# How the KV Window Budget Is Calculated in Needle and How to Tune It for Different Sequence Lengths

> Learn how Needle calculates the KV window budget using architecture and model parameters. Tune config.kv_window to optimize cache for various sequence lengths effectively.

- Repository: [Cactus Compute, Inc./needle](https://github.com/cactus-compute/needle)
- Tags: internals
- Published: 2026-08-14

---

**The KV window budget in Needle is calculated based on architecture constants (11.5 MiB memory budget, 32-token alignment groups) and model parameters (KV heads, hidden size, layers), then tuned via `config.kv_window` to cap or extend the sliding cache for different sequence lengths.**

Needle uses a fixed memory budget to constrain the key-value cache during autoregressive generation. This article explains the mathematical derivation in `kv_budget_window()`, how `effective_kv_window()` applies user overrides, and practical tuning strategies for short, medium, and long sequences.

## How Needle Calculates the KV Window Budget

### The Core Formula

The KV budget calculation lives in [`needle/model/architecture.py`](https://github.com/cactus-compute/needle/blob/main/needle/model/architecture.py) at lines 603–617: [https://github.com/cactus-compute/needle/blob/main/needle/model/architecture.py#L603-L617](https://github.com/cactus-compute/needle/blob/main/needle/model/architecture.py#L603-L617)

```python
def kv_budget_window(config):
    head_dim = (getattr(config, "attn_dim", 0) or config.d_model) // config.num_heads
    kv = config.num_kv_heads * head_dim
    d, L = config.d_model, config.num_layers
    sites = len(tuple(getattr(config, "engram_layers", (2, 15))))
    per_pos = (L * (2 * kv + 2 * (kv // KV_GROUP) * 4)
               + sites * (d + (d // KV_GROUP) * 4))
    window = (KV_BUDGET_BYTES // per_pos) // KV_GROUP * KV_GROUP
    return max(KV_WINDOW_MIN, min(window, config.max_seq_len))

```

**Key components:**

- `head_dim` — Dimensionality per attention head, derived from `d_model / num_heads` or an explicit `attn_dim`
- `kv` — Total KV dimension per position, computed as `num_kv_heads * head_dim`
- `per_pos` — Memory per token position accounting for:
  - Linear KV projections (`2 * kv` for keys and values)
  - Quantized packing overhead (`2 * (kv // KV_GROUP) * 4`)
  - Engram layer storage (`sites * (d + (d // KV_GROUP) * 4)`)
- `KV_BUDGET_BYTES` — Hardcoded constant of **12,058,880 bytes** (11 MiB + 512 KiB)
- `KV_GROUP` — Alignment granularity set to **32 tokens**
- `KV_WINDOW_MIN` — Floor value of **160 tokens**

The function returns the largest window fitting the budget, aligned to 32 tokens, bounded between 160 and `max_seq_len`.

### Budget-to-Window Conversion

The arithmetic follows this path:

1. Compute bytes per position (`per_pos`) from architecture
2. Divide total budget by per-position cost: `KV_BUDGET_BYTES // per_pos`
3. Align down to `KV_GROUP` boundary: `// KV_GROUP * KV_GROUP`
4. Clamp with `max(KV_WINDOW_MIN, min(window, config.max_seq_len))`

This guarantees deterministic memory usage regardless of batch size or prompt length.

## How `effective_kv_window` Applies User Overrides

Users control the final window via `config.kv_window`. The resolution logic appears at lines 614–617: [https://github.com/cactus-compute/needle/blob/main/needle/model/architecture.py#L614-L617](https://github.com/cactus-compute/needle/blob/main/needle/model/architecture.py#L614-L617)

```python
def effective_kv_window(config):
    budget = kv_budget_window(config)
    return min(budget, config.kv_window) if config.kv_window else budget

```

**Behavior matrix:**

| `kv_window` setting | Result |
|---------------------|--------|
| `0` (default) | Use full budget-derived window |
| Positive integer `< budget` | Cap to user-specified value |
| Positive integer `> budget` | Silent cap to budget (no expansion beyond memory limit) |

This design prevents accidental out-of-memory errors while allowing deliberate restriction.

## Tuning the KV Window for Different Sequence Lengths

### Short Sequences (≤ 512 tokens)

For brief prompts and completions, accept the default:

```python
from needle.model.architecture import TransformerConfig, effective_kv_window

short_cfg = TransformerConfig(
    d_model=768,
    num_heads=12,
    num_kv_heads=4,  # GQA reduces KV memory

    num_layers=12,
    max_seq_len=2048,
    # kv_window defaults to 0

)

print(effective_kv_window(short_cfg))  # Typically 512-1024 tokens from budget

```

The budget-derived window usually exceeds short sequence needs. No tuning required.

### Medium Sequences (1K–8K tokens)

Medium-length generation benefits from explicit profiling:

```python
import torch
from needle.model.architecture import TransformerConfig, kv_budget_window

medium_cfg = TransformerConfig(
    d_model=1024,
    num_heads=16,
    num_kv_heads=8,
    num_layers=24,
    max_seq_len=8192,
)

budget_win = kv_budget_window(medium_cfg)
print(f"Budget window: {budget_win}")

# If GPU memory is tight, cap below budget

medium_cfg.kv_window = 2048
print(f"Capped window: {min(budget_win, medium_cfg.kv_window)}")

```

**Tuning principle:** Set `kv_window` to 50–75% of your expected maximum generation length if the budget window exceeds available VRAM after accounting for activations and weights.

