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Model: Lambent/Qwen3-4B-Base-Continued-GRPO-Style-Karcher
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2026-05-29 16:56:43 +08:00
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---
base_model:
- Lambent/Qwen3-4B-Base-Continued-GRPO-Wave
library_name: transformers
tags:
- mergekit
- merge
license: apache-2.0
---
For this one...
... (over)trained a SmolLM2-360M on 5 epochs at swept-for LR and rank on each of the target domains to fit style,
then rewarded the model for lowering perplexity on the proxy model.
In this case, trained an adapter per domain and then Karcher merged them.
I'm not sure if any of the domains had notably different effect, they all basically had the same result on evals.
However, the karcher combination of them seem to have significantly lowered perplexity on lambada_openai, which is interesting enough to publish.
Additionally, attempted to implement MARA from https://im-ant.github.io/mara/ on the GRPO side to help preserve distribution entropy, though I'm unsure how correctly/usefully we did so.
| Task | Metric | Qwen3-4B-Base | GRPO-Merge | Δ Base | GRPO-Wave | Δ Base | Δ Merge | Style-Karcher | Δ Base | Δ Wave |
|:-----|:-------|:-------------:|:----------:|:------:|:---------:|:------:|:-------:|:-------------:|:------:|:------:|
| arc_easy | acc | 0.7891 | 0.7870 | -0.27% | 0.7912 | +0.27% | +0.53% | 0.7883 | -0.10% | -0.37% |
| arc_easy | acc_norm | 0.7609 | 0.7605 | -0.05% | 0.7643 | +0.45% | +0.50% | 0.7576 | -0.43% | -1.04% |
| lambada_openai | acc | 0.6912 | 0.6984 | +1.04% | 0.7006 | +1.36% | +0.31% | **0.7087** | **+2.53%** | +1.16% |
| lambada_openai | perplexity ↓ | 4.2433 | 4.0490 | -4.58% | 3.9616 | -6.64% | -2.16% | **3.8343** | **-9.63%** | -3.21% |
| openbookqa | acc | 0.3160 | 0.3180 | +0.63% | 0.3180 | +0.63% | ±0.00% | 0.3160 | ±0.00% | -0.63% |
| openbookqa | acc_norm | 0.4100 | 0.4120 | +0.49% | 0.4100 | ±0.00% | -0.49% | 0.4080 | -0.49% | -0.49% |
| piqa | acc | 0.7797 | 0.7807 | +0.13% | 0.7813 | +0.21% | +0.08% | 0.7786 | -0.14% | -0.35% |
| piqa | acc_norm | 0.7807 | 0.7807 | ±0.00% | 0.7813 | +0.08% | +0.08% | 0.7807 | ±0.00% | -0.08% |
Some very interesting results on diversity also:
**Diversity Metrics (Qwen3-4B-Base vs Style-Karcher, temperature=1.0, 8 completions per prompt)**
| Domain | Metric | Base | Karcher | Δ |
|--------|--------|:----:|:-------:|:-:|
| ao3_english | Prefix entropy | 3.309 | 3.238 | -2.1% |
| ao3_english | Distinct-1 | 0.618 | **0.683** | **+10.5%** |
| ao3_english | Distinct-2 | 0.962 | **0.984** | +2.3% |
| ao3_english | Pairwise diversity | 0.919 | **0.932** | +1.4% |
| github_python | Prefix entropy | 1.514 | 1.456 | -3.8% |
| github_python | Distinct-1 | 0.610 | **0.624** | +2.3% |
| github_python | Distinct-2 | 0.890 | 0.876 | -1.6% |
| github_python | Pairwise diversity | 0.933 | 0.933 | ±0.0% |
| wikipedia_english | Prefix entropy | 1.974 | 1.892 | -4.2% |
| wikipedia_english | Distinct-1 | 0.599 | 0.559 | -6.7% |
| wikipedia_english | Distinct-2 | 0.932 | 0.898 | -3.6% |
| wikipedia_english | Pairwise diversity | 0.907 | 0.900 | -0.8% |
| bbc_news | Prefix entropy | 2.252 | 2.186 | -2.9% |
| bbc_news | Distinct-1 | 0.557 | **0.577** | +3.6% |
