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SentenceTransformer(
(0): Transformer({'max_seq_length': 32768, 'do_lower_case': False}) with Transformer model: Qwen3Model
(1): Pooling({'word_embedding_dimension': 1024, 'pooling_mode_cls_token': False, 'pooling_mode_mean_tokens': False, 'pooling_mode_max_tokens': False, 'pooling_mode_mean_sqrt_len_tokens': False, 'pooling_mode_weightedmean_tokens': False, 'pooling_mode_lasttoken': True, 'include_prompt': True})
(2): Normalize()
)pip install -U sentence-transformers1from sentence_transformers import SentenceTransformer
2
3# Download from the 🤗 Hub
4model = SentenceTransformer("sentence_transformers_model_id")
5# Run inference
6sentences = [
7 'I have the following sketch of a mathematical proof: \n\nTo prove that α equals β, we will show that the difference α - β is the zero morphism.\n\nFirst, we note that α - β is a morphism, and we aim to demonstrate that it maps every object to zero. We consider the kernel of α - β, which consists of all elements that α - β sends to zero.\n\nWe then observe that the span of the image of the derivation d is contained within the kernel of α - β. This is because, for any element in the image of d, say d(b), we have (α - β)(d(b)) = α(d(b)) - β(d(b)) = 0, by the given condition that α and β agree on all d(b).\n\nBy showing that the image of d generates the entire domain (KaehlerDifferential f), we conclude that the kernel of α - β includes all such generated elements. This implies that α - β sends every element to zero, effectively making α - β the zero morphism.\n\nThus, α must be equal to β.\n\nHere is a helpful lemma for this proof: ',
8 'For a continuous linear map \\( f: M \\to M_2 \\) between locally convex spaces, the kernel of \\( f \\) is the entire domain \\( M \\) if and only if \\( f \\) is the zero map.',
9 "A function \\( f: M \\rightarrow M' \\) is said to be continuously differentiable within a set \\( s \\subseteq M \\) at all points \\( x \\in s \\) and for a given differentiability order \\( n \\in \\mathbb{N} \\cup \\{\\infty\\} \\). The definition requires that for every \\( x \\) in \\( s \\), \\( f \\) satisfies the continuity of its derivatives up to order \\( n \\) within the set \\( s \\).",
10]
11embeddings = model.encode(sentences)
12print(embeddings.shape)
13# [3, 1024]
14
15# Get the similarity scores for the embeddings
16similarities = model.similarity(embeddings, embeddings)
17print(similarities.shape)
18# [3, 3]sentence_0 and sentence_1| sentence_0 | sentence_1 | |
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| type | string | string |
| details |
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I have the following sketch of a mathematical proof: [object Object][object Object]To prove that comap(σ)(C) is an open map, we proceed as follows:[object Object][object Object]1. [object Object]: Let U be an open set in the codomain space, which consists of continuous functions from A to A equipped with the topology of pointwise convergence.[object Object][object Object]2. [object Object]: By the definition of the topology, U can be expressed as a union of basic open sets. Each basic open set has the form {f ∈ C | f(x_i) ∈ U_i} for some points x_i in A and open sets U_i in A. 3. Apply the image under comap(σ): The image of U under comap(σ) is the union of the images of these basic open sets. We need to show that each of these images is open in the preimage space. 4. Analyze the image of each basic open set: Each basic open set {f ∈ C |
I have the following sketch of a mathematical proof: [object Object][object Object]1. [object Object]: We are dealing with a finite group acting on a finite type. This means every element in the group permutes the elements of the type according to the group operation.[object Object][object Object]2. [object Object]: Recall that the orbit-stabilizer theorem states that for any element in the type, the size of its orbit (the set of all elements it can be transformed into by the group action) is equal to the order of the group divided by the order of the stabilizer subgroup of that element.[object Object][object Object]3. [object Object]: The group action partitions the type into disjoint orbits. Each orbit is an equivalence class where all elements can be reached from one another by the group action.[object Object][object Object]4. [object Object]: To find the total number of elements in the type, sum the sizes of all distinct orbits. Each orbit's size is given by the orbit-stabilizer theorem as | group |
