Kolosal - Blog

Autoregressive Decoding: The Sequential Prediction Paradigm

Autoregressive models generate text by predicting one token at a time, conditioned on all previously generated tokens. This process mirrors human language production, where each word depends on the preceding context. For a sequence of tokens {x₁, x₂, ..., xₙ}, the model computes the probability distribution P(xt | x<t) at each step t, selecting the next token xt through sampling or greedy selection.

The sequential nature of this process introduces computational challenges, as generating a sequence of length n requires O(n) forward passes. However, this approach enables fine-grained control over output quality through techniques like temperature scaling and top-k sampling.

At each decoding step, the model outputs a logits vector over the vocabulary, converted to probabilities via the softmax function:

P(xt | x<t) = softmax(W · ht + b)

where h_t is the hidden state at position t, and W, b are learnable parameters. Strategies like beam search maintain multiple candidate sequences to balance diversity and coherence, while nucleus sampling (top-p) dynamically adjusts the probability mass considered for selection.

During training, autoregressive models use teacher forcing—feeding the ground truth previous token instead of model predictions—to stabilize learning. This creates a discrepancy between training (parallel processing of full sequences) and inference (sequential generation), addressed through techniques like scheduled sampling. The shifted-sequence approach, where inputs are offset by one position relative to targets, enables efficient batch processing despite sequential dependencies.

Attention Mechanisms: Contextual Relationships at Scale

The transformer architecture's self-attention mechanism computes pairwise token affinities through query-key-value projections:


                    Attention(Q, K, V) = softmax(QK^T / sqrt(d_k))V

In autoregressive models, a causal mask zeroes out attention weights for future positions, enforcing the constraint that token x_t cannot attend to x_{>t}. This masking enables parallel training while maintaining sequential generation capabilities.

Multi-head attention splits the input into subspaces processed independently, allowing the model to capture diverse linguistic patterns (e.g., syntactic vs. semantic relationships). Positional encodings, either sinusoidal or learned, inject token order information critical for autoregressive modeling.

During inference, key and value vectors (K, V) from previous tokens are cached to avoid recomputation, reducing memory bandwidth usage. For a sequence of length n, this optimization lowers the complexity of incremental decoding from O(n²) to O(n).

Architectural Considerations: Decoder-Only vs. Encoder-Decoder Models

Modern LLMs predominantly use decoder-only architectures, where the same transformer layers handle both context processing and token generation. This contrasts with encoder-decoder models (e.g., T5), which separate input encoding from output decoding. Decoder-only designs offer advantages in:

Training Efficiency: Unified parameters reduce memory footprint and enable larger models.
Inference Latency: KV caching and single-stack processing minimize computational overhead.
Zero-Shot Generalization: Autoregressive pretraining on diverse corpora fosters robust few-shot capabilities.

However, encoder-decoder models remain preferable for tasks requiring bidirectional context analysis, such as translation or summarization. Hybrid approaches, like prefix-LM, attempt to reconcile these trade-offs by allowing limited bidirectional attention in the input prefix.

Implementing LLMs: Transformers Library and llama.cpp

The Transformers library provides a high-level API for loading pretrained models, tokenizing text, and generating outputs:

from transformers import AutoTokenizer, AutoModelForCausalLM; tokenizer = AutoTokenizer.from_pretrained("meta-llama/Llama-2-7b-chat-hf"); model = AutoModelForCausalLM.from_pretrained("meta-llama/Llama-2-7b-chat-hf"); inputs = tokenizer("The capital of France is", return_tensors="pt"); outputs = model.generate(**inputs, max_new_tokens=20); print(tokenizer.decode(outputs[0]))

Key considerations include model quantization, sampling parameters, and hardware acceleration.

For resource-constrained environments, llama.cpp offers CPU-first inference with AVX2 and ARM NEON optimizations:

./quantize models/llama-2-7b.gguf models/llama-2-7b-Q4_K_M.gguf Q4_K_M; ./main -m models/llama-2-7b-Q4_K_M.gguf -p "The capital of France is" -n 20

Advantages include reduced memory footprint, CPU optimization, and minimal dependencies.

On-Device and On-Premise LLM Deployment: Necessity and Challenges

Industries handling sensitive data (healthcare, finance) require local deployment to comply with regulations like GDPR and HIPAA. On-premise LLMs ensure that proprietary data never leaves organizational infrastructure.

Cloud-based APIs introduce network latency (100–500 ms per request), unacceptable for real-time applications. Local deployment guarantees sub-50 ms response times. While cloud LLM APIs charge per token, on-premise deployment shifts costs to fixed infrastructure. For high-volume applications (>10M tokens/day), breakeven occurs within 6–12 months.

Local models can be adapted to domain-specific jargon and workflows through continued pretraining or LoRA-based fine-tuning.

Conclusion

Autoregressive decoding and attention mechanisms form the computational backbone of modern LLMs, enabling their remarkable language capabilities. Practical implementation through frameworks like Transformers and llama.cpp democratizes access to these models, while on-premise deployment addresses critical needs around privacy, latency, and cost.