Neural Language Models

For a machine to truly understand natural language, it must be able to judge how likely a given sentence is to occur in real life. But what makes a sentence likely? This question splits language modeling into two main groups: syntax-driven (grammar-based) models and statistics-driven (common sense-based) models.

Syntax vs. Common Sense: The Chomsky Contradiction

Consider these two famous examples:

1. "Colorless green ideas sleep furiously." (Noam Chomsky)
2. "Jane and me went to see a movie yesterday."

The first sentence is grammatically flawless. It follows English structures perfectly. However, it doesn't make sense - ideas can't be green or colorless, and they can't sleep furiously. The second sentence has a grammatical error - it uses "me" instead of "I". But its meaning is clear, and it sounds like the way people talk in casual conversation.

Model-Based (Syntactic) Approach

A strict linguistic approach assumes that an observed sentence $S$ is generated by an underlying, hidden grammatical structure $G$. To determine the probability of a sentence $p(S)$, we would mathematically have to consider all possible hidden grammatical structures: $$p(S) = \sum_{G} p(S|G)p(G)$$

In practice, this approach is not feasible. Human language has infinite structural variations, and it is extremely difficult to resolve the ambiguity of which grammar rule applies.

Model-Free (Statistical) Approach

Instead of mapping sentences to abstract rules, modern deep learning views language as a means of communicating ideas. The probability of a sentence is determined by how well it aligns with human common sense, which is captured by the statistical patterns of language use. For example, if thousands of people write "Jane and me went to a movie," then it is likely to be a probable sentence.

Atomic Unit of Language

Modern AI, we call this tokenization.

Before a neural network can process a sentence, we must decide on the minimal linguistic unit (token) to feed into the graph.

[Characters]  --->  [??? Subwords ???]  --->  [Words / Spaces]
(Too low-level;       (The Middle Ground:      (Exploding vocabulary;
 No inherent meaning)  e.g., BPE, WordPiece)    Fails on spacing rules)

Finding the right balance involves a trade-off between semantic meaning and vocabulary size:

• Characters: Using individual letters limits our vocabulary to a small set of characters, such as the 26 letters in English. But these letters do not have any meaning on their own. Written language is also not linear. For example, the words "quit", "quite", and "quiet" have similar combinations of characters, but their meanings are very different. This makes it hard for a network to learn the relationships between characters and meanings, as it needs to understand these sudden changes in meaning from the raw characters.
• Words: Splitting text by blank spaces can capture meaning quickly, but it does not work well in practice. This is because punctuation is attached to words. For example, "llama", "llama," and "llama!" would be considered separate vocabulary words. This causes the number of parameters to increase rapidly. Many languages, such as Chinese, do not use blank spaces to separate words at all.
• Subword: Modern systems look for a middle ground using data-driven subword tokenization algorithms (like Byte-Pair Encoding or WordPiece) to split text into meaningful word pieces (e.g., ["trans", "form", "er"]).

Objective of Language Modelling

By moving to a model-free, statistical framework, our goal is now purely mathematical. We have a sequence of tokens $X = (x_1, x_2, \dots, x_l)$, and we want to estimate the joint probability of the entire sequence. The chain rule of probability helps us break this down into a product of conditional probabilities: $$p(X) = \prod_{t=1}^{l} p(x_t \mid x_1, x_2, \dots, x_{t-1})$$

This approach turns language modeling into a task of predicting the next word in a sequence. Given all the words up to a certain point, the goal is to determine the probability of each possible next word. If a network can learn to do this, it can produce text, translate languages, and assess how coherent a piece of writing is.

Statistical Language Modelling

Any sentence $S$ can be expressed as a sequence of $T$ discrete tokens: $$S = (w_1, w_2, \dots, w_T)$$

Each token $w_t$ is picked from a fixed vocabulary $V = \{v_1, v_2, \dots, v_{|V|}\}$. The core objective of a language model is to determine the joint probability $p(S) = p(w_1, w_2, \dots, w_T)$.

A naive approach will be mapping sentence to measure. Given a training text corpus $D$ containing $N$ total sentences, the most intuitive way to estimate $p(S)$ is by using the Maximum Likelihood Estimate (MLE). We simply count how many times the exact sentence $S$ appears in our data and divide it by the total number of sentences: $$p(S) = \frac{\sum_{n=1}^N \mathbb{I}(S = S_n)}{N}$$

Mathematically it's straightforward, the major flaw with sentence-level counting is that human language has a nearly infinite state space. Let's look at the raw math.