### Long Sequences (16K+ tokens)

Long-context models face hard memory constraints. Two tuning approaches:

**Approach 1: Reduce KV dimension via architecture**

```python

# Use fewer KV heads to lower per-position cost

long_cfg = TransformerConfig(
    d_model=2048,
    num_heads=32,
    num_kv_heads=2,  # Aggressive GQA: 16:1 compression

    num_layers=32,
    max_seq_len=32768,
)

print(kv_budget_window(long_cfg))  # Larger window due to smaller kv dimension

```

**Approach 2: Accept truncated context with explicit window**

```python
long_cfg.kv_window = 4096  # Rolling window: oldest tokens evicted

```

This implements **sliding-window attention** behavior—older KV pairs are discarded when the cache fills.

### Low-Memory Hardware Tuning

On consumer GPUs, combine multiple strategies:

```python
efficient_cfg = TransformerConfig(
    d_model=512,
    num_heads=8,
    num_kv_heads=2,      # 4:1 GQA compression

    num_layers=8,        # Shallower model

    max_seq_len=4096,
    kv_window=512,       # Hard cap for deterministic memory

)

```

Profile with `torch.cuda.memory_stats()` to verify headroom:

```python
import torch
from needle.model.architecture import effective_kv_window

def profile_kv_memory(config, batch_size=1):
    window = effective_kv_window(config)
    head_dim = config.d_model // config.num_heads
    kv_dim = config.num_kv_heads * head_dim
    
    # KV cache: (layers, 2, batch, heads, window, head_dim) in fp16

    bytes_per_elem = 2
    kv_memory = (config.num_layers * 2 * batch_size * 
                 config.num_kv_heads * window * head_dim * bytes_per_elem)
    
    return window, kv_memory / (1024**2)  # MiB

win, mem = profile_kv_memory(efficient_cfg)
print(f"Window: {win}, KV cache: {mem:.1f} MiB")

```

## Architecture Constants and Their Impact

| Constant | Value | Effect on Tuning |
|----------|-------|----------------|
| `KV_BUDGET_BYTES` | 12,058,880 | Upper bound on total KV cache; modify only via source edit |
| `KV_GROUP` | 32 | Window granularity; partial windows rounded down |
| `KV_WINDOW_MIN` | 160 | Absolute floor; prevents degenerate caches |

To adjust the global budget, edit [`needle/model/architecture.py`](https://github.com/cactus-compute/needle/blob/main/needle/model/architecture.py) and rebuild. For per-model flexibility, use `kv_window` override.

## Key Source Files

| File | Relevance |
|------|-----------|
| [`needle/model/architecture.py`](https://github.com/cactus-compute/needle/blob/main/needle/model/architecture.py) | `kv_budget_window()`, `effective_kv_window()`, `TransformerConfig` definition |
| [`needle/model/decode.py`](https://github.com/cactus-compute/needle/blob/main/needle/model/decode.py) | Consumes KV window for causal mask construction |
| [`needle/model/export.py`](https://github.com/cactus-compute/needle/blob/main/needle/model/export.py) | Serializes window size to model headers |
| [`tests/test_build.py`](https://github.com/cactus-compute/needle/blob/main/tests/test_build.py) | Validates window calculations across configurations |

## Summary

- The **KV window budget** derives from fixed constants (11.5 MiB, 32-token groups) and model architecture (KV heads, layers, hidden size)
- **`kv_budget_window()`** computes the maximum cache size fitting the memory budget, aligned and clamped to valid ranges
- **`effective_kv_window()`** layers user intent via `config.kv_window`, capping rather than expanding
- **Tuning strategy** depends on sequence length: accept defaults for short sequences, cap explicitly for memory constraints, reduce KV dimension for long contexts

## Frequently Asked Questions

### What happens if I set `kv_window` larger than the budget-derived window?

Needle silently caps to the budget. The `min(budget, config.kv_window)` logic in `effective_kv_window` prevents exceeding the 11.5 MiB allocation, protecting against out-of-memory errors.

### Can I increase `KV_BUDGET_BYTES` without modifying source code?

No. The constant is hardcoded in [`architecture.py`](https://github.com/cactus-compute/needle/blob/main/architecture.py). To raise the budget, edit line defining `KV_BUDGET_BYTES` and reinstall. Consider instead reducing `num_kv_heads` or `num_layers` to fit your target window within the default budget.

### Why does the window calculation include `engram_layers`?

Engram layers (default: layers 2 and 15) store additional per-token state for retrieval-augmented mechanisms. Their memory cost—`d + (d // KV_GROUP) * 4` per site—is included in `per_pos` to ensure the total cache allocation stays within budget.

### How does the KV window interact with Flash Attention or other kernels?

The window size determines the sequence dimension of the KV cache tensor passed to attention kernels. Needle's decode path respects this bound when constructing causal masks; underlying kernels operate on the pre-truncated tensors without additional masking logic.