| bbc_news | Distinct-2 | 0.949 | **0.951** | +0.3% |
| bbc_news | Pairwise diversity | 0.901 | **0.908** | +0.8% |
| arxiv_cs | Prefix entropy | 2.455 | 2.346 | -4.4% |
| arxiv_cs | Distinct-1 | 0.555 | **0.567** | +2.3% |
| arxiv_cs | Distinct-2 | 0.905 | **0.906** | +0.2% |
| arxiv_cs | Pairwise diversity | 0.895 | **0.901** | +0.7% |
Additional experiment (after quantization, should affect further training but not existing quants):
Initializing the \<think\>\</think\> tokens in embedding space.
Original embeddings were identical (cos=1.0) at 0.3x norm, untrained.
Optimized via AdamW on GSM8k reasoning traces with 3-shot prefix, loss on
reasoning+answer tokens, norm clamped to 1.5x avg embedding norm.
After: two distinct vectors (cos=0.07) at 1.5x norm.
GSM8k 3-shot accuracy: 96.7% (29/30) vs 90.0% with original embeddings.
CE loss improvement: +7.8% on held-out eval.
This is a merge of pre-trained language models created using [mergekit](https://github.com/cg123/mergekit).
## Merge Details
### Merge Method
This model was merged using the [Karcher Mean](https://en.wikipedia.org/wiki/Karcher_mean) merge method.
### Models Merged
The following models were included in the merge:
* ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave + ../rlvr-envs/grpo-github_javascript-mara-360m
* ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave + ../rlvr-envs/grpo-arxiv_cs-mara-360m
* ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave + ../rlvr-envs/grpo-general-ao3style-360m
* ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave + ../rlvr-envs/grpo-ao3_english-mara-360m
* ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave + ../rlvr-envs/grpo-arxiv_math-mara-360m
* ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave + ../rlvr-envs/grpo-github_python-mara-360m
* ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave + ../rlvr-envs/grpo-wikipedia_english-mara-360m
* ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave + ../rlvr-envs/grpo-arxiv_physics-mara-360m
* ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave + ../rlvr-envs/grpo-github_cpp-mara-360m
* ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave + ../rlvr-envs/grpo-bbc_news-mara-360m
* ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave + ../rlvr-envs/grpo-github_markdown-mara-360m
### Configuration
The following YAML configuration was used to produce this model:
```yaml
models:
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-ao3_english-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-arxiv_cs-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-arxiv_math-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-arxiv_physics-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-bbc_news-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-github_cpp-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-github_javascript-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-github_markdown-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-github_python-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-wikipedia_english-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-general-ao3style-360m
merge_method: karcher
dtype: bfloat16
tokenizer_source: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave
```

