Cognitive Map
Biology and technology share a common thread of efficient navigation for decision-making. Complex animals like humans or rats navigate for survival, while in AI, models use navigation to uncover patterns, make predictions, and optimize performance. This makes the concept of cognitive mapping or spatial representation mapping important for both domains and plays a vital role in enhancing decision-making for AI models.
Cognitive maps are mental representations (models) of physical environments that help animals (mostly mammals) remember and navigate effectively through different spaces.
In 1948, Tolman experimented with rats. He noticed that the rats could efficiently create mental maps of a maze for navigation, with or without immediate rewards. He introduced the concept of cognitive mapping as a result of this experiment. This idea has applications in psychology and diverse domains, such as machine learning (ML).
In a way, biology and technology share a common thread of efficient navigation for decision-making. Complex animals like humans or rats navigate for survival, finding resources, and avoiding threats, while in AI, models use navigation to uncover patterns, make predictions, and optimize performance. This makes the concept of cognitive mapping or spatial representation mapping important for both domains and plays a vital role in enhancing decision-making for AI models.
Understanding Cognitive Map
In humans, the hippocampus is important to the brain's ability to make maps that help us navigate spaces. This process is made possible by coordinating various cells to map the world around us accurately. Here’s a basic idea of how each cell functions in this process:
Place cells activate when a human is in an environment and create a neural representation of that location.
Grid cells activate in a grid-like pattern as humans move through an environment, creating a neural coordinate system.
Head direction cells activate when the head of an animal is oriented in any direction. This provides a sense of direction within a space.
Border cells activate when an animal is close to a border boundary or edge in its environment. This helps the animal define boundaries within its environment.
Together, they form a neural representation of an animal’s surroundings, including location, orientation, boundaries, and sensory information. With the help of other connected brain regions, these mappings can predict events as the animal moves through space.
This can be compared to the layers of a neural network, which can be thought of as the cells in the hippocampus. They both detect different aspects of their environment, especially in high-dimensional data like an image.
To explore the hidden data space, the model's layers identify various elements in the image, for example—edges, textures, shapes, and colors. This helps create a complete understanding of its environment. When similar images are encountered, the model can navigate more effectively based on this previously mapped environment.
This can be exemplified in reinforcement learning:
States: In reinforcement learning (RL), states are like locations where an animal is positioned. The agent learns the value of each state to navigate effectively.
Neural Successor Representation (SR): Adopted from successor representation in neuroscience, provides a map of expected future states based on its current strategy (policy). Imagine a robot estimating the likelihood of moving from its current spot to various future spots as it moves around.
Temporal difference learning: This assists the RL model in updating the successor map as changes occur in the environment over time.
These representations aid in predicting future situations, planning decisions, and providing predictive models for future outcomes.
Fig. 1 The diagram illustrates place fields, place cells, and their activity patterns in a maze.
Integrating cognitive mapping techniques can improve AI capabilities, especially in multimodal representations. This allows AI algorithms to establish improved cross-modal relationships with evidence of multimodal connections for improved model environment representations.
This can lead to improved navigation for autonomous vehicles and facilitate multimodal AI that can process various modalities simultaneously for more human-like interactions.
Mapping Speech, Objects, and Natural Language In Vector Space
High-dimensional data like speech, text, or gene expression (thousands to billions of dimensions) are complex to navigate compared to time series or temperature data (between 1 and 4 dimensions). Handling this high-dimensional data can be challenging, as the model needs to reduce the dimensionalities to understand the relationships within.
To do this, they use dimension reduction techniques like Principal Component Analysis (PCA), t-Distributed Stochastic Neighbor Embedding (t-SNE), or autoencoders, among others, to represent the data in lower dimensions with all its relationships or information represented in vectors.
The model then uses various metrics or methods to find relationships within the data. It finds the similarity or distance between each data observation to map its environment accurately. You can classify the methods for this process as:
Distance Metrics: Measures the distance between two data points. Examples include Euclidean or Manhattan distance, among other distance measures.
Similarity Metrics: Measures how similar two data points are. Examples include Cosine and Jaccard similarity measures, among others.
Euclidean Distance
Euclidean distance calculates the sum of squared differences between matching elements of two vectors. It is a distance measure, with smaller values indicating closer locations and 0 indicating equal points. However, it is sensitive to outliers and variable scaling. Below is a formula that represents this concept:
Where p and q equal two points in Euclidean n-space, qi, and pi equal euclidean vectors, starting from the origin of the space (initial point). n equals n-space.
For example, using Euclidean distance in clustering algorithms like k-nearest neighbors (KNN) to compare movie reviews. Each review is represented as a point in a high-dimensional space, where dimensions represent word frequencies.
The Euclidean distance between these review points quantifies their dissimilarity. Smaller distances imply similar word usage, hinting at comparable sentiments. This method is widely used in tasks like document clustering and grouping reviews with similar content based on their Euclidean distance in the vector space representation.
Manhattan Distance
The Manhattan distance is calculated as the sum of the absolute differences between the corresponding components of two vectors. It is resistant to extreme values and unaffected by scaling changes, but only considers size disparities and ignores directionality.
