Alternative for Transformers: State Space Modeling in Artificial Intelligence
Imagine a self-driving car 🚗 where we can’t directly “see” all the factors responsible for its movement, but we can observe its position and speed. The state of the car at any given instant of time is a summary of all the hidden variables that were essential to predict its future. This includes not just its position and velocity but also other things such as engine temperature, tire pressure, and fuel available in the tank. The SSM uses this “hidden” state to predict the car’s next position and observable outputs, like its position relative to its current one. These types of tasks are performed by SSM with high accuracy, as SSM is a powerful neural network framework that works over sequential data points, maintaining a compact, fixed-size internal representation called a “hidden state.” This state acts as a summary of all the information from the past sequence that has been processed so far. This post is about exploring the SSMs in a brief manner, which includes understanding their definition, mathematical working, sample Python implementation, applications, limitations, and advantages.
What is State-Space Model (SSM) ?
State-space modeling in AI is a framework that gives all possible states or configurations of problem solving by AI and actions that give understanding about transitions between all these states. State space modeling acts as a fundamental concept in AI similar to searching algorithms.
Components of SSM :-
State: It defines the initial state of the system, basically the state at the starting moment. It includes all the required information for the system in order to predict the future behavior of the system.
Operators: A set of actions performed over a system to transition between different states of the system.
Goal: A set of conditions that, when met, gives a solution to the problem.
Mathematical concept example
SSM describes the dynamics and observable hidden states of any AI system using state and output equations, mentioned in the below figures.
Where the state equation is a first-order differential equation for continuous-time systems or a difference equation for discrete-time systems and gives “how the system’s internal state changes over time.”
And the output equation gives the hidden state of the system from what we can actually observe from the system.
Example use case of SSM in AI application
Simple state-space models in AI are used in automated planning for robotics tasks.
- State: A state will be the robot’s complete configuration initially. This includes its posture, the angle of its joints, the initial values of its sensors, and the state of the world around it, such as the objects around it with which the robot needs to interact.
- Operators: It represents the set of operators needed to do things, such as movements of ARMs of the robot into position X, Y, Z, or “grasp object,” or “navigate to room A.” These all are physical constraints of the robot and the surrounding environment.
- Goal State: The goal state is a defined as a desired outcome.
This scenario of SSM is implemented in a large and continuously changing environment, not discrete like a puzzle. The challenge for robotslies in finding an efficient path in complex real-world environments.
Although in modern architectures of AI that use SSM, such as “Mamba,” the matrices A, B, C, and D defined in state & output equations are not physical constants. These are trainable parameters, those learned through an AI training process.
Sample Python implmentation of SSM
Let’s explore the Python implementation of SSM that models the sequences of words that can be used in document-level sentiment analysis systems.
import torch
import torch.nn as nnclass SimpleSentimentSSM(nn.Module):
def __init__(self, vocab_size, embedding_dim, state_dim):
super().__init__()
self.state_dim = state_dim
# Embedding layer to convert words to vectors
self.embedding = nn.Embedding(vocab_size, embedding_dim)
# Learnable matrices
self.A = nn.Linear(state_dim, state_dim) # State transition
self.B = nn.Linear(embedding_dim, state_dim) # Input-to-state
self.C = nn.Linear(state_dim, 1) # State-to-output (sentiment score)
def forward(self, x):
# x is a tensor of word indices (batch_size, sequence_length)
# Get word embeddings
embeddings = self.embedding(x)
batch_size, seq_len, _ = embeddings.shape
# Initialize hidden state
h = torch.zeros(batch_size, self.state_dim, device=x.device)
# Recurrent loop
for i in range(seq_len):
u_t = embeddings[:, i, :] # Current word embedding
# State Update (h_t+1 = A*h_t + B*u_t)
h = F.relu(self.A(h) + self.B(u_t))
# Final output (y_T = C*h_T)
final_sentiment_score = torch.sigmoid(self.C(h))
return final_sentiment_score# — — Sample Input and Output — -
# Configuration
vocab_size = 1000
embedding_dim = 16
state_dim = 32# Model initialization
model = SimpleSentimentSSM(vocab_size, embedding_dim, state_dim)# Sample input sentence represented by word indices
# Let’s say: “This movie was great!” -> [5, 10, 20, 50]
input_sentence = torch.tensor([[5, 10, 20, 50]])# Forward pass
output_sentiment = model(input_sentence)# Print results
print(f”Sample Input (word indices): {input_sentence}”)
print(f”Sample Output (sentiment score): {output_sentiment.item():.4f}”)# Example interpretation: a score close to 1 indicates positive sentiment, 0 for negative.
if output_sentiment.item() > 0.5:
print(“Interpretation: The model predicts a positive sentiment. 👍”)
else:
print(“Interpretation: The model predicts a negative sentiment. 👎”)
Sample Input: Sentence having sequences of words.
Sample Output: The sentiment mentioned is represented by a sequence of words.
Applications
- NLP application models such as Mamba handle long and complex document processing.
-Analysis of genomics data analysis as genomics data is represented by a long and complex sequential format.
-Audio data modeling where audio samples are complex audio waveforms.
-Multi-dimensional vision video data analysis, as it contains sequential and complex video frames, captures various digital image data points.
Advantages
-Linear Scaling
-Stateful Computation
-Combining Strengths
Limitations
-Limited Expressiveness for State Tracking
-Must have hybrid architectures format
-Shorter community of developers
Conclusions
SSMs are improving the working of AI systems over long sequential datasets that encourage new algorithms that might overtake the Transformers that are currently used for processing long sequential data points. Recent models such as Mamba use the power of SSMs in their architecture. I hope this post gives brief details about SSMs’ working and applications of this framework in artificial intelligence.