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{
"</think>": 151668,
"</tool_call>": 151658,
"</tool_response>": 151666,
"<think>": 151667,
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"<|endoftext|>": 151643,
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"<|fim_prefix|>": 151659,
"<|fim_suffix|>": 151661,
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"<|vision_start|>": 151652
}

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{%- if tools %}
{{- '<|im_start|>system\n' }}
{%- if messages[0].role == 'system' %}
{{- messages[0].content + '\n\n' }}
{%- endif %}
{{- "# Tools\n\nYou may call one or more functions to assist with the user query.\n\nYou are provided with function signatures within <tools></tools> XML tags:\n<tools>" }}
{%- for tool in tools %}
{{- "\n" }}
{{- tool | tojson }}
{%- endfor %}
{{- "\n</tools>\n\nFor each function call, return a json object with function name and arguments within <tool_call></tool_call> XML tags:\n<tool_call>\n{\"name\": <function-name>, \"arguments\": <args-json-object>}\n</tool_call><|im_end|>\n" }}
{%- else %}
{%- if messages[0].role == 'system' %}
{{- '<|im_start|>system\n' + messages[0].content + '<|im_end|>\n' }}
{%- endif %}
{%- endif %}
{%- set ns = namespace(multi_step_tool=true, last_query_index=messages|length - 1) %}
{%- for message in messages[::-1] %}
{%- set index = (messages|length - 1) - loop.index0 %}
{%- if ns.multi_step_tool and message.role == "user" and not(message.content.startswith('<tool_response>') and message.content.endswith('</tool_response>')) %}
{%- set ns.multi_step_tool = false %}
{%- set ns.last_query_index = index %}
{%- endif %}
{%- endfor %}
{%- for message in messages %}
{%- if (message.role == "user") or (message.role == "system" and not loop.first) %}
{{- '<|im_start|>' + message.role + '\n' + message.content + '<|im_end|>' + '\n' }}
{%- elif message.role == "assistant" %}
{%- set content = message.content %}
{%- set reasoning_content = '' %}
{%- if message.reasoning_content is defined and message.reasoning_content is not none %}
{%- set reasoning_content = message.reasoning_content %}
{%- else %}
{%- if '</think>' in message.content %}
{%- set content = message.content.split('</think>')[-1].lstrip('\n') %}
{%- set reasoning_content = message.content.split('</think>')[0].rstrip('\n').split('<think>')[-1].lstrip('\n') %}
{%- endif %}
{%- endif %}
{%- if loop.index0 > ns.last_query_index %}
{%- if loop.last or (not loop.last and reasoning_content) %}
{{- '<|im_start|>' + message.role + '\n<think>\n' + reasoning_content.strip('\n') + '\n</think>\n\n' + content.lstrip('\n') }}
{%- else %}
{{- '<|im_start|>' + message.role + '\n' + content }}
{%- endif %}
{%- else %}
{{- '<|im_start|>' + message.role + '\n' + content }}
{%- endif %}
{%- if message.tool_calls %}
{%- for tool_call in message.tool_calls %}
{%- if (loop.first and content) or (not loop.first) %}
{{- '\n' }}
{%- endif %}
{%- if tool_call.function %}
{%- set tool_call = tool_call.function %}
{%- endif %}
{{- '<tool_call>\n{"name": "' }}
{{- tool_call.name }}
{{- '", "arguments": ' }}
{%- if tool_call.arguments is string %}
{{- tool_call.arguments }}
{%- else %}
{{- tool_call.arguments | tojson }}
{%- endif %}
{{- '}\n</tool_call>' }}
{%- endfor %}
{%- endif %}
{{- '<|im_end|>\n' }}
{%- elif message.role == "tool" %}
{%- if loop.first or (messages[loop.index0 - 1].role != "tool") %}
{{- '<|im_start|>user' }}
{%- endif %}
{{- '\n<tool_response>\n' }}
{{- message.content }}
{{- '\n</tool_response>' }}
{%- if loop.last or (messages[loop.index0 + 1].role != "tool") %}
{{- '<|im_end|>\n' }}
{%- endif %}
{%- endif %}
{%- endfor %}
{%- if add_generation_prompt %}
{{- '<|im_start|>assistant\n' }}
{%- if enable_thinking is defined and enable_thinking is false %}
{{- '<think>\n\n</think>\n\n' }}
{%- endif %}
{%- endif %}

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{
"architectures": [
"Qwen3ForCausalLM"
],
"attention_bias": false,
"attention_dropout": 0.0,
"bos_token_id": 151643,
"dtype": "bfloat16",
"eos_token_id": 151643,
"head_dim": 128,
"hidden_act": "silu",
"hidden_size": 2560,
"initializer_range": 0.02,
"intermediate_size": 9728,
"layer_types": [
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"full_attention",
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],
"max_position_embeddings": 32768,
"max_window_layers": 36,
"model_type": "qwen3",
"num_attention_heads": 32,
"num_hidden_layers": 36,
"num_key_value_heads": 8,
"rms_norm_eps": 1e-06,
"rope_scaling": null,
"rope_theta": 1000000,
"sliding_window": null,
"tie_word_embeddings": true,
"transformers_version": "4.57.3",
"use_cache": true,
"use_sliding_window": false,
"vocab_size": 151669
}

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{
"_from_model_config": true,
"bos_token_id": 151643,
"eos_token_id": 151643,
"transformers_version": "4.57.3"
}

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models:
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-ao3_english-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-arxiv_cs-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-arxiv_math-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-arxiv_physics-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-bbc_news-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-github_cpp-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-github_javascript-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-github_markdown-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-github_python-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-wikipedia_english-mara-360m
- model: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave+../rlvr-envs/grpo-general-ao3style-360m
merge_method: karcher
dtype: bfloat16
tokenizer_source: ../rlvr-envs/Qwen3-4B-Base-Continued-GRPO-Wave

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