From dc0d0eb6a908039e289296d2012f0e6074cb6316 Mon Sep 17 00:00:00 2001 From: Xiao-Yong Jin Date: Thu, 29 Jun 2023 23:16:04 -0500 Subject: [PATCH] Implement customizable RoPE MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The original RoPE has pre-defined parameters theta_i = 10000^(āˆ’2(iāˆ’1)/d), for i in [1, 2, ..., d/2] Our customizable RoPE, ggml_rope_custom_inplace, uses theta_i = scale * base^(āˆ’2(iāˆ’1)/d), for i in [1, 2, ..., d/2] with the default matches the original scale = 1.0 base = 10000 The new command line arguments --rope-freq-base --rope-freq-scale set the two new RoPE parameter. Recent researches show changing these two parameters extends the context limit with minimal loss. 1. Extending Context to 8K kaiokendev https://kaiokendev.github.io/til#extending-context-to-8k 2. Extending Context Window of Large Language Models via Positional Interpolation Shouyuan Chen, Sherman Wong, Liangjian Chen, Yuandong Tian https://arxiv.org/abs/2306.15595 3. NTK-Aware Scaled RoPE allows LLaMA models to have extended (8k+) context size without any fine-tuning and minimal perplexity degradation. https://www.reddit.com/user/bloc97 https://www.reddit.com/r/LocalLLaMA/comments/14lz7j5/ntkaware_scaled_rope_allows_llama_models_to_have/ For the bold, try adding the following command line parameters to your favorite model: -c 16384 --rope-freq-base 80000 --rope-freq-scale 0.5 --- examples/common.cpp | 16 +++++++++++++ examples/common.h | 2 ++ examples/main/main.cpp | 12 ++++++++-- examples/server/server.cpp | 18 +++++++++++++++ ggml-metal.m | 6 +++++ ggml-metal.metal | 6 +++-- ggml.c | 40 +++++++++++++++++++++++++-------- ggml.h | 11 +++++++++ llama.cpp | 46 +++++++++++++++++++++++++------------- llama.h | 2 ++ 10 files changed, 131 insertions(+), 28 deletions(-) diff --git a/examples/common.cpp b/examples/common.cpp index 3278a0643..2ff8dc39d 100644 --- a/examples/common.cpp +++ b/examples/common.cpp @@ -168,6 +168,18 @@ bool gpt_params_parse(int argc, char ** argv, gpt_params & params) { break; } params.n_ctx = std::stoi(argv[i]); + } else if (arg == "--rope-freq-base") { + if (++i >= argc) { + invalid_param = true; + break; + } + params.rope_freq_base = std::stof(argv[i]); + } else if (arg == "--rope-freq-scale") { + if (++i >= argc) { + invalid_param = true; + break; + } + params.rope_freq_scale = std::stof(argv[i]); } else if (arg == "--memory-f32") { params.memory_f16 = false; } else if (arg == "--top-p") { @@ -469,6 +481,8 @@ void gpt_print_usage(int /*argc*/, char ** argv, const gpt_params & params) { fprintf(stderr, " i.e. `--logit-bias 15043+1` to increase likelihood of token ' Hello',\n"); fprintf(stderr, " or `--logit-bias 15043-1` to decrease likelihood of token ' Hello'\n"); fprintf(stderr, " -c N, --ctx-size N size of the prompt context (default: %d)\n", params.n_ctx); + fprintf(stderr, " --rope_freq_base N RoPE base frequency (default: %.1f)\n", params.rope_freq_base); + fprintf(stderr, " --rope_freq_scale N RoPE frequency scaling factor (default: %g)\n", params.rope_freq_scale); fprintf(stderr, " --ignore-eos ignore end of stream token and continue generating (implies --logit-bias 2-inf)\n"); fprintf(stderr, " --no-penalize-nl do not penalize newline token\n"); fprintf(stderr, " --memory-f32 use f32 instead of f16 for memory key+value (default: disabled)\n"); @@ -549,6 +563,8 @@ std::tuple llama_init_from_gpt_par