If our vocabulary $V$ contains $100,000$ unique words, and we look at sentences up to a standard length of $T = 50$ words, the total number of possible sentences is a massive geometric series: $$\text{Total Possible Sentences} = \sum_{t=1}^{50} |V|^t = |V|^1 + |V|^2 + \dots + |V|^{50}$$

This calculation results in an extremely large number ($100,000^{50}$), far exceeding the total number of atoms in the observable universe.

Most of these combinations are nonsense, but the number of human sentences that are grammatically correct and make sense is still enormous. No collection of texts, no matter how large, can include every possible valid sentence, even if it gathers billions of pages from the internet.

"I Like Llama" Paradox

A corpus can only hold a small part of the language space. If a sentence does not appear word-for-word in the training data, the indicator function $\mathbb{I}(S = S_n)$ evaluates to $0$.

For example, if you search for the phrase "I like llama" in the Google Books Ngram Viewer, which indexes millions of scanned books from centuries of human writing, the system may return an error saying the phrase cannot be found.

Using our naive formula, a machine would look at that result and declare: $$p(\text{"I like llama"}) = 0$$

This is a massive error. The sentence is perfectly legible, logical, and likely to be spoken by a human, yet our model treats it with the same mathematical impossibility as a string of random characters.

To build a truly reliable language model, we must stop counting sentences exactly. We need a method that breaks sentences into smaller parts, so the model can work with phrases it has never seen before.

n-Gram Language Model

Sentence counting revealed a major mathematical problem: Data Sparsity. The total number of possible sentences grows exponentially with sentence length, so no training text corpus can contain every valid sentence. The key idea behind the $n$-gram language model is to address this issue by limiting the amount of information considered. We don't try to calculate the probability of an entire sentence at once. Instead, we use the chain rule of probability and make a Markov assumption, breaking the sentence down into smaller parts.

The Markov Assumption and the Context Trade-Off

Using the chain rule of probability, the exact joint probability of a sentence $S = (w_1, w_2, \dots, w_T)$ is written as: $$p(S) = \prod_{t=1}^{T} p(w_t \mid w_1, w_2, \dots, w_{t-1})$$

An $n$-gram model simplifies this by assuming that the probability of the next word $w_t$ depends only on the preceding $n-1$ words, completely ignoring any history before that: $$p(w_t \mid w_1, w_2, \dots, w_{t-1}) \approx p(w_t \mid w_{t-n+1}, \dots, w_{t-1})$$

This approximation creates a trade-off in the architecture:

• High $n$ (Longer Context): This captures long-range dependencies. For example, in the sentence "In Korea, more than half of all the residents speak Korean," predicting the last word requires a context window of at least $n=10$ to look back at the word "Korea". As $n$ grows, data sparsity becomes a problem because unique $10$-word phrases are rare in a corpus.
• Low $n$ (Shorter Context): This prevents data sparsity because short phrases, like bigrams or trigrams, appear often in text. The drawback is that the model becomes limited in its ability to track ideas across a long sentence.

Calculating $n$-Gram Probabilities via Maximum Likelihood Estimation (MLE)

To train an $n$-gram model, we calculate its parameters directly from our corpus by counting string frequencies. By applying the definition of conditional probability ($p(A \mid B) = \frac{p(A, B)}{p(B)}$), we get: $$p(w_t \mid w_{t-n+1}, \dots, w_{t-1}) = \frac{c(w_{t-n+1}, \dots, w_{t-1}, w_t)}{\sum_{w' \in V} c(w_{t-n+1}, \dots, w_{t-1}, w')}$$

Where $c(\cdot)$ represents the raw count of how many times that specific word sequence appears in our training text, and $V$ is our vocabulary.

Zero-Probability Problem and Smoothing Techniques

If a sentence contains even one $n$-gram that doesn't appear in our training data, its conditional probability is zero. Since the sentence probability is the product of these individual terms, the entire sentence is given a probability of zero. To solve this problem, we use smoothing techniques to allocate a small portion of our total probability to sequences we haven't seen.

