Train LLMs for multi-turn tool-integrated reasoning end-to-end using RL without supervised pretraining. SimpleTIR stabilizes training by filtering void turns (responses lacking code blocks or final answers) to prevent gradient explosion from distributional drift, enabling discovery of emergent reasoning patterns like self-correction and cross-validation on mathematical benchmarks.
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Train LLMs for multi-turn tool-integrated reasoning end-to-end using RL without supervised pretraining. SimpleTIR stabilizes training by filtering void turns (responses lacking code blocks or final answers) to prevent gradient explosion from distributional drift, enabling discovery of emergent reasoning patterns like self-correction and cross-validation on mathematical benchmarks.
SimpleTIR: Stable End-to-End RL for Multi-Turn Tool-Integrated Reasoning
Outcome
Enable base language models to learn multi-turn tool-integrated reasoning (code generation, execution, reflection, correction) end-to-end through reinforcement learning without requiring supervised fine-tuning or domain-specific pretraining, achieving state-of-the-art performance on mathematical reasoning benchmarks while maintaining stable training dynamics.
Problem Context
When training language models for multi-turn tool-integrated reasoning—where models generate code, execute it, observe results, and iterate—the training process becomes fundamentally unstable. The root cause lies in distributional drift: external tool outputs (execution results, error messages) exist far outside the model's pretraining distribution. When the model generates a response that leads to unexpected tool feedback, subsequent token generations fall into extremely low-probability regions of the learned distribution.
These low-probability tokens compound across turns. After three or four incorrect generations followed by tool feedback, the model assigns vanishingly small probabilities to valid continuations. During backpropagation, this produces catastrophic gradient norm explosions. Importance ratio terms explode, gradient magnitudes spike orders of magnitude above normal RL training, and the policy diverges into nonsensical behavior. The naive approach crashes entirely—gradient explosion destroys the learned policy.
Existing solutions impose external structure: supervised fine-tuning on human examples, careful curriculum learning, or complex reward shaping. These sacrifice the core promise of end-to-end learning: discovering reasoning strategies naturally from task feedback alone.
Core Concept
SimpleTIR introduces a minimal but surgically effective filtering mechanism targeting the symptom of distributional drift: "void turns"—individual model responses that contain neither a complete code block nor a final answer. These represent generation failures caused by the model assigning high probability to out-of-distribution token sequences.
By filtering entire trajectories containing void turns before computing policy losses, SimpleTIR prevents the high-magnitude gradients associated with problematic sequences while preserving credit assignment for successful reasoning chains. The mechanism is algorithm-agnostic, works as a plug-and-play wrapper around existing policy optimization methods, and requires no threshold tuning.
The theoretical grounding reveals that gradient norm depends inversely on token probabilities and is exacerbated by two compounding factors: unbounded importance ratios for low-probability tokens and sustained high gradient magnitudes when the policy assigns low probability to sampled sequences. Filtering void turns blocks the worst offenders without requiring complex annealing or uncertainty estimation.
Architecture Overview
SimpleTIR operates within a hierarchical MDP framework:
Prompt Level: Input text describing the task (e.g., "Solve this math problem")
Turn Level: Each turn represents one round of agent action + environment feedback (model generates response, tool executes code, returns result)
Token Level: Within each turn, the model samples individual tokens from its policy distribution
The training loop uses Group Relative Policy Optimization (GRPO), a recent variance-reduction technique that normalizes rewards within groups of trajectories sampled from the same prompt:
Sample batch of prompts
For each prompt, collect G trajectories (different reasoning paths)
Compute rewards for each trajectory (final answer correctness determines signal)
Normalize advantage estimates within each group using mean and standard deviation
Compute policy loss using clipped surrogate objective (PPO-style)
Filter trajectories containing void turns before backpropagation
Update model parameters
The key architectural distinction: void turn detection and filtering happens at the trajectory level, not token level. This preserves full credit assignment for trajectories that successfully navigate distributional drift, only excluding those that fail catastrophically.
Implementation
Step 1: Void Turn Detection
Detect void turns by parsing model output. A void turn contains neither a complete code block nor a final answer.
