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Model: tensorhydra/gpt-oss-20b-numinamath
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---
license: mit
base_model: gpt-oss-20b
tags:
- math
- reasoning
- lora
- mixture-of-experts
- transformers
- peft
datasets:
- AI-MO/NuminaMath-TIR
---
# GPT-OSS-20B NuminaMath
## Overview
This repository provides GPT-OSS-20B model fine-tuned on the NuminaMath-TIR dataset which consists of 70k data points to improve mathematical olympiad reasoning and structured problem solving.
The adapters are designed to be used with the base model gpt-oss-20b, a Mixture-of-Experts (MoE) transformer architecture. Fine-tuning focuses on improving the models ability to generate step-by-step reasoning, symbolic manipulation, and detailed mathematical explanations when solving math problems.
Instead of updating the full model weights, parameter-efficient fine-tuning (PEFT) was used to modify only a small number of parameters in the attention layers. This allows the adapters to significantly improve reasoning ability while keeping training compute requirements relatively low.
The resulting LoRA adapters can be loaded on top of the base model to enhance its performance on mathematical olympiad reasoning tasks such as algebra, arithmetic, and problem-solving explanations.
---
# Model Details
| Field | Value |
| ------------------ | ------------------------------ |
| Base Model | gpt-oss-20b |
| Architecture | Mixture-of-Experts Transformer |
| Fine-Tuning Method | LoRA (PEFT) |
| Precision | BF16 |
| Context Length | 8192 tokens |
| Training Hardware | NVIDIA H100 |
| Framework | PyTorch + Transformers + PEFT |
---
# Training Data
## Dataset
The model was fine-tuned using the **NuminaMath-TIR dataset**, which contains mathematical problems paired with structured reasoning traces and final answers.
Dataset link:
https://huggingface.co/datasets/AI-MO/NuminaMath-TIR
The dataset includes problems across several mathematical domains including:
* arithmetic
* algebra
* number theory
* geometry
* calculus
* reasoning-based problem solving
The dataset emphasizes **step-by-step explanations**, allowing the model to learn how to produce reasoning chains rather than only final answers.
---
## Dataset Processing
The dataset was originally provided as a **CSV file** and processed prior to training.
Processing pipeline:
1. Loaded using **pandas**
2. Columns normalized to:
* `prompt`
* `response`
3. Empty rows removed
4. Converted to **Hugging Face Dataset format**
5. Randomized train/validation split
Dataset split:
| Split | Percentage |
| ---------- | ---------- |
| Train | 95% |
| Validation | 5% |
---
# Instruction Format
Training samples were converted into the following **chat-style instruction format** compatible with the GPT-OSS tokenizer.
```
<|im_start|>user
{prompt}
<|im_end|>
<|im_start|>assistant
{response}
<|im_end|>
```
This format enables the model to learn **structured conversational reasoning** and aligns with the instruction format used in many modern LLMs.
---
# Training Procedure
The model was fine-tuned using **LoRA adapters applied only to attention layers**.
Because **gpt-oss-20b is a Mixture-of-Experts (MoE) architecture**, LoRA was intentionally **not applied to expert layers** in order to preserve the routing structure and maintain training stability.
---
## LoRA Target Modules
Adapters were applied to the following projection layers:
```
q_proj
k_proj
v_proj
o_proj
```
These correspond to the **query, key, value, and output projections** within the attention mechanism.
---
## LoRA Configuration
| Parameter | Value |
| --------- | ----- |
| Rank (r) | 64 |
| Alpha | 128 |
| Dropout | 0.05 |
| Bias | none |
Only attention projections were modified, ensuring minimal disruption to the base model while still enabling meaningful behavioral improvements.
---
# Training Hyperparameters
| Parameter | Value |
| ----------------- | ------------- |
| Epochs | 2 |
| Learning Rate | 2e-4 |
| Optimizer | AdamW (fused) |
| Adam β1 | 0.9 |
| Adam β2 | 0.95 |
| Weight Decay | 0.01 |
| Warmup Ratio | 0.03 |
| Max Gradient Norm | 1.0 |
Batch configuration:
| Parameter | Value |
| --------------------- | ----- |
| Per Device Batch Size | 4 |
| Gradient Accumulation | 4 |
| Effective Batch Size | 16 |
Maximum sequence length:
```
8192 tokens
```
---
# Training Infrastructure
Training was performed on the following hardware:
```
1× NVIDIA H100 GPU
```
Training optimizations included:
* Flash Attention 2
* BF16 mixed precision
* TF32 enabled
* Gradient checkpointing
* memory-optimized LoRA configuration
MoE compatibility adjustments included:
* LoRA applied **only to attention layers**
* CPU offloading disabled
* gradient checkpointing configured with `use_reentrant=False`
Training frameworks used:
* PyTorch
* Hugging Face Transformers
* PEFT
* Hugging Face Datasets
---
# Evaluation
Validation was performed periodically during training using **validation loss**.