I have the following sketch of a mathematical proof: [object Object][object Object]To establish the functoriality of projective resolutions in the homotopy category of ( \mathbb{N} )-indexed chain complexes, we proceed as follows:[object Object][object Object]1. [object Object]: For each object (module) ( X ) in the category ( C ), we first construct a projective resolution of ( X ). A projective resolution is an exact sequence of projective modules ending in ( X ). The existence of such resolutions is a standard result in homological algebra.[object Object][object Object]2. [object Object]: Consider a morphism ( f: X \to Y ) in ( C ). We need to show that ( f ) induces a morphism between the projective resolutions of ( X ) and ( Y ). This induced morphism should respect the homotopy equivalence in the homotopy category.[object Object][object Object]3. [object Object]: The construction of the projective resolution should be such that it respects the composition of morphisms. If we have a second morphism ( g: Y \to Z ), then the composition ( gf: X \to Z ) should induce a morp... | The [object Object], denoted as [object Object], is a category whose objects are topological spaces and whose morphisms are homotopy classes of continuous functions between these spaces. In simpler terms, two continuous functions between topological spaces are considered equivalent in this category if one can be continuously deformed into the other. This deformation is known as a homotopy, and the category is constructed by taking the quotient of the category of topological spaces under the equivalence relation induced by homotopy. |
MultipleNegativesRankingLoss with these parameters:
1{
2 "scale": 20.0,
3 "similarity_fct": "cos_sim"
4}per_device_train_batch_size: 4per_device_eval_batch_size: 4num_train_epochs: 1fp16: Truemulti_dataset_batch_sampler: round_robinoverwrite_output_dir: Falsedo_predict: Falseeval_strategy: noprediction_loss_only: Trueper_device_train_batch_size: 4per_device_eval_batch_size: 4per_gpu_train_batch_size: Noneper_gpu_eval_batch_size: Nonegradient_accumulation_steps: 1eval_accumulation_steps: Nonetorch_empty_cache_steps: Nonelearning_rate: 5e-05weight_decay: 0.0adam_beta1: 0.9adam_beta2: 0.999adam_epsilon: 1e-08max_grad_norm: 1num_train_epochs: 1max_steps: -1lr_scheduler_type: linearlr_scheduler_kwargs: {}warmup_ratio: 0.0warmup_steps: 0log_level: passivelog_level_replica: warninglog_on_each_node: Truelogging_nan_inf_filter: Truesave_safetensors: Truesave_on_each_node: Falsesave_only_model: Falserestore_callback_states_from_checkpoint: Falseno_cuda: Falseuse_cpu: Falseuse_mps_device: Falseseed: 42data_seed: Nonejit_mode_eval: Falseuse_ipex: Falsebf16: Falsefp16: Truefp16_opt_level: O1half_precision_backend: autobf16_full_eval: Falsefp16_full_eval: Falsetf32: Nonelocal_rank: 0ddp_backend: Nonetpu_num_cores: Nonetpu_metrics_debug: Falsedebug: []dataloader_drop_last: Falsedataloader_num_workers: 0dataloader_prefetch_factor: Nonepast_index: -1disable_tqdm: Falseremove_unused_columns: Truelabel_names: Noneload_best_model_at_end: Falseignore_data_skip: Falsefsdp: []fsdp_min_num_params: 0fsdp_config: {'min_num_params': 0, 'xla': False, 'xla_fsdp_v2': False, 'xla_fsdp_grad_ckpt': False}tp_size: 0fsdp_transformer_layer_cls_to_wrap: Noneaccelerator_config: {'split_batches': False, 'dispatch_batches': None, 'even_batches': True, 'use_seedable_sampler': True, 'non_blocking': False, 'gradient_accumulation_kwargs': None}deepspeed: Nonelabel_smoothing_factor: 0.0optim: adamw_torchoptim_args: Noneadafactor: Falsegroup_by_length: Falselength_column_name: lengthddp_find_unused_parameters: Noneddp_bucket_cap_mb: Noneddp_broadcast_buffers: Falsedataloader_pin_memory: Truedataloader_persistent_workers: Falseskip_memory_metrics: Trueuse_legacy_prediction_loop: Falsepush_to_hub: Falseresume_from_checkpoint: Nonehub_model_id: Nonehub_strategy: every_savehub_private_repo: Nonehub_always_push: Falsegradient_checkpointing: Falsegradient_checkpointing_kwargs: Noneinclude_inputs_for_metrics: Falseinclude_for_metrics: []eval_do_concat_batches: Truefp16_backend: autopush_to_hub_model_id: Nonepush_to_hub_organization: Nonemp_parameters:auto_find_batch_size: Falsefull_determinism: Falsetorchdynamo: Noneray_scope: lastddp_timeout: 1800torch_compile: Falsetorch_compile_backend: Nonetorch_compile_mode: Noneinclude_tokens_per_second: Falseinclude_num_input_tokens_seen: Falseneftune_noise_alpha: Noneoptim_target_modules: Nonebatch_eval_metrics: Falseeval_on_start: Falseuse_liger_kernel: Falseeval_use_gather_object: Falseaverage_tokens_across_devices: Falseprompts: Nonebatch_sampler: batch_samplermulti_dataset_batch_sampler: round_robin1@inproceedings{reimers-2019-sentence-bert,
2 title = "Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks",
3 author = "Reimers, Nils and Gurevych, Iryna",
4 booktitle = "Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing",
5 month = "11",
6 year = "2019",
7 publisher = "Association for Computational Linguistics",
8 url = "https://arxiv.org/abs/1908.10084",
9}1@misc{henderson2017efficient,
2 title={Efficient Natural Language Response Suggestion for Smart Reply},
3 author={Matthew Henderson and Rami Al-Rfou and Brian Strope and Yun-hsuan Sung and Laszlo Lukacs and Ruiqi Guo and Sanjiv Kumar and Balint Miklos and Ray Kurzweil},
4 year={2017},
5 eprint={1705.00652},
6 archivePrefix={arXiv},
7 primaryClass={cs.CL}
8}