The most naive fix is to pretend every possible $n$-gram has been seen at least $\alpha$ times (where $0 < \alpha \le 1$): $$p_{\text{add}-\alpha} = \frac{\alpha + c(w_{t-n+1}, \dots, w_t)}{\alpha|V| + \sum_{w'} c(w_{t-n+1}, \dots, w')}$$

The Structural Flaw: This treats all unseen words completely equally. It asserts that an completely implausible phrase has the exact same probability of appearing as a highly logical, grammatically correct phrase that simply missed the training set.

Instead of uniform padding, we can calculate a smoothed probability recursively by falling back to a simpler, lower-order $(n-1)$-gram model if our higher-order $n$-gram count is zero: $$p_S(w_t \mid w_{t-n+1}, \dots, w_{t-1}) = \lambda p(w_t \mid w_{t-n+1}, \dots, w_{t-1}) + (1 - \lambda) p_S(w_t \mid w_{t-n+2}, \dots, w_{t-1})$$

Where the hyperparameter $\lambda \in [0, 1]$ controls the blending weight and must be tuned on a validation set to avoid over-fitting.

The industry-standard classical smoothing technique is Modified Kneser-Ney. This method doesn't just look at raw frequencies. It uses an optimized discounting factor, which subtracts a fixed value from non-zero counts. The technique also considers how often a word is used in different contexts. For example, a word with a high count may still have its continuation probability reduced if it mostly appears in a single phrase, such as "San Francisco", and rarely in other situations.

Failure of $n$-Grams

Despite advanced smoothing algorithms like Kneser-Ney, $n$-gram models suffer from a fundamental flaw: they have absolutely no capacity for semantic generalization. Consider a training corpus that contains the phrases:

• "chases a cat"
• "chases a dog"
• "chases a rabbit"

As human beings, we instantly spot the underlying semantic rule: the phrase "chases a" is highly likely to be followed by a noun belonging to the conceptual class [animal].

If we test our $n$-gram model on an unseen phrase like "chases a llama", it treats the words "cat", "dog", "rabbit", and "llama" as completely orthogonal, independent discrete units. It cannot see that a llama shares semantic properties with a dog or a cat. Unless the exact sequence "chases a llama" was explicitly printed in the training text, its raw maximum likelihood estimate is a definitive zero.

To overcome this generalization wall without resorting to brittle, manually-built dictionaries, language models require a paradigm shift: we must move away from matching discrete string tokens and find a way to represent words as continuous, mathematically dense vectors that capture semantic similarity.

Here is a refined, highly scannable version of your blog post. It keeps every single equation intact but wraps them in clear geometric intuition, visual formatting, and real-world analogies so your readers don't get lost in the math.

Neural Network Learning

Classical $n$-gram models have a basic problem: they consider each word as a separate symbol. For example, if an $n$-gram model sees the phrases "chases a cat" and "chases a dog", it cannot figure out that "chases a llama" is also a likely sequence. This is because it does not understand what a "llama" is.

Neural Language Models address this issue by representing words as points in a continuous vector space. When a network is trained on a collection of texts, it learns to place words with similar meanings close to each other in this space.

Softmax Function

In a neural language model, the probability of predicting a target word $w_t$ given a context vector $\mathbf{h}$ is calculated using the Softmax function: $$p(w_t = k \mid \mathbf{h}) = \frac{\exp(\mathbf{u}_k^\top \mathbf{h})}{\sum_{j \in V} \exp(\mathbf{u}_j^\top \mathbf{h})}$$

Where:

• $\mathbf{u}_k$ is the target vector for the $k$-th word in the vocabulary.
• $\mathbf{h}$ is the hidden context vector representing all the preceding words.

For the model to assign a high probability to a word, the dot product $\mathbf{u}_k^\top \mathbf{h}$ must be large. Geometrically, this requires the context vector $\mathbf{h}$ and the target word vector $\mathbf{u}_k$ to align and point in the same direction.

The Math of Word Similarity

Suppose we have two entirely different context windows, $\mathbf{h}_j$ and $\mathbf{h}_k$, that are consistently followed by the exact same target words. For the model to output identical conditional probabilities for a target word $w_l$ across both contexts ($p(w_l \mid \mathbf{h}_j) = p(w_l \mid \mathbf{h}_k)$), the equation must be: $$\mathbf{u}_l^\top (\mathbf{h}_j - \mathbf{h}_k) = 0$$

Assuming $\mathbf{u}_l$ is not a zero vector, the model achieves this by making the hidden context vectors $\mathbf{h}_j$ and $\mathbf{h}_k$ nearly identical ($\mathbf{h}_j \approx \mathbf{h}_k$).

