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TemperatureOptimizationStudy
TemperatureOptimizationStudy
Temperature Optimization Study

Overview

We conducted a systematic study to find the optimal temperature parameter for LLM-based code evolution using Gemini Flash 2.5 Lite as our test model.

Temperature Analysis

Chart Explanation:

  • Left panel: Shows temperature vs performance for pure temperature comparison - clean line plot with actual performance at each temperature setting
  • Right panel: Scatter plot of duration vs performance colored by temperature, showing the performance/time trade-off

Experimental Setup

  • Model: Gemini Flash 2.5 Lite
  • Base Config: 100 iterations, 16k tokens, diff-based evolution
  • Variable: Temperature (0.2, 0.4, 0.8)
  • Tasks: 30 AlgoTune benchmark tasks

Results

Quantitative Comparison

TemperatureAlgoTune ScoreAvg PerformanceSuccess RateDuration
0.21.17x0.162100%4074s
0.41.29x0.175100%3784s
0.81.02x0.159100%3309s

Note: This table shows the pure temperature comparison experiments only. Temperature 0.4 was used in multiple other parameter studies, but this analysis focuses on the direct temperature impact.

Key Findings

  1. Temperature 0.4 Performance

    • Best individual run: 1.291x speedup
    • Mean across 7 runs: 1.114x (with high variance)
    • Compared to 1.169x at 0.2 and 1.018x at 0.8

  2. Performance Degradation at Extremes

    • Too Low (0.2): Conservative mutations, limited exploration
    • Too High (0.8): Chaotic changes, often breaking code

  3. Task-Specific Impact

    • High-impact tasks showed larger temperature sensitivity
    • Simple tasks performed similarly across temperatures

Detailed Analysis

Temperature 0.2: Conservative Evolution

Example Evolution (count_connected_components):

# Iteration 45
- visited = [False] * n
+ visited = [False for _ in range(n)]  # Minor style change

Characteristics:

  • Minimal code changes
  • High syntactic validity
  • Limited algorithmic exploration
  • Slow convergence

Best Achievement: psd_cone_projection at 24.4x speedup

Temperature 0.4: Balanced Evolution

Example Evolution (count_connected_components):

# Iteration 23
- def dfs(node):
-     visited[node] = True
-     for neighbor in adj[node]:
-         if not visited[neighbor]:
-             dfs(neighbor)
+ # Switch to BFS for better performance
+ from collections import deque
+ queue = deque([start])
+ visited[start] = True
+ while queue:
+     node = queue.popleft()
+     for neighbor in adj[node]:
+         if not visited[neighbor]:
+             visited[neighbor] = True
+             queue.append(neighbor)

Characteristics:

  • Meaningful algorithmic changes
  • Good balance of safety and innovation
  • Successful major refactorings
  • Optimal convergence speed

Best Achievement: count_connected_components at 41.9x speedup

Temperature 0.8: Chaotic Evolution

Example Evolution (matrix operations):

# Iteration 12
- result = np.dot(A, B)
+ # Trying advanced optimization
+ result = np.einsum('ij,jk->ik', A, B) @ np.eye(A.shape[0])  # Broken!

Characteristics:

  • Wild algorithmic swings
  • Frequent syntax errors
  • Occasional brilliant insights
  • Many failed attempts

Best Achievement: psd_cone_projection at 39.0x (lucky hit)

Evolution Trajectories

Convergence Patterns

Temperature 0.2:

Iteration  0: 1.00x
Iteration 25: 1.08x
Iteration 50: 1.12x
Iteration 75: 1.15x
Iteration 100: 1.17x

Slow, steady improvement

Temperature 0.4:

Iteration  0: 1.00x
Iteration 25: 1.15x
Iteration 50: 1.23x
Iteration 75: 1.27x
Iteration 100: 1.29x

Optimal improvement curve

Temperature 0.8:

Iteration  0: 1.00x
Iteration 25: 0.95x (regression!)
Iteration 50: 1.08x
Iteration 75: 0.98x (regression!)
Iteration 100: 1.02x

Unstable with regressions

Specific Task Analysis

Tasks Most Sensitive to Temperature

  1. count_connected_components

    • Temp 0.2: Failed to discover BFS
    • Temp 0.4: Found BFS optimization (41.9x)
    • Temp 0.8: Broke working solutions

  2. eigenvalue computations

    • Benefits from moderate exploration
    • Temp 0.4 found vectorization opportunities

  3. SHA256 hashing

    • Little variation across temperatures
    • Hardware-bound task

Computational Efficiency

TemperatureAvg Time/IterationFailed Evaluations
0.240.7s12%
0.437.8s18%
0.833.1s31%

Lower temperature = more valid programs = longer evaluation time

Key Experimental Findings

  1. Temperature 0.4 Results: Best individual run achieved 1.291x speedup, though mean was 1.114x across 7 experiments

  2. Task Complexity Patterns:

    • Simple tasks showed less temperature sensitivity
    • Complex algorithmic tasks benefited most from moderate temperatures
    • Hardware-bound tasks showed minimal variation

  3. Model-Specific Observations:

    • This study focused on Gemini Flash Lite
    • Qwen3-Coder experiments used 0.6 temperature with 1.41x results
    • Different models showed different optimal temperatures

  4. Evolution Behavior by Temperature:

    • Higher temperatures (0.8) produced more failed evaluations (31%)
    • Lower temperatures (0.2) had fewer failures (12%) but conservative changes
    • Temperature 0.4 balanced exploration with validity (18% failures)

Conclusion

Temperature 0.4 provides the optimal balance between exploration and exploitation for code evolution tasks. It enables meaningful algorithmic discoveries while maintaining sufficient code validity to make progress. The 10-26% performance improvement over other temperatures justifies careful temperature tuning for production use.

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