Metrics monitored:
* training loss
* validation loss
The model was trained for exactly 2 epochs on the entire dataset without automated checkpoint selection. The final validation loss is 0.4039 for 2 full epochs.
![Training Loss](loss_plot.png)
---
# Intended Use
This model is intended for:
* mathematical reasoning research
* educational demonstrations
* experimentation with reasoning-focused fine-tuning
* evaluation of math-capable language models
It is **not intended for high-stakes mathematical or scientific applications**.
---
# Limitations
Despite improvements from fine-tuning, the model still has several limitations:
* The model may generate **incorrect reasoning steps**.
* Mathematical derivations may lack **formal rigor**.
* Some areas of mathematics may be **underrepresented in the dataset**.
* Performance depends strongly on the **capabilities of the base model**.
Users should treat model outputs as **assistive suggestions rather than authoritative answers**.
---
# Ethical Considerations
Language models trained for reasoning may produce **confident but incorrect explanations**.
For educational or academic use:
* outputs should be verified independently
* the model should not be treated as an authoritative mathematical source
---
# Acknowledgements
This work builds upon the open-source ecosystem including:
* Hugging Face Transformers
* the PEFT library for parameter-efficient fine-tuning
* the NuminaMath dataset
* research on Mixture-of-Experts transformer architectures
---
# Citation
Dataset:
https://huggingface.co/datasets/AI-MO/NuminaMath-TIR
Training Notebook:
https://www.kaggle.com/code/tensorhydra/gpt-oss-20b-finetune-numinamath

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{# Copyright 2025-present Unsloth. Apache 2.0 License. Unsloth chat template fixes. Edited from ggml-org & OpenAI #}
{#-
In addition to the normal inputs of `messages` and `tools`, this template also accepts the
following kwargs:
- "builtin_tools": A list, can contain "browser" and/or "python".
- "model_identity": A string that optionally describes the model identity.
- "reasoning_effort": A string that describes the reasoning effort, defaults to "medium".
#}
{#- Tool Definition Rendering ============================================== #}
{%- macro render_typescript_type(param_spec, required_params, is_nullable=false) -%}
{%- if param_spec.type == "array" -%}
{%- if param_spec['items'] -%}
{%- if param_spec['items']['type'] == "string" -%}
{{- "string[]" }}
{%- elif param_spec['items']['type'] == "number" -%}
{{- "number[]" }}
{%- elif param_spec['items']['type'] == "integer" -%}
{{- "number[]" }}
{%- elif param_spec['items']['type'] == "boolean" -%}
{{- "boolean[]" }}
{%- else -%}
{%- set inner_type = render_typescript_type(param_spec['items'], required_params) -%}
{%- if inner_type == "object | object" or inner_type|length > 50 -%}
{{- "any[]" }}
{%- else -%}
{{- inner_type + "[]" }}
{%- endif -%}
{%- endif -%}
{%- if param_spec.nullable -%}
{{- " | null" }}
{%- endif -%}
{%- else -%}
{{- "any[]" }}
{%- if param_spec.nullable -%}
{{- " | null" }}
{%- endif -%}
{%- endif -%}
{%- elif param_spec.type is defined and param_spec.type is iterable and param_spec.type is not string and param_spec.type is not mapping and param_spec.type[0] is defined -%}
{#- Handle array of types like ["object", "object"] from Union[dict, list] #}
{%- if param_spec.type | length > 1 -%}
{{- param_spec.type | join(" | ") }}
{%- else -%}
{{- param_spec.type[0] }}
{%- endif -%}
{%- elif param_spec.oneOf -%}
{#- Handle oneOf schemas - check for complex unions and fallback to any #}
{%- set has_object_variants = false -%}
{%- for variant in param_spec.oneOf -%}
{%- if variant.type == "object" -%}
{%- set has_object_variants = true -%}
{%- endif -%}
{%- endfor -%}
{%- if has_object_variants and param_spec.oneOf|length > 1 -%}
{{- "any" }}
{%- else -%}