Let's look at an example. Imagine a micro-corpus consisting of just three sentences:

1. There are three teams left for the qualification.
2. Four teams have passed the first round.
3. Four groups are playing in the field.

During training, the model must assign a high probability to "teams" when it encounters either "three" or "four". To optimize its parameters, the network projects the input representations for "three" and "four" to almost the same location in the embedding space ($\mathbf{h}_{\text{three}} \approx \mathbf{h}_{\text{four}}$).

Simultaneously, because "teams" and "groups" both follow the word "four", their target vectors ($\mathbf{u}_{\text{teams}}$ and $\mathbf{u}_{\text{groups}}$) are also pulled close together. Now, what happens if we test the model on a completely unseen bigram: "three groups"?

1. The model reads the context word "three".
2. It maps it to its context vector $\mathbf{h}_{\text{three}}$, which sits right next to $\mathbf{h}_{\text{four}}$.
3. Because $\mathbf{h}_{\text{three}} \approx \mathbf{h}_{\text{four}}$, and $\mathbf{h}_{\text{four}}$ already aligns perfectly with $\mathbf{u}_{\text{groups}}$, the dot product $\mathbf{u}_{\text{groups}}^\top \mathbf{h}_{\text{three}}$ is automatically high.

The model assigns a high probability to "three groups" even though it was never trained on this combination. This serves as a mathematical proof of the Distributional Hypothesis: words that appear in similar contexts have similar mathematical representations, and therefore similar meanings.

Continuous Bag-of-Words (CBOW)

Traditional language models look at the words that come before them when generating text from left to right. But if we want to learn more about the meaning of words, we don't need to only consider the words that come before. We can use a different approach, called a Markov Random Field Language Model (MRF-LM). In this model, each word is connected to the words around it - the words that come before and after it. Specifically, each word $w_i$ is linked to its $2n$ neighboring words, with $n$ words on either side.

Calculating the true joint probability $p(w_1, \dots, w_T)$ over an undirected Markov Random Field is computationally intractable. This is because it requires calculating a massive global normalization constant $Z$ that covers every possible text combination.

Instead, we can calculate the conditional probability of a single word given its immediate neighbors, known as its Markov blanket: $$p(w_i \mid w_{i-n}, \dots, w_{i-1}, w_{i+1}, \dots, w_{i+n}) = \frac{\exp\left(\mathbf{e}_{w_i}^\top \left[\sum_{k=1}^n \mathbf{e}_{w_{i-k}} + \sum_{k=1}^n \mathbf{e}_{w_{i+k}}\right]\right)}{\sum_{v \in V} \exp\left(\mathbf{e}_{v}^\top \left[\sum_{k=1}^n \mathbf{e}_{w_{i-k}} + \sum_{k=1}^n \mathbf{e}_{w_{i+k}}\right]\right)}$$

Instead of maximizing standard log-likelihood, we train the network by maximizing its Pseudo-Likelihood, which is simply the sum of these local conditionals: $$\log \text{PL} = \sum_{i=1}^T \log p(w_i \mid w_{i-n}, \dots, w_{i-1}, w_{i+1}, \dots, w_{i+n})$$

This formulation gives rise to the classic Continuous Bag-of-Words (CBOW) model. Rather than using a deep sequential network, it sums or averages the continuous vectors of surrounding context words to directly predict a missing center word.

Note: Flipping this architecture so that a single center word predicts the surrounding context words yields the Skip-gram model, which implicitly factorizes a semantic Pointwise Mutual Information (PPMI) matrix.

We can train models like CBOW or Skip-gram on billions of raw internet pages without manual data labeling. This allows us to learn a high-quality word embedding matrix, $E$, through unsupervised learning. Once trained, we can extract this matrix and use it as a basic set of features for other tasks.

Consider a sentiment analysis task where you are given a tiny dataset of only two training examples: "happy" is positive and "sad" is negative.

• If you use raw one-hot encodings, a classifier can never generalize. Any novel word other than these exact two will have an orthogonal vector, leaving the model blind.
• By replacing one-hot vectors with dense, pretrained word embeddings, we leverage a core principle of semi-supervised learning: data points lie on a lower-dimensional manifold where target attributes change smoothly.

