Center rewards coefficient (#3124)

* feat: add center_rewards_coefficient for reward modeling

- Add center_rewards_coefficient parameter to Pydantic schema with paper reference
- Pass parameter through base builder and causal builder to training args
- Add documentation section with usage examples and theoretical background
- Enable parameter in reward modeling example configs with recommended value
- Enables reward centering for improved training stability in RLHF workflows

Implements auxiliary loss from Eisenstein et al. 2023 (https://huggingface.co/papers/2312.09244)
to incentivize mean-zero reward outputs without post-training normalization.

* Update description

* test: add unit tests for center_rewards_coefficient integration

* Update src/axolotl/core/builders/base.py

Co-authored-by: NanoCode012 <kevinvong@rocketmail.com>

* Update docs/reward_modelling.qmd

Co-authored-by: NanoCode012 <kevinvong@rocketmail.com>

* Update docs/reward_modelling.qmd

Co-authored-by: NanoCode012 <kevinvong@rocketmail.com>

* reference to TRL documentation.

* add new reward model configuration for qwen3 with comprehensive parameters

* Verified center_rewards_coefficient is correctly passed through the trainer builder to training arguments.

* Refactor reward modeling documentation to consolidate information on center_rewards_coefficient

* Remove unit tests for center_rewards_coefficient integration as part of codebase cleanup.

* linting

* nit

* Apply suggestions from code review

Co-authored-by: NanoCode012 <kevinvong@rocketmail.com>

* lint

---------

Co-authored-by: NanoCode012 <kevinvong@rocketmail.com>
Co-authored-by: Salman Mohammadi <salman.mohammadi@outlook.com>

examples/qwen3/reward-model.yaml

@@ -0,0 +1,44 @@
+base_model: Skywork/Skywork-Reward-V2-Qwen3-8B
+model_type: AutoModelForSequenceClassification
+num_labels: 1
+
+reward_model: true
+center_rewards_coefficient: 0.01  # Incentivize mean-zero rewards for improved stability
+chat_template: qwen3
+datasets:
+  - path: argilla/distilabel-intel-orca-dpo-pairs
+    type: bradley_terry.chat_template
+
+val_set_size: 0.0
+output_dir: ./outputs/out
+
+sequence_len: 8192
+sample_packing: false
+eval_sample_packing: false
+pad_to_sequence_len: true
+
+deepspeed: deepspeed_configs/zero1.json
+
+wandb_project:
+wandb_entity:
+wandb_watch:
+wandb_name:
+wandb_log_model:
+
+gradient_accumulation_steps: 4
+micro_batch_size: 1
+eval_batch_size: 1
+num_epochs: 3
+optimizer: adamw_bnb_8bit
+lr_scheduler: linear
+learning_rate: 0.00002
+
+bf16: true
+tf32: true
+
+gradient_checkpointing: true
+gradient_checkpointing_kwargs:
+  use_reentrant: false
+warmup_ratio: 0.1
+logging_steps: 1
+weight_decay: 0.01