lparams.use_mlock = params.use_mlock; lparams.logits_all = params.perplexity; lparams.embedding = params.embedding; + lparams.rope_freq_base = params.rope_freq_base; + lparams.rope_freq_scale = params.rope_freq_scale; llama_model * model = llama_load_model_from_file(params.model.c_str(), lparams); if (model == NULL) { diff --git a/examples/common.h b/examples/common.h index 96f2228f8..11ba4dba6 100644 --- a/examples/common.h +++ b/examples/common.h @@ -32,6 +32,8 @@ struct gpt_params { int32_t main_gpu = 0; // the GPU that is used for scratch and small tensors float tensor_split[LLAMA_MAX_DEVICES] = {0}; // how split tensors should be distributed across GPUs int32_t n_probs = 0; // if greater than 0, output the probabilities of top n_probs tokens. + float rope_freq_base = 10000.0f; // RoPE base frequency + float rope_freq_scale = 1.0f; // RoPE frequency scaling factor // sampling parameters std::unordered_map logit_bias; // logit bias for specific tokens diff --git a/examples/main/main.cpp b/examples/main/main.cpp index 0f6391acb..3a31a3210 100644 --- a/examples/main/main.cpp +++ b/examples/main/main.cpp @@ -84,9 +84,17 @@ int main(int argc, char ** argv) { return 0; } + if (params.rope_freq_base != 10000.0) { + fprintf(stderr, "%s: warning: changing RoPE frequency base to %g (default 10000.0)\n", __func__, params.rope_freq_base); + } + + if (params.rope_freq_scale != 1.0) { + fprintf(stderr, "%s: warning: scaling RoPE frequency by %g (default 1.0)\n", __func__, params.rope_freq_scale); + } + if (params.n_ctx > 2048) { - fprintf(stderr, "%s: warning: model might not support context sizes greater than 2048 tokens (%d specified);" - "expect poor results\n", __func__, params.n_ctx); + fprintf(stderr, "%s: warning: base model only supports context sizes no greater than 2048 tokens (%d specified);" + " you are on your own\n", __func__, params.n_ctx); } else if (params.n_ctx < 8) { fprintf(stderr, "%s: warning: minimum context size is 8, using minimum size.\n", __func__); params.n_ctx = 8; diff --git a/examples/server/server.cpp b/examples/server/server.cpp index 2cbfc0018..491a84e7e 100644 --- a/examples/server/server.cpp +++ b/examples/server/server.cpp @@ -608,6 +608,8 @@ static void server_print_usage(const char *argv0, const gpt_params ¶ms, fprintf(stderr, " -v, --verbose verbose output (default: %s)\n", server_verbose ? "enabled" : "disabled"); fprintf(stderr, " -t N, --threads N number of threads to use during computation (default: %d)\n", params.n_threads); fprintf(stderr, " -c N, --ctx-size N size of the prompt context (default: %d)\n", params.n_ctx); + fprintf(stderr, " --rope-freq-base N RoPE base frequency (default: %.1f)\n", params.rope_freq_base); + fprintf(stderr, " --rope-freq-scale N RoPE frequency scaling factor (default: %g)\n", params.rope_freq_scale); fprintf(stderr, " -b N, --batch-size N batch size for prompt processing (default: %d)\n", params.n_batch); fprintf(stderr, " --memory-f32 use f32 instead of f16 for memory key+value (default: disabled)\n"); fprintf(stderr, " not recommended: doubles context memory required and no measurable increase in quality\n"); @@ -722,6 +724,22 @@ static void server_params_parse(int argc, char **argv, server_params &sparams, } params.n_ctx = std::stoi(argv[i]); } + else if (arg == "--rope-freq-base") + { + if (++i >= argc) { + invalid_param = true; + break; + } + params.rope_freq_base = std::stof(argv[i]); + } + else if (arg == "--rope-freq-scale") + { + if (++i >= argc) { + invalid_param = true; + break; + } + params.rope_freq_scale = std::stof(argv[i]); + } else if (arg == "--memory-f32" || arg == "--memory_f32") { params.memory_f16 = false; diff --git a/ggml-metal.m b/ggml-metal.m index fd69c41fe..b8b9de69b 100644 --- a/ggml-metal.m +++ b/ggml-metal.m @@ -874,6 +874,10 @@ void ggml_metal_graph_compute( const int n_past = ((int32_t *)(src1->data))[0]; + float freq_base, freq_scale; + memcpy(&freq_base, (int32_t *) src1->data + 4, sizeof(float)); + memcpy(&freq_scale, (int32_t *) src1->date + 5, sizeof(float)); + [encoder setComputePipelineState:ctx->pipeline_rope]; [encoder setBuffer:id_src0 offset:offs_src0 atIndex:0]; [encoder setBuffer:id_dst offset:offs_dst atIndex:1]; @@ -896,6 +900,8 @@ void ggml_metal_graph_compute( [encoder setBytes:&n_past length:sizeof( int) atIndex:18]; [encoder setBytes:&n_dims length:sizeof( int) atIndex:19]; [encoder setBytes:&mode length:sizeof( int) atIndex:20]; + [encoder setBytes:&freq_base length:sizeof(float) atIndex:21]; + [encoder setBytes:&freq_scale length:sizeof(float) atIndex:22]; [encoder dispatchThreadgroups:MTLSizeMake(ne01, ne02, ne03) threadsPerThreadgroup:MTLSizeMake(1, 1, 1)]; } break; diff --git a/ggml-metal.metal b/ggml-metal.metal index e62fe6842..16916585f 100644 --- a/ggml-metal.metal +++ b/ggml-metal.metal @@ -615,17 +615,19 @@ kernel void kernel_rope( constant int & n_past, constant int & n_dims, constant int & mode, + constant float & freq_base, + constant float & freq_scale, uint3 tpig[[thread_position_in_grid]]) { const int64_t i3 = tpig[2]; const int64_t i2 = tpig[1]; const int64_t i1 = tpig[0]; const bool is_neox = mode & 2; - const float theta_scale = pow(10000.0, -2.0f/n_dims); + const float theta_scale = pow(freq_base, -2.0f/n_dims); const int64_t p = ((mode & 1) == 0 ? n_past + i2 : i2); - float theta = (float)p; + float theta = freq_scale * (float)p; if (!is_neox) { for (int64_t i0 = 0; i0 < ne0; i0 += 2) { diff --git a/ggml.c b/ggml.c index d257c3d65..269aacb5d 100644 --- a/ggml.c +++ b/ggml.c @@ -6943,6 +6943,8 @@ struct ggml_tensor * ggml_rope_impl( int n_past, int n_dims, int mode, + float freq_base, + float freq_scale, int n_ctx, bool inplace) { GGML_ASSERT(n_past >= 0); @@ -6956,12 +6958,14 @@ struct ggml_tensor * ggml_rope_impl( ggml_scratch_save(ctx); - struct ggml_tensor * b = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 4); + struct ggml_tensor * b = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, 6); ((int32_t *) b->data)[0] = n_past; ((int32_t *) b->data)[1] = n_dims; ((int32_t *) b->data)[2] = mode; ((int32_t *) b->data)[3] = n_ctx; + memcpy((int32_t *) b->data + 4, &freq_base, sizeof(float)); + memcpy((int32_t *) b->data + 5, &freq_scale, sizeof(float)); ggml_scratch_load(ctx); @@ -6980,7 +6984,7 @@ struct ggml_tensor * ggml_rope( int n_dims, int mode, int n_ctx) { - return ggml_rope_impl(ctx, a, n_past, n_dims, mode, n_ctx, false); + return ggml_rope_impl(ctx, a, n_past, n_dims, mode, 10000.0f, 1.0f, n_ctx, false); } struct ggml_tensor * ggml_rope_inplace( @@ -6990,7 +6994,19 @@ struct ggml_tensor * ggml_rope_inplace( int n_dims, int mode, int n_ctx) { - return ggml_rope_impl(ctx, a, n_past, n_dims, mode, n_ctx, true); + return ggml_rope_impl(ctx, a, n_past, n_dims, mode, 10000.0f, 1.0f, n_ctx, true); +} + +struct