In an n-dimensional space (where each point has n coordinates), the Manhattan distance between two points, x and y, is calculated as follows:
For example, in image processing, Manhattan distance measures how pixel values differ in two images. When algorithms calculate this distance for corresponding pixels, they find dissimilar regions, hinting at objects, defects, or features of interest.
A small distance suggests similar pixel values or regions, while a more significant distance or magnitude signals dissimilarity between pixel values. This metric offers a simple and efficient way to compare images, revealing similar and dissimilar regions in high-dimensional pixel spaces.
Cosine Similarity
Cosine similarity measures how similar two vectors are by considering their angles. It tells us if two vectors point in the same direction, regardless of their lengths. This metric looks at the orientation of vectors and gives a measure of similarity based on that, without caring about how long the vectors are.
For example, two documents are represented as vectors in a multi-dimensional space. Each document's vector points in a direction based on its content. Using Cosine similarity, you get a score that tells you how similar or different the documents are. This score guides decisions like finding information, organizing documents, and recommending content.
The equation to determine the angle of vectors is as follows:
Where A and B are vectors.
Jaccard similarity
The Jaccard similarity, often known as the Jaccard Index, is widely used to assess the similarity between two sets. It is especially beneficial when working with collections of different magnitudes.
Where:
J = Jaccard distance
A = set 1
B = set 2
For example, to understand customer preferences for online shopping, you can apply the Jaccard similarity to assess the similarity between two customers' purchase histories. Each customer's purchase history can be represented as a set of products.
By measuring the intersection of purchased products divided by the union of products in the two sets, we can gauge how similar their shopping preferences are. This approach helps with tasks like recommending products to a customer based on the purchasing patterns of others with similar tastes.
Using distance and similarity metrics to map latent spaces enables AI to build effective internal representations of complex data. Incorporating attention and transfer learning improves these cognitive maps, allowing focus on critical elements and rapid adaptation to new scenarios. These techniques make the AI representations flexible, context-aware, and powerful for multimodal tasks.
Benefits of Cognitive Maps in AI
Cognitive maps generally boost AI's understanding of the environment, broadening its navigation, language comprehension, decision-making, and adaptability capabilities. This progress propels the capabilities of AI systems.
The advantages of cognitive maps in artificial intelligence systems include:
Enhanced spatial awareness: Representation mapping helps AI systems develop a spatial understanding of the world. Alternatively, AI systems can create internal models of their environment, including the layout of physical spaces and the relationships between objects or landmarks.
Enhanced representation and language capabilities: It enhances language understanding, integrates multimodal information into semantic representations, and enables nuanced conversational AI with rich contextual comprehension.
Efficient adaptation and generalization: With transfer learning, AI can leverage knowledge from different domains to rapidly adapt and generalize better in different scenarios. Agent-based AI systems, on the other hand, can learn, plan, and react to changing situations.
Current Challenges in Cognitive Mapping
Cognitive mapping is a powerful way to represent knowledge, but it comes with some inherent complexities, especially in AI systems:
Adapting to change: As environments change, representations must adapt to be relevant to these changing surroundings. It can be difficult for AI. This challenge is about creating ways for cognitive maps to adjust to new information quickly, ensuring they stay accurate and effective in navigating real-world situations.
AI integration challenge: Integrating cognitive maps into AI systems is a challenge. It involves careful engineering to ensure smooth synergy between different components without disrupting the efficiency and effectiveness of the system.
Complexity in mapping data: Despite needing large datasets to form internal representation mapping, cross-modal interactions from these datasets are challenging. You might require multiple modalities, such as visual and speech data, making it complex to ensure effective learning across diverse modes.
Real-world Applications
Cognitive mapping significantly improves the capacity of AI systems to observe, understand, and engage with their environment, which has far-reaching consequences for many domains, such as autonomous navigation, NLU, and robotics. The effects of cognitive mapping on various domains are as follows:
Robotics: Representation mapping provides everyday robots like Atlas with spatial awareness to build internal maps, enabling enhanced navigation around obstacles and tasks.
Navigation systems for autonomous vehicles: Cognitive mapping enables autonomous vehicles to navigate complex environments. It helps create systems that understand the relationship between locations, landmarks, and other elements within an environment for safe and efficient movement.
Natural language understanding: It enhances natural language understanding by improving comprehension of spatial terminology and contextual clues used in conversations. It allows a better understanding of words related to environments, spatial connections, and navigation. This is especially helpful for chatbots and virtual assistants when users ask about directions, locations, or spatial relationships.
Conclusion
Cognitive mapping is a crucial ability for both animals and artificial systems. In animals, it involves brain regions like the hippocampus creating mental maps of space, helping them navigate and remember essential places. Artificial intelligence (AI) uses similar principles, with neural networks learning from complex data to build internal representations. Techniques like successor representations act as maps for expected future states, aiding in planning and prediction.
Modern AI incorporates biologically inspired features like spatial memory and attention. Cognitive maps in AI are flexible internal representations that enable understanding, contextualizing inputs, making inferences, and taking purposeful actions—signs of intelligent behavior. As cognitive mapping advances in biology and AI, we can anticipate more efficient, flexible, and human-like spatial reasoning and intelligence.