graph LR idea_026caa3e_a121_405a_97a9_1dbe887597e6["Transformer Architecture"] idea_0859f001_2440_4fa0_956b_9d09ad6a4008["Single-Node End-to-End Replication of a GPT-2-Grade Model"] idea_0bc50385_51ee_4142_a9a7_3eb23e5132d2["Perplexity as a Language Model Evaluation Metric"] idea_134d76b8_e5db_4565_86b7_aa49cb7eecf7["Instruction Tuning of Large Language Models"] idea_1559efe3_8366_4f17_b093_74892c51e927["Sine and Cosine Function Graphs Trigonometry"] idea_1ae48a6d_c005_4501_90ce_2c48efb26a8e["Autoregressive Language Modeling"] idea_1cde3625_c7b3_4694_a913_a7351affca03["Log Likelihood in Probabilistic Language Models"] idea_2091cfd9_1c36_4fcd_a4e1_2aa25cb5d431["Muon and Orthogonalised-Momentum Optimisers for Pretraining"] idea_20a07eb6_bbd2_4da8_a3e9_05351af5d541["Tokenizer Artefacts Behind Arithmetic and Spelling Failures"] idea_2132fb22_760b_47ad_a3f5_b8bea6818535["Matrix Multiplication Rules in Linear Algebra"] idea_26c72438_a206_4cd5_8d94_b4d955991b15["Causal Masking That Prevents a Token Attending to Its Future"] idea_28d3fde8_1e14_429f_b344_6389a6f642c7["Byte Pair Encoding"] idea_28f8e056_82d8_4577_856d_73fb3875a368["Rotation Matrices"] idea_2f4e9d3e_314f_421c_857f_1a1d1840a544["FlashAttention"] idea_3372de9b_11ab_4b61_b59a_d4a994eec965["Neural Scaling Laws"] idea_348fa3ba_f930_4b98_b286_a02ec690972b["Vector Components and Coordinates in Euclidean Space"] idea_35762d20_d5fd_4100_90a4_09e6bda3d352["Encoder and Vision Models That Still Ship Absolute Positional Embeddings"] idea_357f3a42_62ac_4cb6_8286_402137835a8f["Learned Reward Models Where No Verifier Exists"] idea_37b8cfba_6282_48ad_ba16_36ee53fed4a8["Attention Mechanism"] idea_380b1a1a_6c4b_4026_a920_80ec6f426d1c["Dot Product"] idea_39b3bbcc_05da_4992_aad3_f48527707aaa["Softmax Function"] idea_3e13e9d6_51df_45d0_aeab_ecdaab415757["Probability Distributions over Finite Outcomes"] idea_3e490fe5_6daf_4e09_85ab_7787a2e45edb["Positional Encoding and Length Extrapolation"] idea_42a66e36_e5d9_4094_a320_439ca9d3a3dc["Dense Models Where Memory Footprint Beats Parameter Count"] idea_4520548e_1f4c_4323_8d91_806862b3a3b1["The Unembedding Projection from Hidden State to Vocabulary Logits"] idea_45939e47_b677_4c01_9cc5_223c2b684c27["Group-Relative Policy Optimization and Verifiable Rewards"] idea_46647ead_fe14_4353_8a24_9331a5274341["Beam Search Decoding for Sequence Generation"] idea_4cd5b655_dc4d_4bac_8efd_a9d8eacee3a7["Feedforward Networks (MLPs) in Transformers"] idea_4d89cc27_dbaa_4486_8f00_99cbc853af60["GPU Memory