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‎README.md‎

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# $\lambda$-RLM
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Code for $\lambda$-Recursive Language Models: typed functional recursion for reliable long-context reasoning.
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Code for **The $\mathbf{Y}$-Combinator for LLMs: \\ Solving Long-Context Rot with $\lambda$-Calculus**: a framework for long-context reasoning that replaces free-form recursive code generation with a typed functional runtime grounded in $\lambda$-calculus.
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<p align="center">
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<img src="intro.png" alt="Lambda-RLM results figure" width="900" />
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</p>
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Standard LLM inference is limited by context windows and is opaque — models improvise decomposition unpredictably. $\lambda$-RLM solves this by:
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Standard LLM inference is constrained by context windows and often relies on implicit, hard-to-predict decomposition strategies. $\lambda$-RLM addresses this by:
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- **Pre-computing** the optimal decomposition plan before any LLM call (deterministic)
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- **Mapping inference** to Lambda Calculus primitives: β-reduction at leaves, symbolic combinators for composition
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- **Splitting** long inputs into parallel chunks where each fits in the model's context window
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- **Composing** results via pre-verified operators (MERGE_COUNTS, SEARCH_UNION, SUMMARIZE_REDUCE, etc.)
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- **Planning decomposition ahead of execution** with a deterministic recursive strategy
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- **Expressing inference through functional structure**, with model calls at local steps and symbolic operators for composition
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- **Breaking long inputs into manageable chunks** that fit within the model context window
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- **Combining intermediate results** through structured operators such as `MERGE_COUNTS`, `SEARCH_UNION`, and `SUMMARIZE_REDUCE`
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---
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pip install -e .
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```
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We support access models through APIs, for example, you can request a [NVIDIA NIM API key](https://build.nvidia.com) to access available models.
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We support access different avaialble models through APIs, for example, you can request a [NVIDIA NIM API key](https://build.nvidia.com) or a [TOGETHER AI API key](https://api.together.ai/) to access available models of the given API.
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```bash
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export NVIDIA_API_KEY="nvapi-..."
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```
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```bash
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export TOGETHER_API_KEY="tgp_..."
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```
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### Supported Task Types
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| Task | Composition Operator | Strategy |
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|---|---|---|
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| `aggregation` | MERGE_COUNTS | SPLIT → MAP → sum counts |
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| `search` | SEARCH_UNION | SPLIT → MAP → union doc IDs |
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| `classification` | CONCAT | SPLIT → MAP → concat labels |
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| `pairwise` | CONCAT + symbolic CROSS | MAP(classify) → CROSS(O(N²), free) |
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| `summarization` | SUMMARIZE_REDUCE + M | SPLIT → MAP → M(final synthesis) |
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| `extraction` | CONCAT | SPLIT → MAP → concat fields |
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| `code_understanding` | CONCAT | SPLIT → MAP → concat analysis |
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| `multi_hop` | SUMMARIZE_REDUCE + M | SPLIT → MAP(extract) → M(synthesize) |
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### Supported datasets:
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- `sniah` — Sequential-NIAH examples loaded from the public GitHub JSONL source
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- `oolong` — single-document QA examples loaded from `THUDM/LongBench-v2`
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- `browsecomp` — multi-document QA examples loaded from `THUDM/LongBench-v2`
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- `codeqa` — code repository understanding examples loaded from a local JSONL file or from `THUDM/LongBench-v2`
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## Usage
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rlm = LambdaRLM(
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backend_kwargs={
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"model_name": "qwen/qwen3-next-80b-a3b-thinking",
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"model_name": "meta/llama-3.3-70b-instruct",
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"api_key": os.environ["NVIDIA_API_KEY"],
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"base_url": "https://integrate.api.nvidia.com/v1",
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}
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print(result.response)
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```
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## Repository structure
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### Normal RLM
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This repository uses upstream Normal RLM components for comparison: `https://github.com/alexzhang13/rlm`
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The upstream code is licensed under the MIT License. See `THIRD_PARTY_NOTICES.md` for attribution and licensing details.
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Key files:
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- `rlm/core/rlm.py` — main REPL-based RLM loop
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- `rlm/environments/local_repl.py` — sandboxed Python REPL execution, context storage, and helper functions
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- `rlm/utils/parsing.py` — parsing of ```repl``` code blocks and FINAL markers; formatting of execution output back into the model history
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- `rlm/clients/openai.py` — OpenAI-compatible client used with NVIDIA NIM
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### Lambda-RLM
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- `rlm/lambda_rlm.py` — LambdaRLM implementation, including task detection, planning, and deterministic execution through $\Phi$
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## Benchmarking
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The benchmark entry point is used for running experiments with same dataset and comparing the behavior, latency, and output quality under the same setup between Normal RLM (rlm) and Lambda-RLM (lambda_rlm)
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### Supported datasets:
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- `sniah` — Sequential-NIAH examples loaded from a local JSONL file or from the public GitHub JSONL source
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- `oolong` — single-document QA examples loaded from `THUDM/LongBench-v2`
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- `browsecomp` — multi-document QA examples loaded from `THUDM/LongBench-v2`
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- `codeqa` — code repository understanding examples loaded from a local JSONL file or from `THUDM/LongBench-v2`
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### Supported models:
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- todo
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### Compare both methods on the same dataset
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```bash
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python benchmarks/benchmark.py --datasets sniah --methods rlm lambda_rlm --n-samples-per-bucket 1 --max-iter 8 --max-depth 2 --context-window 100000 --output-dir ./results_compare
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python benchmarks/benchmark.py --datasets sniah --model meta/llama-3.3-70b-instruct --methods rlm lambda_rlm --n-samples-per-bucket 2 --max-iter 8 --max-depth 2 --context-window 100000 --output-dir ./results/llama-3.3-70b-instruct
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```
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Outputs are written to the specified output directory, typically including:
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### Run only Normal RLM
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```bash
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python benchmarks/benchmark.py --datasets sniah --methods rlm --n-samples-per-bucket 1 --max-iter 8 --max-depth 2 --context-window 100000 --output-dir ./results_compare
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python benchmarks/benchmark.py --datasets sniah --model meta/llama-3.3-70b-instruct --methods rlm --n-samples-per-bucket 2 --max-iter 8 --max-depth 2 --context-window 100000 --output-dir ./results/llama-3.3-70b-instruct_rlm
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```
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### Run only Lambda-RLM
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```bash
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python benchmarks/benchmark.py --datasets sniah --methods lambda_rlm --n-samples-per-bucket 1 --max-iter 8 --max-depth 2 --context-window 100000 --output-dir ./results_compare
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```
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## Repository structure
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### Normal RLM
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This repository uses upstream Normal RLM components for comparison.
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Upstream repository:
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`https://github.com/alexzhang13/rlm`
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The upstream code is licensed under the MIT License. See `THIRD_PARTY_NOTICES.md` for attribution and licensing details.
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Key files:
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- `rlm/core/rlm.py` — main REPL-based RLM loop
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- `rlm/environments/local_repl.py` — sandboxed Python REPL execution, context storage, and helper functions
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- `rlm/utils/parsing.py` — parsing of ```repl``` code blocks and FINAL markers; formatting of execution output back into the model history
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- `rlm/clients/openai.py` — OpenAI-compatible client used with NVIDIA NIM
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### Lambda-RLM
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- `rlm/lambda_rlm.py` — LambdaRLM implementation, including task detection, planning, and deterministic execution through Φ
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python benchmarks/benchmark.py --datasets sniah --model meta/llama-3.3-70b-instruct --methods lambda_rlm --n-samples-per-bucket 2 --max-iter 8 --max-depth 2 --context-window 100000 --output-dir ./results/llama-3.3-70b-instruct_lambda_rlm
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```