{%- for variant in param_spec.oneOf -%}
{{- render_typescript_type(variant, required_params) -}}
{%- if variant.description %}
{{- "// " + variant.description }}
{%- endif -%}
{%- if variant.default is defined %}
{{ "// default: " + variant.default|tojson }}
{%- endif -%}
{%- if not loop.last %}
{{- " | " }}
{% endif -%}
{%- endfor -%}
{%- endif -%}
{%- elif param_spec.type == "string" -%}
{%- if param_spec.enum -%}
{{- '"' + param_spec.enum|join('" | "') + '"' -}}
{%- else -%}
{{- "string" }}
{%- if param_spec.nullable %}
{{- " | null" }}
{%- endif -%}
{%- endif -%}
{%- elif param_spec.type == "number" -%}
{{- "number" }}
{%- elif param_spec.type == "integer" -%}
{{- "number" }}
{%- elif param_spec.type == "boolean" -%}
{{- "boolean" }}
{%- elif param_spec.type == "object" -%}
{%- if param_spec.properties -%}
{{- "{\n" }}
{%- for prop_name, prop_spec in param_spec.properties.items() -%}
{{- prop_name -}}
{%- if prop_name not in (param_spec.required or []) -%}
{{- "?" }}
{%- endif -%}
{{- ": " }}
{{ render_typescript_type(prop_spec, param_spec.required or []) }}
{%- if not loop.last -%}
{{-", " }}
{%- endif -%}
{%- endfor -%}
{{- "}" }}
{%- else -%}
{{- "object" }}
{%- endif -%}
{%- else -%}
{{- "any" }}
{%- endif -%}
{%- endmacro -%}
{%- macro render_tool_namespace(namespace_name, tools) -%}
{{- "## " + namespace_name + "\n\n" }}
{{- "namespace " + namespace_name + " {\n\n" }}
{%- for tool in tools %}
{%- set tool = tool.function %}
{{- "// " + tool.description + "\n" }}
{{- "type "+ tool.name + " = " }}
{%- if tool.parameters and tool.parameters.properties -%}
{{- "(_: " }}
{{- "{\n" }}
{%- for param_name, param_spec in tool.parameters.properties.items() %}
{{- "// " + param_spec.description + "\n" }}
{{- param_name }}
{%- if param_name not in (tool.parameters.required or []) -%}
{{- "?" }}
{%- endif -%}
{{- ": " }}
{{- render_typescript_type(param_spec, tool.parameters.required or []) }}
{%- if param_spec.default is defined -%}
{%- if param_spec.enum %}
{{- ", // default: " + param_spec.default }}
{%- elif param_spec.oneOf %}
{{- "// default: " + param_spec.default }}
{%- else %}
{{- ", // default: " + param_spec.default|tojson }}
{%- endif -%}
{%- endif -%}
{%- if not loop.last %}
{{- ",\n" }}
{%- else %}
{{- "\n" }}
{%- endif -%}
{%- endfor %}
{{- "}) => any;\n\n" }}
{%- else -%}
{{- "() => any;\n\n" }}
{%- endif -%}
{%- endfor %}
{{- "} // namespace " + namespace_name }}
{%- endmacro -%}
{%- macro render_builtin_tools(browser_tool, python_tool) -%}
{%- if browser_tool %}
{{- "## browser\n\n" }}
{{- "// Tool for browsing.\n" }}
{{- "// The `cursor` appears in brackets before each browsing display: `[{cursor}]`.\n" }}
{{- "// Cite information from the tool using the following format:\n" }}
{{- "// `【{cursor}†L{line_start}(-L{line_end})?】`, for example: `【6†L9-L11】` or `【8†L3】`.\n" }}
{{- "// Do not quote more than 10 words directly from the tool output.\n" }}
{{- "// sources=web (default: web)\n" }}
{{- "namespace browser {\n\n" }}
{{- "// Searches for information related to `query` and displays `topn` results.\n" }}
{{- "type search = (_: {\n" }}
{{- "query: string,\n" }}
{{- "topn?: number, // default: 10\n" }}
{{- "source?: string,\n" }}
{{- "}) => any;\n\n" }}
{{- "// Opens the link `id` from the page indicated by `cursor` starting at line number `loc`, showing `num_lines` lines.\n" }}
{{- "// Valid link ids are displayed with the formatting: `【{id}†.*】`.\n" }}
{{- "// If `cursor` is not provided, the most recent page is implied.\n" }}
{{- "// If `id` is a string, it is treated as a fully qualified URL associated with `source`.\n" }}
{{- "// If `loc` is not provided, the viewport will be positioned at the beginning of the document or centered on the most relevant passage, if available.\n" }}
{{- "// Use this function without `id` to scroll to a new location of an opened page.\n" }}
{{- "type open = (_: {\n" }}