Hierarchy"] idea_4e7a9c35_dd9c_40b5_b907_d6fdeedeb485["Tokenization"] idea_55f443c4_8d2f_4ddc_a47e_92c40b2f39b0["Large Language Models Predict Next Words Using Transformer Attention Mechanisms"] idea_560b907b_90d1_421d_9b57_16f84bd4063b["Full Multi-Head Attention Where the KV Cache Is Not the Constraint"] idea_5887a366_4a4f_43b0_a5d3_355c524198e9["Grouped-Query and Multi-Query Attention"] idea_5ee4ce8a_ca1d_4097_bbc9_b34b3c299631["A Vector Represents a Discrete Symbol as a List of Numbers"] idea_5f68aa37_e831_49c9_a5ec_b8143369eca1["Rotary Position Embeddings (RoPE)"] idea_5f964e9f_1680_4dd2_9522_7ffe33552992["Self Attention Mechanism in Transformers"] idea_617957b9_fd69_4219_b136_d16b1d8d3e80["Dot Product for Vector Similarity Scoring"] idea_69de4d34_a1d7_4f63_b191_c145d1c8ed7d["Quadratic Cost of Self-Attention in Sequence Length"] idea_6e10cddd_724a_4c35_87e2_056a2a21157e["Bayes' Theorem in Probability"] idea_75d76a55_fcd9_409e_8563_d94cdca1e5f2["Token Embeddings"] idea_7c6b5143_f6d8_4a7c_80dc_78b171112e4b["Multi-Head Attention"] idea_7ce0fed4_73af_4498_ad54_42178e7209ec["Recurrent Sequence-to-Sequence Translation with a Single Context Vector"] idea_7fe4a0a9_381c_4509_835d_55eaa386afbc["Multi-Head Latent Attention and Low-Rank KV Compression"] idea_844f43d7_914b_4db3_9ce9_c8465d1edf5b["Temperature and Sampling in Language Model Decoding"] idea_885a21d3_8eb3_4f6c_bfaf_4e13887dab30["Large Language Models in Natural Language Processing"] idea_8dc6b374_6fc8_4905_8df8_5f6c566128cf["Weighted Sum Plus Bias Activation Calculation Methods"] idea_92f0bfa6_5942_4965_985e_d16291ed5d0c["Power Laws"] idea_95a51e4e_b288_428b_af41_646e6680b8b8["Top-p and Top-k Truncation of the Sampling Tail"] idea_96f7f65a_928a_4ce9_8f6f_6cefe2b2f969["Residual Connections and Layer Normalization"] idea_98f9edb2_7a0c_4dec_a9e5_57106880b42b["Sequential Dependency as the Barrier to Parallel Training"] idea_9c67b7b9_775d_4570_9c4b_07726805cad0["Explicit Attention Matrices for Interpretability and Custom Masks"] idea_9cdb37b8_738a_4621_a3ff_8725390507e6["Reinforcement Learning from Human Feedback (RLHF)"] idea_9eb258ac_8cf0_4488_a818_c7042a530a0e["Pretraining of Large Language Models at Scale"] idea_a7ace413_fb9b_4e75_a012_b3e4bfbc71e2["KL Divergence"] idea_aab21bef_33a6_428f_af4e_340436c8ac35["Agent-Driven Overnight Search Over Training Code"] idea_ad9fa65f_e4c0_464b_8ad0_a5a5f57e61f1["Mean and Standard Deviation"] idea_af4e05dd_920f_49a7_ae93_83f80d448c58["Mixture of Experts in Deep Learning"] idea_b243628c_ef71_42ec_a2c9_beecf5bb501b["Cross-Entropy as an Optimisation