‎benchmarks/benchmark.py‎

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import json
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import math
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import sys
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import os as _os
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# Ensure the project root (parent of benchmarks/) is on sys.path so `import rlm` works
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# whether the script is run as `python benchmarks/benchmark.py` or `python -m benchmarks.benchmark`.
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sys.path.insert(0, str(__import__("pathlib").Path(__file__).resolve().parent.parent))
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import matplotlib
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matplotlib.use("Agg")
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import matplotlib.pyplot as plt
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import matplotlib.ticker as mtick
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import numpy as np
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_PLOT_AVAILABLE = True
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except ImportError:
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#
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# Tokens for non-S-Niah datasets are estimated as chars // 4.
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import math as _math
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BIN_LABELS: list[str] = ["8k", "16k", "32k", "64k", "128k", "256k"]
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_BIN_EXPS: list[int] = list(range(13, 19)) # 13..18
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_BIN_BOUNDARIES: list[float] = [

‎intro.png‎

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‎rlm/lambda_rlm.py‎

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from rlm.clients import BaseLM, get_client
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from rlm.core.lm_handler import LMHandler
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from rlm.core.types import ClientBackend, EnvironmentType, RLMChatCompletion, UsageSummary
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from rlm.core.types import ClientBackend, EnvironmentType, RLMChatCompletion
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from rlm.environments.local_repl import LocalREPL
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from rlm.logger import RLMLogger
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