ggml_tensor * ggml_rope_custom_inplace( + struct ggml_context * ctx, + struct ggml_tensor * a, + int n_past, + int n_dims, + int mode, + float freq_base, + float freq_scale, + int n_ctx) { + return ggml_rope_impl(ctx, a, n_past, n_dims, mode, freq_base, freq_scale, n_ctx, true); } // ggml_rope_back @@ -11948,7 +11964,7 @@ static void ggml_compute_forward_rope_f32( const struct ggml_tensor * src1, struct ggml_tensor * dst) { GGML_ASSERT(src1->type == GGML_TYPE_I32); - GGML_ASSERT(ggml_nelements(src1) == 4); + GGML_ASSERT(ggml_nelements(src1) == 6); if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) { return; @@ -11958,6 +11974,9 @@ static void ggml_compute_forward_rope_f32( const int n_dims = ((int32_t *) src1->data)[1]; const int mode = ((int32_t *) src1->data)[2]; const int n_ctx = ((int32_t *) src1->data)[3]; + float freq_base, freq_scale; + memcpy(&freq_base, (int32_t *) src1->data + 4, sizeof(float)); + memcpy(&freq_scale, (int32_t *) src1->data + 5, sizeof(float)); assert(n_past >= 0); @@ -11986,7 +12005,7 @@ static void ggml_compute_forward_rope_f32( // row index used to determine which thread to use int ir = 0; - const float theta_scale = powf(10000.0, -2.0f/n_dims); + const float theta_scale = powf(freq_base, -2.0f/n_dims); const bool is_neox = mode & 2; const bool is_glm = mode & 4; @@ -11998,7 +12017,7 @@ static void ggml_compute_forward_rope_f32( if (ir++ < ir0) continue; if (ir > ir1) break; - float theta = (float)p; + float theta = freq_scale * (float)p; if (is_glm) { theta = MIN(p, n_ctx - 2); @@ -12075,7 +12094,7 @@ static void ggml_compute_forward_rope_f16( const struct ggml_tensor * src1, struct ggml_tensor * dst) { GGML_ASSERT(src1->type == GGML_TYPE_I32); - GGML_ASSERT(ggml_nelements(src1) == 4); + GGML_ASSERT(ggml_nelements(src1) == 6); if (params->type == GGML_TASK_INIT || params->type == GGML_TASK_FINALIZE) { return; @@ -12085,6 +12104,9 @@ static void ggml_compute_forward_rope_f16( const int n_dims = ((int32_t *) src1->data)[1]; const int mode = ((int32_t *) src1->data)[2]; const int n_ctx = ((int32_t *) src1->data)[3]; + float freq_base, freq_scale; + memcpy(&freq_base, (int32_t *) src1->data + 4, sizeof(float)); + memcpy(&freq_scale, (int32_t *) src1->data + 5, sizeof(float)); assert(n_past >= 0); @@ -12113,7 +12135,7 @@ static void ggml_compute_forward_rope_f16( // row index used to determine which thread to use int ir = 0; - const float theta_scale = powf(10000.0, -2.0f/n_dims); + const float theta_scale = powf(freq_base, -2.0f/n_dims); const bool is_neox = mode & 2; const bool is_glm = mode & 4; @@ -12125,7 +12147,7 @@ static void ggml_compute_forward_rope_f16( if (ir++ < ir0) continue; if (ir > ir1) break; - float theta = (float)p; + float theta = freq_scale * (float)p; if (is_glm) { theta = MIN(p, n_ctx - 2); diff --git a/ggml.h b/ggml.h index d0710c555..fcb47e7ac 100644 --- a/ggml.h +++ b/ggml.h @@ -1107,6 +1107,17 @@ extern "C" { int mode, int n_ctx); + // custom RoPE, in-place, returns view(a) + GGML_API struct ggml_tensor * ggml_rope_custom_inplace( + struct ggml_context * ctx, + struct ggml_tensor * a, + int n_past, + int n_dims, + int mode, + float freq_base, + float freq_scale, + int n_ctx); + // rotary position embedding backward, i.e compute dx from dy // a - dy GGML_API struct ggml_tensor * ggml_rope_back( diff --git a/llama.cpp b/llama.cpp index 02afdeb14..935130b63 100644 --- a/llama.cpp +++ b/llama.cpp @@ -79,14 +79,15 @@ void llama_nop(struct ggml_tensor * tensor) { // don't offload by default (void) tensor; } -static const std::map & MEM_REQ_SCRATCH0() +static const std::map & MEM_REQ_SCRATCH0(int n_ctx) { static std::map k_sizes = { - { MODEL_3B, 256ull * MB }, - { MODEL_7B, 512ull * MB }, - { MODEL_13B, 512ull * MB }, - { MODEL_30B, 512ull * MB }, - { MODEL_65B, 1024ull * MB }, + /* empirical scaling, still a guess */ + { MODEL_3B, ((size_t) n_ctx / 16ull + 128ull) * MB }, + { MODEL_7B, ((size_t) n_ctx / 16ull + 256ull) * MB }, + { MODEL_13B, ((size_t) n_ctx / 12ull + 256ull) * MB }, + { MODEL_30B, ((size_t) n_ctx / 10ull + 256ull) * MB }, + { MODEL_65B, ((size_t) n_ctx / 8ull + 512ull) * MB }, }; return k_sizes; } @@ -167,6 +168,8 @@ struct llama_hparams { uint32_t n_head = 32; uint32_t n_layer = 32; uint32_t n_rot = 64; + float rope_freq_base = 10000.0f; + float rope_freq_scale = 1.0f; enum llama_ftype ftype = LLAMA_FTYPE_MOSTLY_F16; bool operator!=(const llama_hparams & other) const { @@ -619,7 +622,7 @@ struct llama_model_loader { *ctx_size_p = *mmapped_size_p = 0; for (const llama_load_tensor & lt : tensors_map.tensors) { *ctx_size_p += sizeof(struct ggml_tensor) + GGML_OBJECT_SIZE; - *(use_mmap ? mmapped_size_p : ctx_size_p) += lt.size; + *(use_mmap ? mmapped_size_p : ctx_size_p) += lt.size + 16; } } @@ -812,6 +815,8 @@ struct llama_context_params llama_context_default_params() { struct llama_context_params result = { /*.seed =*/ LLAMA_DEFAULT_SEED, /*.n_ctx =*/ 512, + /*.rope_freq_base =*/ 10000.0f, + /*.rope_freq_scale =*/ 1.0f, /*.n_batch =*/ 512, /*.gpu_layers =*/ 0, /*.main_gpu =*/ 0, @@ -925,6 +930,8 @@ static void llama_model_load_internal( llama_model & model, llama_vocab & vocab, int n_ctx, + float rope_freq_base, + float rope_freq_scale, int n_batch, int n_gpu_layers, int main_gpu, @@ -963,6 +970,8 @@ static void llama_model_load_internal( } hparams.n_ctx = n_ctx; + hparams.rope_freq_base = rope_freq_base; + hparams.rope_freq_scale = rope_freq_scale; } const uint32_t n_ff = ((2*(4*hparams.n_embd)/3 + hparams.n_mult - 1)/hparams.n_mult)*hparams.n_mult; @@ -976,6 +985,8 @@ static void llama_model_load_internal( fprintf(stderr, "%s: n_head = %u\n", __func__, hparams.n_head); fprintf(stderr, "%s: n_layer = %u\n", __func__, hparams.n_layer); fprintf(stderr, "%s: n_rot = %u\n", __func__, hparams.n_rot); + fprintf(stderr, "%s: freq_base = %.1f\n", __func__, hparams.rope_freq_base); + fprintf(stderr, "%s: freq_scale = %g\n", __func__, hparams.rope_freq_scale); fprintf(stderr, "%s: ftype = %u (%s)\n", __func__, hparams.ftype, llama_ftype_name(hparams.ftype)); fprintf(stderr, "%s: n_ff = %u\n", __func__, n_ff); fprintf(stderr, "%s: model size = %s\n", __func__, llama_model_type_name(model.type)); @@ -1127,7 +1138,7 @@ static void llama_model_load_internal( const size_t mem_required = ctx_size + mmapped_size - vram_weights + // weights in VRAM not in memory - MEM_REQ_SCRATCH0().at(model.type) + + MEM_REQ_SCRATCH0(hparams.n_ctx).at(model.type) + MEM_REQ_SCRATCH1().at(model.type) + MEM_REQ_EVAL().at (model.type); @@ -1229,6 +1240,8 @@ static bool llama_model_load( llama_model & model, llama_vocab & vocab, int n_ctx, + float rope_freq_base, + float rope_freq_scale, int n_batch, int n_gpu_layers, int main_gpu, @@ -1241,7 +1254,7 @@ static bool llama_model_load( llama_progress_callback