# Void turn detection logicdefis_void_turn(response_text: str) -> bool:
"""Check if model response is a void turn."""# Check for complete code blocks (backtick-delimited)
has_complete_code = (
response_text.count("```python") > 0and
response_text.count("```") >= 2# Opening and closing
)
# Check for final answer marker
has_final_answer = "final_answer("in response_text.lower()
# Void if neither code block nor final answerreturnnot (has_complete_code or has_final_answer)
deffilter_void_trajectories(trajectories: list[dict]) -> list[dict]:
"""Remove trajectories containing any void turn."""
filtered = []
for trajectory in trajectories:
contains_void = any(
is_void_turn(turn['response'])
for turn in trajectory['turns']
)
ifnot contains_void:
filtered.append(trajectory)
return filtered
Step 2: Reward Computation
Evaluate trajectory correctness. For mathematical reasoning, reward is binary (correct final answer = 1, incorrect = 0) or scaled by partial credit.
defcompute_trajectory_reward(trajectory: dict, expected_answer: str) -> float:
"""Compute reward for trajectory based on final answer correctness."""
turns = trajectory['turns']
ifnot turns:
return0.0
last_response = turns[-1]['response']
# Extract final answer from final_answer() call
answer_match = Noneif'final_answer('in last_response:
start = last_response.find('final_answer(')
if start != -1:
# Simple extraction; in practice use proper parsing
content = last_response[start + len('final_answer('):]
end = content.find(')')
if end != -1:
answer_match = content[:end].strip().strip('"').strip("'")
# Normalize both answers (remove whitespace, lowercase for strings)if answer_match and expected_answer:
answer_match = str(answer_match).strip().lower()
expected = str(expected_answer).strip().lower()
if answer_match == expected:
return1.0return0.0defbatch_compute_rewards(trajectories: list[dict],
expected_answers: list[str]) -> list[float]:
"""Compute rewards for a batch of trajectories."""return [
compute_trajectory_reward(traj, expected)
for traj, expected inzip(trajectories, expected_answers)
]
Step 3: GRPO Advantage Computation with Feedback Masking
Normalize advantages within groups and apply masking to exclude tool feedback tokens from loss.
import numpy as np
defcompute_group_advantages(rewards: np.ndarray,
gamma: float = 1.0) -> np.ndarray:
"""
Compute advantages normalized within trajectory group (GRPO).
Args:
rewards: shape (G,) where G is number of trajectories per group
gamma: discount factor (typically 1.0 for episodic tasks)
Returns:
advantages: shape (G,) normalized within group
"""# Normalize advantages using group statistics
mean_reward = np.mean(rewards)
std_reward = np.std(rewards)
# Avoid division by zeroif std_reward < 1e-8:
std_reward = 1.0
advantages = (rewards - mean_reward) / std_reward
return advantages
defcreate_feedback_mask(turn: dict, max_length: int) -> np.ndarray:
"""
Create binary mask for tokens. Mask=1 for agent response, 0 for tool feedback.
Args:
turn: dict with keys 'response' (agent text) and 'feedback' (tool output)
max_length: maximum sequence length for padding
Returns:
mask: shape (max_length,) where 1=count, 0=ignore in loss
"""
mask = np.zeros(max_length, dtype=np.float32)
# Agent response tokens are counted
response_length = len(turn['response'].split()) # Approximate tokenization
mask[:min(response_length, max_length)] = 1.0# Tool feedback tokens are masked out (remain 0)# This ensures credit assignment targets policy actions onlyreturn mask
defapply_masking_to_loss(token_losses: np.ndarray,
masks: list[np.ndarray]) -> tuple[np.ndarray, np.ndarray]:
"""
Apply token masks to loss and return masked loss + normalization factors.
Args:
token_losses: shape (batch_size, max_seq_len)
masks: list of masks, each shape (max_seq_len,)
Returns:
masked_losses: (batch_size, max_seq_len) with feedback tokens zeroed
normalizers: (batch_size,) denominator for averaging
"""
batch_size = token_losses.shape[0]
masked_losses = token_losses.copy()
normalizers = np.zeros(batch_size)
for i, mask inenumerate(masks):
masked_losses[i] *= mask
normalizers[i] = np.sum(mask) + 1e-8# Avoid division by zeroreturn masked_losses, normalizers
Step 4: PPO Loss Computation with Clipping
Standard PPO clipped surrogate loss applied only to non-masked tokens.
defcompute_ppo_loss(log_probs_new: np.ndarray,
log_probs_old: np.ndarray,
advantages: np.ndarray,
epsilon: float = 0.2,
masks: list[np.ndarray] = None) -> float:
"""
Compute PPO clipped surrogate loss.
Args:
log_probs_new: log probabilities under current policy, shape (batch,)
log_probs_old: log probabilities under old policy, shape (batch,)
advantages: normalized advantage estimates, shape (batch,)
epsilon: PPO clip threshold (0.2 or 0.28 common values)
masks: optional list of token masks for masking feedback
Returns:
loss: scalar loss value
"""# Compute importance ratios
ratio = np.exp(log_probs_new - log_probs_old)
# Clipped surrogate objective
unclipped = ratio * advantages
clipped = np.clip(ratio, 1 - epsilon, 1 + epsilon) * advantages
loss = -np.minimum(unclipped, clipped)
# Apply masking if providedif masks isnotNone:
normalizers = np.array([np.sum(m) + 1e-8for m in masks])
loss_per_sample = loss / normalizers
else:
loss_per_sample = loss
return np.mean(loss_per_sample)
defcompute_tir_training_objective(trajectories: list[dict],
log_probs_new: list[np.ndarray],
log_probs_old: list[np.ndarray],
rewards: np.ndarray,
epsilon: float = 0.2,
masks: list[list[np.ndarray]] = None) -> float:
"""
Full SimpleTIR training objective: GRPO + feedback masking + trajectory filtering.