Objective"] idea_b36de16b_09ff_43ed_a231_8b001c6de60d["Dot Product Operation for Vectors in Linear Algebra"] idea_b39d1370_c081_4a68_ad1b_b50ca99870f7["Decoding as a Memory-Bandwidth-Bound Workload"] idea_b6e4378d_1cbb_41a7_b89b_c5d026d16423["Unicode and UTF-8 Byte Encoding of Text"] idea_bd0ce92b_08d9_448a_95f3_a24fd862685a["Causal Masking for Autoregressive Generation"] idea_c4939875_4474_448b_98d6_96ff4f331df6["Policy Gradient Methods (PPO)"] idea_cea01eae_b1a3_49ff_a362_87d8d796874c["Backpropagation: Computing Gradients via the Chain Rule"] idea_d0299636_6dfd_4e6b_b491_3074d1aec36e["Large Language Model Pretraining and Training Corpus Quality"] idea_d09a3be6_d61f_4ad5_ae7f_5edb8905cb40["Greedy Decoding and Its Degeneration into Repetition"] idea_db9e963a_9972_471c_bc63_1c6566582a7d["Cross-Entropy Loss"] idea_dbf562d0_1ab2_4073_abef_c2ec084b8713["Materialising the Full Attention Matrix in High-Bandwidth Memory"] idea_df51313c_4ae6_4cad_b2d0_342b3508bd25["High-Dimensional Vector Spaces in Machine Learning"] idea_df7c909a_d36d_4b10_9e66_8e6c6ec89a4a["Softmax Function in Deep Learning"] idea_e4fe9fbf_bf5b_4fa9_84b1_a2b4db28e7ae["Stochastic Gradient Descent and the Adam Optimizer"] idea_eb1d2389_8413_4617_9886_1430d18b54e1["Direct Preference Optimization Without a Separate Reward Model"] idea_ee709cbd_eaab_4f90_8759_77b884f5b336["Weighted Sum Aggregation for Value Vectors"] idea_f127094c_0eac_440d_a8b0_42b702ccdaf1["Chain Rule of Probability for Sequences"] idea_f1ea7bff_39c3_4e2b_9bac_025a4bd75c62["Tokenization and the Vocabulary Trade-Off"] idea_f3cd8ca5_4b24_425f_9595_87cea67fca82["Exponential Function Properties in Algebra"] idea_f4ce9f25_56ce_42f1_8ba0_817d71bf12df["Dense Parameter Scaling Where Every Token Activates Every Weight"] idea_f7b9d806_5a3c_484e_9bfe_de8dbf62467a["Neural Network Architecture with Input Hidden Output Layers"] idea_f7ed21f1_3751_4714_b12d_850bb3d6e2b2["One-Hot Encoding"] idea_fc3428ef_cd41_4f3a_9393_2fb147d92600["KV Caching and Grouped-Query Attention"] idea_fcb2741c_5927_4c5e_aed6_1a58d5cadac8["Positional Encoding"] idea_ffcb7720_c1e7_4cdd_bbee_8a1bde6e4104["Activation Functions"] idea_2f4e9d3e_314f_421c_857f_1a1d1840a544 --> idea_9c67b7b9_775d_4570_9c4b_07726805cad0 idea_75d76a55_fcd9_409e_8563_d94cdca1e5f2 --> idea_5f964e9f_1680_4dd2_9522_7ffe33552992 idea_d09a3be6_d61f_4ad5_ae7f_5edb8905cb40 --> idea_46647ead_fe14_4353_8a24_9331a5274341 idea_5f964e9f_1680_4dd2_9522_7ffe33552992 --> idea_69de4d34_a1d7_4f63_b191_c145d1c8ed7d idea_1ae48a6d_c005_4501_90ce_2c48efb26a8e --> idea_fc3428ef_cd41_4f3a_9393_2fb147d92600 