Using a simple Cosine Similarity metric, our model can instantly classify novel words it has never seen in the training set: $$\text{Classify}(w) = \begin{cases} \text{Positive} & \text{if } \text{cos}(\mathbf{e}_w, \mathbf{e}_{\text{happy}}) > \text{cos}(\mathbf{e}_w, \mathbf{e}_{\text{sad}}) \\ \text{Negative} & \text{otherwise} \end{cases}$$

Problems with Pretrained Vectors

Pretrained word vectors are highly effective, but they have their limitations. The properties captured by a vector space are limited to those required to meet its original training objective.

In a typical CBOW or language modeling framework, words like "happy", "sad", and "angry" often appear in similar linguistic contexts. For example, they frequently follow the phrase "I feel...". As a result, the language model groups these words closely together in the vector space because they can be used interchangeably in sentences.

This can cause problems if you use these embeddings in a sentiment classifier without considering their limitations. The vectors for "happy", "sad", and "angry" are near each other, making it hard for the model to tell them apart. When you have limited data, the performance of your model is limited by the assumptions made during pretraining.

Recurrent Language Models

While neural language models have made significant progress with continuous vector embeddings, they still face a major limitation: the $n$-th order Markov property. This means that when predicting the next word, the model can only consider a fixed number of preceding words, usually the last $n-1$ words.

Human language does not fit neatly into fixed windows. For example, consider a mystery novel that says: "Born and raised in Paris, Henri loved the bustling cafes, the art museums, and the beautiful language of his childhood. Thirty years later, walking down a street in Tokyo, he bumped into an old friend and greeted him in flawlessly spoken..." To predict the final word (French), a model needs to recall a detail mentioned much earlier - the fact that Henri was born and raised in Paris. A model with a fixed window will miss this clue because the relevant context will have already been forgotten.

To overcome this limitation, a new approach is needed. This is where the Recurrent Neural Network Language Model (RNN-LM) comes in, which introduces a completely new architecture.

In a typical sequence-to-sequence setup, like Part-of-Speech tagging, an RNN reads an input sequence $X$ to predict a target sequence $Y$, such as mapping "Children" to "Noun". To turn this tagger into a Language Model, the target sequence is shifted by one time step, so the network always predicts the next word. By chaining these predictions, the RNN-LM models the probability of a sentence using its entire history, rather than just a small window. This process compresses a long sequence ($w_1, w_2, \dots, w_{t-1}$) into a single, dense memory vector $\mathbf{h}_{t-1}$.

The forward pass of an RNN-LM processes text one step at a time. At each step, the network performs three main operations. First, it updates its memory state. To do this, the network reads the embedding of the current word ($\mathbf{e}_{w_t}$) and combines it with its previous memory ($\mathbf{h}_{t-1}$) to create a new internal memory state ($\mathbf{h}_t$). This step takes all the information the network has seen from the start of the text and condenses it. $$\mathbf{h}_t = f(\mathbf{e}_{w_t}, \mathbf{h}_{t-1})$$

While the transition function $f$ can technically be a simple vanilla RNN cell, standard practice relies on a Gated Recurrent Unit (GRU) or a Long Short-Term Memory (LSTM) network to act as structural circuit breakers that prevent gradients from vanishing over long spans of text.

Second, to predict the next likely word, the freshly updated summary vector $\mathbf{h}_t$ undergoes the output distribution computation, where it is projected into the vast vocabulary space via an affine transformation and normalized using a Softmax function: $$\mathbf{\mu}_{t+1} = \text{softmax}(V\mathbf{h}_t + \mathbf{c})$$

Here, $V$ is the weight matrix that projects the hidden state to the vocabulary, $\mathbf{c}$ is the bias vector, and $\mathbf{\mu}_{t+1}$ is a vector of probabilities for every unique word in our vocabulary $V$. This vector represents the conditional distribution $p(w_{t+1} \mid w_{\le t})$.

The model uses boundary tokens to start the process. This creates a problem: how do we calculate the probability of the first word in a sentence ($p(w_1)$) when there's no prior memory vector? We solve this by introducing a special token, the beginning-of-sentence symbol ($\langle s \rangle$). At step zero, the network initializes its own memory using this token: $$\mathbf{h}_0 = f(\mathbf{e}_{\langle s \rangle}, \mathbf{h}_{\text{init}})$$

By initializing the network with a standard learned vector ($\mathbf{h}_{\text{init}}$) and feeding it this explicit start token, the recursive loop gracefully kicks off, allowing the network to process the rest of the sequence uniformly.