Args:
trajectories: list of trajectories (already filtered for void turns)
log_probs_new: list of log-probability arrays per trajectory
log_probs_old: list of old log-probability arrays
rewards: array of rewards for trajectories
epsilon: PPO clip parameter
masks: nested list of masks (per-trajectory, per-turn)
Returns:
loss: scalar training loss
"""# Compute group advantages using GRPO normalization
advantages = compute_group_advantages(rewards)
# Aggregate loss across all tokens in all trajectories
total_loss = 0.0
total_count = 0for i, trajectory inenumerate(trajectories):
adv = advantages[i]
log_new = log_probs_new[i] # shape (num_tokens,)
log_old = log_probs_old[i] # shape (num_tokens,)# Per-token PPO loss
ratio = np.exp(log_new - log_old)
unclipped = ratio * adv
clipped = np.clip(ratio, 1 - epsilon, 1 + epsilon) * adv
token_loss = -np.minimum(unclipped, clipped)
# Apply feedback maskingif masks isnotNone:
traj_masks = masks[i] # list of masks per turn
masked_loss = token_loss * np.concatenate(traj_masks)
normalizer = np.sum(np.concatenate(traj_masks)) + 1e-8else:
masked_loss = token_loss
normalizer = len(token_loss)
total_loss += np.sum(masked_loss) / normalizer
total_count += 1return total_loss / total_count
Step 5: Training Loop with Void Turn Filtering
Main training loop integrating all components.
import torch
from torch.optim import Adam
classSimpleTIRTrainer:
"""End-to-end RL trainer for multi-turn tool-integrated reasoning."""def__init__(self, model, learning_rate: float = 1e-6,
ppo_epsilon: float = 0.2, max_turns: int = 5):
self.model = model
self.optimizer = Adam(model.parameters(), lr=learning_rate)
self.ppo_epsilon = ppo_epsilon
self.max_turns = max_turns
defrollout(self, prompts: list[str], env) -> list[dict]:
"""
Generate trajectories by rolling out policy.
Args:
prompts: list of problem descriptions
env: environment with code execution capability
Returns:
trajectories: list of {turns, reward, void_flagged}
"""
trajectories = []
for prompt in prompts:
turns = []
context = prompt
trajectory_done = False
turn_count = 0whilenot trajectory_done and turn_count < self.max_turns:
# Generate response from policywith torch.no_grad():
response = self.model.generate(
context,
max_length=16384,
temperature=1.0,
top_p=0.95
)
turns.append({
'response': response,
'context': context
})
# Check for final answer (trajectory termination)if'final_answer('in response:
trajectory_done = Trueelse:
# Extract and execute code
code = self._extract_code_block(response)
if code:
feedback = env.execute_code(code)
context += f"\n\nCode Execution Result:\n{feedback}"
turns[-1]['feedback'] = feedback
else:
# Void turn: no code block
trajectory_done = True
turn_count += 1
trajectories.append({
'turns': turns,
'prompt': prompt,
'void_flagged': any(
is_void_turn(turn['response']) for turn in turns
)
})
return trajectories
deftrain_step(self, trajectories: list[dict],
expected_answers: list[str]) -> float:
"""
Single training step: filter voids, compute loss, update parameters.
"""# Filter trajectories containing void turns
valid_trajectories = filter_void_trajectories(trajectories)
iflen(valid_trajectories) == 0:
print("Warning: all trajectories filtered as void")
return0.0# Compute rewards only for valid trajectories
expected_valid = [
expected_answers[i] for i, traj inenumerate(trajectories)
ifnot traj['void_flagged']
]
rewards = batch_compute_rewards(valid_trajectories, expected_valid)
# Forward pass: compute log probabilities under current policy
log_probs_new = []
log_probs_old = []
for trajectory in valid_trajectories:
# Recompute log probs (new policy)
trajectory_log_probs = self._compute_log_probs(
trajectory,
require_grad=True
)
log_probs_new.append(trajectory_log_probs)
# Use cached log probs (old policy)
trajectory_log_probs_old = self._compute_log_probs(
trajectory,
require_grad=False
)
log_probs_old.append(trajectory_log_probs_old)
# Create feedback masks
masks = []
for trajectory in valid_trajectories:
traj_masks = [
create_feedback_mask(turn, max_length=16384)
for turn in trajectory['turns']
]
masks.append(traj_masks)
# Compute loss with all components
advantages = compute_group_advantages(np.array(rewards))
loss = 0.0for i inrange(len(valid_trajectories)):
# PPO loss with masking
ratio = torch.exp(
log_probs_new[i] - log_probs_old[i]
)
adv = advantages[i]
unclipped = ratio * adv
clipped = torch.clamp(
ratio,
1 - self.ppo_epsilon,
1 + self.ppo_epsilon
) * adv
trajectory_loss = -torch.mean(
torch.minimum(unclipped, clipped)
)
loss += trajectory_loss
loss = loss / len(valid_trajectories)
# Backward pass with gradient clippingself.optimizer.zero_grad()
loss.backward()
torch.nn.utils.clip_grad_norm_(
self.model.parameters(),
max_norm=1.0
)
self.optimizer.step()
return loss.item()
def_extract_code_block(self, text: str) -> str:
"""Extract Python code from markdown code blocks."""