progress_callback, void *progress_callback_user_data) { try { - llama_model_load_internal(fname, model, vocab, n_ctx, n_batch, n_gpu_layers, main_gpu, tensor_split, low_vram, memory_type, + llama_model_load_internal(fname, model, vocab, n_ctx, rope_freq_base, rope_freq_scale, n_batch, n_gpu_layers, main_gpu, tensor_split, low_vram, memory_type, use_mmap, use_mlock, vocab_only, progress_callback, progress_callback_user_data); return true; } catch (const std::exception & err) { @@ -1293,6 +1306,8 @@ static bool llama_eval_internal( const int n_head = hparams.n_head; const int n_vocab = hparams.n_vocab; const int n_rot = hparams.n_embd/hparams.n_head; + const float freq_base = hparams.rope_freq_base; + const float freq_scale = hparams.rope_freq_scale; const int n_gpu_layers = model.n_gpu_layers; auto & mem_per_token = lctx.mem_per_token; @@ -1384,11 +1399,11 @@ static bool llama_eval_internal( offload_func_kq(tmpq); ggml_set_name(tmpq, "tmpq"); - struct ggml_tensor * Kcur = ggml_rope_inplace(ctx0, ggml_reshape_3d(ctx0, tmpk, n_embd/n_head, n_head, N), n_past, n_rot, 0, 0); + struct ggml_tensor * Kcur = ggml_rope_custom_inplace(ctx0, ggml_reshape_3d(ctx0, tmpk, n_embd/n_head, n_head, N), n_past, n_rot, 0, freq_base, freq_scale, 0); offload_func_kq(Kcur); ggml_set_name(Kcur, "Kcur"); - struct ggml_tensor * Qcur = ggml_rope_inplace(ctx0, ggml_reshape_3d(ctx0, tmpq, n_embd/n_head, n_head, N), n_past, n_rot, 0, 0); + struct ggml_tensor * Qcur = ggml_rope_custom_inplace(ctx0, ggml_reshape_3d(ctx0, tmpq, n_embd/n_head, n_head, N), n_past, n_rot, 0, freq_base, freq_scale, 0); offload_func_kq(Qcur); ggml_set_name(Qcur, "Qcur"); @@ -2559,9 +2574,10 @@ struct llama_model * llama_load_model_from_file( ggml_type memory_type = params.f16_kv ? GGML_TYPE_F16 : GGML_TYPE_F32; - if (!llama_model_load(path_model, *model, model->vocab, params.n_ctx, params.n_batch, params.n_gpu_layers, - params.main_gpu, params.tensor_split, params.low_vram, memory_type, params.use_mmap, params.use_mlock, - params.vocab_only, params.progress_callback, params.progress_callback_user_data)) { + if (!llama_model_load(path_model, *model, model->vocab, params.n_ctx, params.rope_freq_base, params.rope_freq_scale, + params.n_batch, params.n_gpu_layers, params.main_gpu, params.tensor_split, params.low_vram, memory_type, + params.use_mmap, params.use_mlock, params.vocab_only, params.progress_callback, + params.progress_callback_user_data)) { delete model; fprintf(stderr, "%s: failed to load model\n", __func__); return nullptr; @@ -2638,7 +2654,7 @@ struct llama_context * llama_new_context_with_model( ctx->buf_compute.resize(MEM_REQ_EVAL().at(ctx->model.type)); - ctx->buf_scratch[0].resize(MEM_REQ_SCRATCH0().at(ctx->model.type)); + ctx->buf_scratch[0].resize(MEM_REQ_SCRATCH0(hparams.n_ctx).at(ctx->model.type)); ctx->buf_scratch[1].resize(MEM_REQ_SCRATCH1().at(ctx->model.type)); } diff --git a/llama.h b/llama.h index c1e7dab9f..224cd0911 100644 --- a/llama.h +++ b/llama.h @@ -85,6 +85,8 @@ extern "C" { struct llama_context_params { uint32_t seed; // RNG seed, -1 for random int32_t n_ctx; // text context + float rope_freq_base; // RoPE base frequency + float rope_freq_scale; // RoPE frequency scaling factor int32_t n_batch; // prompt processing batch size int32_t n_gpu_layers; // number of layers to store in VRAM int32_t main_gpu; // the GPU that is used for scratch and small tensors