Comparing Language Models

We modelled three major architectural paradigm shifts:

• Count-based n-gram models: Rely on raw string frequency and localized context windows.
• Neural n-gram models: Map words to a continuous vector space to enable semantic generalization.
• Recurrent Language Models (RNN-LMs): Eliminate the fixed context window completely by maintaining a dynamic memory state across time.

To determine which model to deploy in practice, we need a universal way to score them: a metric known as Perplexity.

Perplexity

Mathematically, the perplexity ($\text{PPL}$) of a language model $M$ over a test corpus of $N$ tokens is defined as: $$\text{PPL} = b^{-\frac{1}{N} \sum_{n=1}^N \log_b p_M(w_n \mid w_{

The equation may look complicated, but its basic behavior is simple. Exponential and logarithm functions always increase, so the order of the models stays the same even if we remove the base $b$. If we do this, the exponent becomes the standard Negative Log-Likelihood ($\text{NLL}$) cost function that we minimize when training neural networks. $$\text{Normalized Exponent} = -\frac{1}{N} \sum_{n=1}^N \log p_M(w_n \mid w_{

This term ($\log p_M(w_n \mid w_{

The intuition is simple: perplexity measures uncertainty. If a model has a perplexity of $50$, it means that when predicting the next token, it is as uncertain as if it had to choose randomly among $50$ equally plausible words. A better language model is one with lower perplexity.

The Illusion of the Missing Feedback Loop

When comparing the block diagrams of standard sequence-to-sequence tasks and an RNN-LM, the explicit feedback connections, where a previous prediction is fed back into the hidden layers, seem to be missing. However, this is just a visual effect of how the sequence graphs are laid out. In an RNN-LM, the target output at time step $t$ is the same as the input token at time step $t+1$. The network uses its previous text outputs to update its internal state, allowing it to keep track of information over long periods of time.

Head-to-Head Comparison: n-Gram vs. Neural vs. RNN-LM

Evaluating these models directly is challenging because their performance depends on several factors, including the size of the training corpus, the target vocabulary, and the available computing resources. But when they are tested in real-world applications like Automatic Speech Recognition or Machine Translation, some clear patterns become apparent:

The Power of Model Scale

• The Recurrent Advantage: RNN-LMs (particularly those utilizing gated cells like LSTMs) consistently out-perform feedforward neural $n$-gram models. By maintaining an open-ended hidden trajectory, they effectively parse long-range dependencies that feedforward windows miss entirely.
• The Parameter Bonus: As you scale up the internal capacity of a neural language model (increasing embedding dimensions or hidden layer units), the model's perplexity drops significantly, translating to a direct reduction in downstream Word Error Rates ($\text{WER}$).

The Hybrid Paradox: Why We Mix Count-Based and Neural Models

The structural superiority of RNN-LMs might lead us to think that old count-based $n$-gram models are no longer useful. However, in many human language applications, the best results are achieved by combining the two approaches. This involves creating a hybrid model that blends the predictions of a count-based $n$-gram model with those of an RNN-LM. $$p_{\text{hybrid}}(w_n \mid \text{context}) = \alpha \cdot p_{\text{count-based}}(w_n \mid \text{context}) + (1-\alpha) \cdot p_{\text{RNN-LM}}(w_n \mid \text{context})$$

This phenomenon reveals that the two architectures capture complementary properties of natural language:

• What Neural Models Dominate: Abstract semantics, long-term contextual themes, and soft conceptual generalization (e.g., knowing that "llama", "cat", and "dog" behave similarly after the phrase "chases a").
• What Count-Based Models Dominate: Precise, low-level surface patterns. Count-based models excel at memorizing exact, rare name combinations, highly specific jargon, or rigid idiomatic expressions that might be smoothed over or washed out during the distributed gradient updates of a massive neural network.

By combining them, the hybrid system gains the expansive, generalization power of continuous vector spaces without losing the rock-solid memorization accuracy of raw frequency tables.

Moving Forward

With statistical language modeling foundations complete, we have optimized how machines read and evaluate text sequences. In our next module, we will explore how to reverse this information highway: taking these dense context summaries and forcing the network to dynamically generate entirely new sequences from scratch.