{{- "id?: number | string, // default: -1\n" }}
{{- "cursor?: number, // default: -1\n" }}
{{- "loc?: number, // default: -1\n" }}
{{- "num_lines?: number, // default: -1\n" }}
{{- "view_source?: boolean, // default: false\n" }}
{{- "source?: string,\n" }}
{{- "}) => any;\n\n" }}
{{- "// Finds exact matches of `pattern` in the current page, or the page given by `cursor`.\n" }}
{{- "type find = (_: {\n" }}
{{- "pattern: string,\n" }}
{{- "cursor?: number, // default: -1\n" }}
{{- "}) => any;\n\n" }}
{{- "} // namespace browser\n\n" }}
{%- endif -%}
{%- if python_tool %}
{{- "## python\n\n" }}
{{- "Use this tool to execute Python code in your chain of thought. The code will not be shown to the user. This tool should be used for internal reasoning, but not for code that is intended to be visible to the user (e.g. when creating plots, tables, or files).\n\n" }}
{{- "When you send a message containing Python code to python, it will be executed in a stateful Jupyter notebook environment. python will respond with the output of the execution or time out after 120.0 seconds. The drive at '/mnt/data' can be used to save and persist user files. Internet access for this session is UNKNOWN. Depends on the cluster.\n\n" }}
{%- endif -%}
{%- endmacro -%}
{#- System Message Construction ============================================ #}
{%- macro build_system_message() -%}
{%- if model_identity is not defined %}
{{- "You are ChatGPT, a large language model trained by OpenAI.\n" -}}
{%- else %}
{{- model_identity }}
{%- endif %}
{{- "Knowledge cutoff: 2024-06\n" }}
{{- "Current date: " + strftime_now("%Y-%m-%d") + "\n\n" }}
{%- if reasoning_effort is not defined %}
{%- set reasoning_effort = "medium" %}
{%- endif %}
{{- "Reasoning: " + reasoning_effort + "\n\n" }}
{%- if builtin_tools is defined %}
{{- "# Tools\n\n" }}
{%- set available_builtin_tools = namespace(browser=false, python=false) %}
{%- for tool in builtin_tools %}
{%- if tool == "browser" %}
{%- set available_builtin_tools.browser = true %}
{%- elif tool == "python" %}
{%- set available_builtin_tools.python = true %}
{%- endif %}
{%- endfor %}
{{- render_builtin_tools(available_builtin_tools.browser, available_builtin_tools.python) }}
{%- endif -%}
{{- "# Valid channels: analysis, commentary, final. Channel must be included for every message." }}
{%- if tools is defined -%}
{{- "\nCalls to these tools must go to the commentary channel: 'functions'." }}
{%- endif -%}
{%- endmacro -%}
{#- Main Template Logic ================================================= #}
{#- Set defaults #}
{#- Render system message #}
{{- "<|start|>system<|message|>" }}
{{- build_system_message() }}
{{- "<|end|>" }}
{#- Extract developer message #}
{%- if messages[0].role == "developer" or messages[0].role == "system" %}
{%- set developer_message = messages[0].content %}
{%- set loop_messages = messages[1:] %}
{%- else %}
{%- set developer_message = "" %}
{%- set loop_messages = messages %}
{%- endif %}
{#- Render developer message #}
{%- if developer_message or tools %}
{{- "<|start|>developer<|message|>" }}
{%- if developer_message %}
{{- "# Instructions\n\n" }}
{{- developer_message }}
{%- endif %}
{%- if tools -%}
{{- "\n\n" }}
{{- "# Tools\n\n" }}
{{- render_tool_namespace("functions", tools) }}
{%- endif -%}
{{- "<|end|>" }}
{%- endif %}
{#- Render messages #}
{%- set last_tool_call = namespace(name=none) %}
{%- for message in loop_messages -%}
{#- At this point only assistant/user/tool messages should remain #}
{%- if message.role == 'assistant' -%}
{%- if "tool_calls" in message %}
{#- We assume max 1 tool call per message, and so we infer the tool call name #}
{#- in "tool" messages from the most recent assistant tool call name #}
{%- set tool_call = message.tool_calls[0] %}
{%- if tool_call.function %}
{%- set tool_call = tool_call.function %}
{%- endif %}
{%- if message.content %}