idea_4520548e_1f4c_4323_8d91_806862b3a3b1 --> idea_df7c909a_d36d_4b10_9e66_8e6c6ec89a4a idea_1559efe3_8366_4f17_b093_74892c51e927 --> idea_fcb2741c_5927_4c5e_aed6_1a58d5cadac8 idea_5f964e9f_1680_4dd2_9522_7ffe33552992 --> idea_026caa3e_a121_405a_97a9_1dbe887597e6 idea_95a51e4e_b288_428b_af41_646e6680b8b8 --> idea_46647ead_fe14_4353_8a24_9331a5274341 idea_b6e4378d_1cbb_41a7_b89b_c5d026d16423 --> idea_4e7a9c35_dd9c_40b5_b907_d6fdeedeb485 idea_7c6b5143_f6d8_4a7c_80dc_78b171112e4b --> idea_026caa3e_a121_405a_97a9_1dbe887597e6 idea_df7c909a_d36d_4b10_9e66_8e6c6ec89a4a --> idea_5f964e9f_1680_4dd2_9522_7ffe33552992 idea_9eb258ac_8cf0_4488_a818_c7042a530a0e --> idea_3372de9b_11ab_4b61_b59a_d4a994eec965 idea_e4fe9fbf_bf5b_4fa9_84b1_a2b4db28e7ae --> idea_2091cfd9_1c36_4fcd_a4e1_2aa25cb5d431 idea_9eb258ac_8cf0_4488_a818_c7042a530a0e --> idea_134d76b8_e5db_4565_86b7_aa49cb7eecf7 idea_55f443c4_8d2f_4ddc_a47e_92c40b2f39b0 --> idea_844f43d7_914b_4db3_9ce9_c8465d1edf5b idea_96f7f65a_928a_4ce9_8f6f_6cefe2b2f969 --> idea_026caa3e_a121_405a_97a9_1dbe887597e6 idea_026caa3e_a121_405a_97a9_1dbe887597e6 --> idea_69de4d34_a1d7_4f63_b191_c145d1c8ed7d idea_0859f001_2440_4fa0_956b_9d09ad6a4008 --> idea_aab21bef_33a6_428f_af4e_340436c8ac35 idea_9cdb37b8_738a_4621_a3ff_8725390507e6 --> idea_eb1d2389_8413_4617_9886_1430d18b54e1 idea_5f68aa37_e831_49c9_a5ec_b8143369eca1 --> idea_fcb2741c_5927_4c5e_aed6_1a58d5cadac8 idea_4d89cc27_dbaa_4486_8f00_99cbc853af60 --> idea_2f4e9d3e_314f_421c_857f_1a1d1840a544 idea_5f964e9f_1680_4dd2_9522_7ffe33552992 --> idea_26c72438_a206_4cd5_8d94_b4d955991b15 idea_3372de9b_11ab_4b61_b59a_d4a994eec965 --> idea_aab21bef_33a6_428f_af4e_340436c8ac35 idea_4e7a9c35_dd9c_40b5_b907_d6fdeedeb485 --> idea_28d3fde8_1e14_429f_b344_6389a6f642c7 idea_2132fb22_760b_47ad_a3f5_b8bea6818535 --> idea_5f964e9f_1680_4dd2_9522_7ffe33552992 idea_7ce0fed4_73af_4498_ad54_42178e7209ec --> idea_026caa3e_a121_405a_97a9_1dbe887597e6 idea_f4ce9f25_56ce_42f1_8ba0_817d71bf12df --> idea_af4e05dd_920f_49a7_ae93_83f80d448c58 idea_fcb2741c_5927_4c5e_aed6_1a58d5cadac8 --> idea_5f68aa37_e831_49c9_a5ec_b8143369eca1 idea_af4e05dd_920f_49a7_ae93_83f80d448c58 --> idea_f4ce9f25_56ce_42f1_8ba0_817d71bf12df idea_28d3fde8_1e14_429f_b344_6389a6f642c7 --> idea_f1ea7bff_39c3_4e2b_9bac_025a4bd75c62 idea_9cdb37b8_738a_4621_a3ff_8725390507e6 --> idea_45939e47_b677_4c01_9cc5_223c2b684c27 idea_3372de9b_11ab_4b61_b59a_d4a994eec965 --> idea_f4ce9f25_56ce_42f1_8ba0_817d71bf12df idea_45939e47_b677_4c01_9cc5_223c2b684c27 --> idea_357f3a42_62ac_4cb6_8286_402137835a8f