFjOWU7jY4INwRxoS7LoccLFIYNgtWYMP-o0mBlb0fFXZt0F1mwPgWyccdzJLWs9-j5H07CoBF1td24QxH3XpkSZ0R14xhy8J8YyIXIjeDHtykeZ-GwZBGnUtRd48fnB2B4=)
41. [geekytech.co.uk](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQEUR-giIzhMqcYwd5LaAlnqCFfHKkHYpklCsAhV5QhiYBb54meFyP-my5d-lMv5AjPeHW-XEIG4YT01ttoYZedrLornQz7ghCbJDKrO09W8NBvHccw7AxeFaPXNHVMuB1qWLOH0Gikip6h4-LRNBzEI3os=)
42. [hawksem.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHojD56TrQFe07L301Uha7Tq8c8pOjuiHsYSPeAK4gKc--O-mSqzbx341O5oI4KdQfSyv-Q-6M1b0kaDmQI6xPgpA1R2HYLeku4PsqCF0srRi1a4fwiCaWpPeZo7l1t4ZcrzntfG5JXv3moforqy6-GxYM=)
43. [mention.network](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFPSHQEDusP75VOe-bXB8A_OY4tszsPMCodawABZxk_H--zeGtGwtthfjbeAjEpLFiVhyh5sW3BLk3Ef-ZPd_FURjY6llffJS7-RETE_OSWShBW6Y5o-y2GB_sPcjxgV8pcN6qHiGAJ8SpYHpNLnTDT0yOK9JxbKg115wLFYQHKyf9ZfwVfEAdWS8Q_gjKK65RN_8BeAQCykppD)
44. [arxiv.org](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFNMx8GU2nCTrRb6eFsjMZGgsHOc4h5lMuIO5X9kGXSQh08GkJ4_v5PBrABDd3PSCF-T65JL4YqyrZBbTZvpy7fxjlItC8f4KR00eWK7cXzd7_v_L8d3w==)
45. [bruceclay.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQH9cWYtvqH1ziew2HYOM8FQ-KEmHivKZLwMrmSjVN58GtRlqiO-ztgXPd2dqAToad-sOcT-hU8gvuqLOkB3dp5OYf1nbBa6wVAzNlWRaMUX7IfPS-l9bM0s3zBEH9FYZQOG4X3gzlptA8oQCCJNwwveVvhoIlSVrNXZ0v2JX5ExkwfLsOdckKLnaPUe6kYENA==)
46. [arxiv.org](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQFOS_bWQZHiZMWDlz27MU0vbt9LDXZ7AVW-FqLic6VZJw1I3dHDrDTskVTzUL9slb29HDlsoEXdQj_8W7F2IOPozaqrYQpaJpWUrB9LcqlvSqRMKJZ6Tw==)
47. [towardsai.net](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGm7oA1SnecHUrsOjJzEpy3YxXcj4r81olFMFEUn4xeNviZEBJkZRHqv03kVhK2PmMfvOLi9JaTZmU5gX7SMqWNufzS7VWr4B_-Uo1SDJ8feoBj9FmbWduAACKTw4u_4Oxo53_7wFyfF5aRXioLg-zppU7_o0Bocv4BZGLX-0y1Q_dt6PWvKO9_tY2DPfPCx5tPa98HnVthnUYJqvazK6nEgzU=)
48. [medium.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQHXr75CQoSvNPAUd44RUKF-EUAWrs4lvYucCMo3c8GON5djMBJrWYd7GgO4Nd9smvdq7c-EFawiF5hKrr39em7g-stLFr0URezvQO3axNGmCjHEp56uyIvw-skww8cnAgM2nHiPUkfm2zGwLzHQau8rViJwyqc_XOqHAD_Mb44fIE6_H7OEnDN-fEX5SYE4vgebYr1MYr5kG83w-FV408hgd4K7UG1lC0v5_7LhTGpLd4I6WwLlsm3juspirNMSrIigbSMnIaU=)
49. [microsoft.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGKGJaBJKk4v56QW_cDKYOug2djP3ljpb734HDKGCCeHCAA5kMD2AiU2aa6BgNfSyRKRselAdKNX1T9aTkVnZplWBpa1GwuvDYSXWnp6M6U0u8--XzLZIWmkh2vWljAyrmESb01arcMpzss4rcU8_3SbHUjznm6dTIxxHesyOmZ77qs887PzP8bfwPojkb8l2DW3CoydTMEFcuPpZvvuupaDT-dnYBfSPnWvXIWvfX2njEQ58cIsKWrjshPWwC-aw1BZDqB09kdyQ==)
50. [substack.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQGmbXkdZeOPJDU9MwW_JXaKs2oR4i4NCWSS77m_Q1hYaNgxGx3LQT6mN3Us9VVCtsMz1VNjmikJ2sDV5CSiMv_DtJ3jSW4-azVjYPgWLL0c9vCnjrO9YpRlO-evP4163yL71sfwAvqA70eGJJAG1GmGm4-gLYHECKGV)
51. [quora.com](https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQE6C85T7U9gA24EtyBZH0HB6-MtjDIqGefPGfZYT9UCK07HXlS3yAIXKnfOAZ4yJdOg7Y_Iu5F2cTz4I_kly0yh0P1vzTMTjZ3w59s3IBYTwCA8LVpqyx0sFdbhyqWapWbfTVd7gj3HT19ri8A6ZFy4ww==)