{{- "<|start|>assistant<|channel|>analysis<|message|>" + message.content + "<|end|>" }}
{%- endif %}
{{- "<|start|>assistant to=" }}
{{- "functions." + tool_call.name + "<|channel|>commentary json<|message|>" }}
{{- tool_call.arguments|tojson }}
{{- "<|call|>" }}
{%- set last_tool_call.name = tool_call.name %}
{%- elif "thinking" in message and loop.last and not add_generation_prompt %}
{#- Only render the CoT if the final turn is an assistant turn and add_generation_prompt is false #}
{#- This is a situation that should only occur in training, never in inference. #}
{{- "<|start|>assistant<|channel|>analysis<|message|>" + message.thinking + "<|end|>" }}
{#- <|return|> indicates the end of generation, but <|end|> does not #}
{#- <|return|> should never be an input to the model, but we include it as the final token #}
{#- when training, so the model learns to emit it. #}
{{- "<|start|>assistant<|channel|>final<|message|>" + message.content + "<|return|>" }}
{%- set last_tool_call.name = none %}
{%- elif "thinking" in message %}
{#- CoT is dropped during all previous turns, so we never render it for inference #}
{{- "<|start|>assistant<|channel|>final<|message|>" + message.content + "<|end|>" }}
{%- set last_tool_call.name = none %}
{%- elif loop.last and not add_generation_prompt %}
{#- <|return|> indicates the end of generation, but <|end|> does not #}
{#- <|return|> should never be an input to the model, but we include it as the final token #}
{#- when training, so the model learns to emit it. #}
{{- "<|start|>assistant<|message|>" + message.content + "<|return|>" }}
{%- else %}
{{- "<|start|>assistant<|message|>" + message.content + "<|end|>" }}
{%- set last_tool_call.name = none %}
{%- endif %}
{%- elif message.role == 'tool' -%}
{%- if last_tool_call.name is none %}
{{- raise_exception("Message has tool role, but there was no previous assistant message with a tool call!") }}
{%- endif %}
{{- "<|start|>functions." + last_tool_call.name }}
{{- " to=assistant<|channel|>commentary<|message|>" + message.content|tojson + "<|end|>" }}
{%- else -%}
{{- "<|start|>user<|message|>" + message.content + "<|end|>" }}
{%- endif -%}
{%- endfor -%}
{#- Generation prompt #}
{%- if add_generation_prompt -%}
<|start|>assistant
{%- endif -%}
{# Copyright 2025-present Unsloth. Apache 2.0 License. Unsloth chat template fixes. Edited from ggml-org & OpenAI #}

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{
"architectures": [
"GptOssForCausalLM"
],
"attention_bias": true,
"attention_dropout": 0.0,
"dtype": "bfloat16",
"eos_token_id": 200002,
"experts_per_token": 4,
"head_dim": 64,
"hidden_act": "silu",
"hidden_size": 2880,
"initial_context_length": 4096,
"initializer_range": 0.02,
"intermediate_size": 2880,
"layer_types": [
"sliding_attention",
"full_attention",
"sliding_attention",
"full_attention",
"sliding_attention",
"full_attention",
"sliding_attention",
"full_attention",
"sliding_attention",
"full_attention",
"sliding_attention",
"full_attention",
"sliding_attention",
"full_attention",
"sliding_attention",
"full_attention",
"sliding_attention",
"full_attention",
"sliding_attention",
"full_attention",
"sliding_attention",
"full_attention",
"sliding_attention",
"full_attention"
],
"max_position_embeddings": 131072,
"model_type": "gpt_oss",
"num_attention_heads": 64,
"num_experts_per_tok": 4,
"num_hidden_layers": 24,
"num_key_value_heads": 8,
"num_local_experts": 32,
"output_router_logits": false,
"pad_token_id": 200017,
"rms_norm_eps": 1e-05,
"rope_scaling": {
"beta_fast": 32.0,
"beta_slow": 1.0,
"factor": 32.0,
"original_max_position_embeddings": 4096,
"rope_type": "yarn",
"truncate": false
},
"rope_theta": 150000,
"router_aux_loss_coef": 0.9,
"sliding_window": 128,
"swiglu_limit": 7.0,
"tie_word_embeddings": false,
"transformers_version": "4.57.1",
"unsloth_fixed": true,
"use_cache": true,
"vocab_size": 201088
}

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