idea_37b8cfba_6282_48ad_ba16_36ee53fed4a8 --> idea_5f964e9f_1680_4dd2_9522_7ffe33552992 idea_f7ed21f1_3751_4714_b12d_850bb3d6e2b2 --> idea_75d76a55_fcd9_409e_8563_d94cdca1e5f2 idea_b243628c_ef71_42ec_a2c9_beecf5bb501b --> idea_0bc50385_51ee_4142_a9a7_3eb23e5132d2 idea_f3cd8ca5_4b24_425f_9595_87cea67fca82 --> idea_df7c909a_d36d_4b10_9e66_8e6c6ec89a4a idea_69de4d34_a1d7_4f63_b191_c145d1c8ed7d --> idea_7fe4a0a9_381c_4509_835d_55eaa386afbc idea_f1ea7bff_39c3_4e2b_9bac_025a4bd75c62 --> idea_75d76a55_fcd9_409e_8563_d94cdca1e5f2 idea_af4e05dd_920f_49a7_ae93_83f80d448c58 --> idea_42a66e36_e5d9_4094_a320_439ca9d3a3dc idea_5887a366_4a4f_43b0_a5d3_355c524198e9 --> idea_7fe4a0a9_381c_4509_835d_55eaa386afbc idea_b39d1370_c081_4a68_ad1b_b50ca99870f7 --> idea_42a66e36_e5d9_4094_a320_439ca9d3a3dc idea_5887a366_4a4f_43b0_a5d3_355c524198e9 --> idea_560b907b_90d1_421d_9b57_16f84bd4063b idea_f127094c_0eac_440d_a8b0_42b702ccdaf1 --> idea_1ae48a6d_c005_4501_90ce_2c48efb26a8e idea_026caa3e_a121_405a_97a9_1dbe887597e6 --> idea_4520548e_1f4c_4323_8d91_806862b3a3b1 idea_69de4d34_a1d7_4f63_b191_c145d1c8ed7d --> idea_3e490fe5_6daf_4e09_85ab_7787a2e45edb idea_4e7a9c35_dd9c_40b5_b907_d6fdeedeb485 --> idea_75d76a55_fcd9_409e_8563_d94cdca1e5f2 idea_cea01eae_b1a3_49ff_a362_87d8d796874c --> idea_96f7f65a_928a_4ce9_8f6f_6cefe2b2f969 idea_db9e963a_9972_471c_bc63_1c6566582a7d --> idea_1ae48a6d_c005_4501_90ce_2c48efb26a8e idea_4cd5b655_dc4d_4bac_8efd_a9d8eacee3a7 --> idea_af4e05dd_920f_49a7_ae93_83f80d448c58 idea_5f964e9f_1680_4dd2_9522_7ffe33552992 --> idea_2f4e9d3e_314f_421c_857f_1a1d1840a544 idea_2f4e9d3e_314f_421c_857f_1a1d1840a544 --> idea_560b907b_90d1_421d_9b57_16f84bd4063b idea_5f964e9f_1680_4dd2_9522_7ffe33552992 --> idea_fc3428ef_cd41_4f3a_9393_2fb147d92600 idea_fc3428ef_cd41_4f3a_9393_2fb147d92600 --> idea_5887a366_4a4f_43b0_a5d3_355c524198e9 idea_b39d1370_c081_4a68_ad1b_b50ca99870f7 --> idea_2f4e9d3e_314f_421c_857f_1a1d1840a544 idea_df7c909a_d36d_4b10_9e66_8e6c6ec89a4a --> idea_b243628c_ef71_42ec_a2c9_beecf5bb501b idea_c4939875_4474_448b_98d6_96ff4f331df6 --> idea_9cdb37b8_738a_4621_a3ff_8725390507e6 idea_26c72438_a206_4cd5_8d94_b4d955991b15 --> idea_7c6b5143_f6d8_4a7c_80dc_78b171112e4b idea_ee709cbd_eaab_4f90_8759_77b884f5b336 --> idea_5f964e9f_1680_4dd2_9522_7ffe33552992 idea_75d76a55_fcd9_409e_8563_d94cdca1e5f2 --> idea_026caa3e_a121_405a_97a9_1dbe887597e6 idea_75d76a55_fcd9_409e_8563_d94cdca1e5f2 --> idea_fcb2741c_5927_4c5e_aed6_1a58d5cadac8 idea_134d76b8_e5db_4565_86b7_aa49cb7eecf7 --> 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