start = text.find("```python")
if start == -1:
return""
start += len("```python")
end = text.find("```", start)
if end == -1:
return""return text[start:end].strip()
def_compute_log_probs(self, trajectory: dict,
require_grad: bool) -> torch.Tensor:
"""Compute log probabilities of trajectory tokens."""# In practice: use model.forward() to get logits,# compute log softmax, extract log probs for sampled tokens# This is pseudocode; real implementation requires tokenization detailspass
Practical Guidance
Hyperparameters Reference
Parameter
SimpleTIR Value
Notes
Learning Rate (Actor)
1e-6
Conservative; use Adam optimizer
PPO Clip Epsilon
0.2–0.28
0.2 for stability, 0.28 for flexibility
Batch Size (Training)
512
Tokens per update; adjust for GPU memory
Batch Size (Sampling)
1,280
Trajectories collected per step
Max Response Length
16,384 tokens
Large to allow multi-step reasoning
Max Interaction Turns
5–10
Depends on task complexity
Temperature
1.0
Keep high for exploration
Discount Factor (γ)
1.0
Episodic tasks (no bootstrapping)
GAE Lambda (λ)
1.0
Use MC return (full trajectory)
Gradient Clipping
1.0 (global norm)
Critical for training stability
PPO Epochs
4
Reuse per batch before sampling new
Entropy Coefficient
0
Not used in SimpleTIR
KL Coefficient (β)
0
Not used (no reference model)
When to Use SimpleTIR
Good fit:
Training LLMs for math problem solving (AIME, competition math)
Multi-step reasoning with tool feedback (code execution, symbolic math systems)
Base models without supervised pretraining (cost-effective)
Scenarios where you want emergent reasoning patterns (self-correction, cross-validation)
Projects with sufficient compute for end-to-end RL (~16–32 GPUs for 7B models)
Tasks with clear correctness signals (mathematical reasoning, coding)
Start with SimpleTIR if: You want to avoid supervised fine-tuning cold starts and have well-defined reward signals. The method works best on benchmarks with binary or easily scored outcomes.
When NOT to Use SimpleTIR
Poor fit:
Tasks with ambiguous, subjective, or sparse rewards (creative writing, open-ended chat)
Training on smaller models (<1B parameters) where distributional drift is less severe
Scenarios requiring immediate deployment (RL training is inherently slow)
Problems where supervised fine-tuning is already working well and cost is not a concern
Domains without reliable execution environments (no clear "tool feedback")
Real-time systems needing low latency (expensive generation lengths)
Avoid SimpleTIR if: Your reward signal is noisy, sparse, or ill-defined. Distributional drift filtering only works when you can reliably detect generation failures (void turns). If your task doesn't have discrete "success/failure" outcomes, the method will either filter too much or too little.
Common Pitfalls
Insufficient void turn detection: If your void turn detection is too permissive (allows partial code), filtering will not prevent gradient explosion. Be strict: require complete code blocks with balanced backticks and explicit final_answer() calls.
Entropy decay: The method produces zero entropy coefficient by design. If exploration collapses early, add small entropy bonus (0.01–0.05) or increase temperature during rollout.
Reward signal design: Binary rewards (correct/incorrect) work best. Scaled rewards (partial credit) can work but require careful normalization. Avoid continuous rewards without clear scale.
Masking misalignment: If feedback tokens are tokenized differently than expected, the mask will misalign with the loss computation, defeating the purpose. Verify that feedback masks match actual token boundaries.
Turn count limits: Five turns is typical for math but may be insufficient for harder problems. Monitor the proportion of trajectories hitting max turns; if >30%, increase max_turns.
Memory scaling: 16,384 token max length can consume significant GPU memory. If OOM occurs, reduce response length or batch size, but be aware this limits complex reasoning chains.
Importance ratio explosion: Even with void filtering, if old policy is very stale (many PPO epochs without refreshing), importance ratios can explode. Keep PPO epochs low (4) and refresh policy frequently.
